JP2008203045A - Method for estimating drying rate of coating layer on base material, and method for acquiring drying rate distribution of coating layer on base material - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for estimating a drying rate of a coating layer on a base material and a program applicable to the case of an organic solvent, or the case where a hot wind temperature exceeds 373K greatly, even if a wet component in the coating layer is single; a method and a program for acquiring a drying rate distribution by using data acquired by the estimation method; and a recording medium for recording the programs. <P>SOLUTION: When hot wind heating or the like is performed to the surface of the coating layer on the base material, a film heat transfer coefficient h<SB>s</SB>of the coating layer surface, a mass of moisture w<SB>w1</SB>in the coating layer after t<SB>1</SB>seconds, and a mass change Δw<SB>w</SB>of the moisture in the coating layer during an interval of 0 to t seconds are determined by using prescribed formulas from a surface temperature of the coating layer or the like, and the drying rate of the coating layer is estimated by using the formula: R=(-Δw<SB>w</SB>/Δt)/A. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a method for estimating the drying rate of a coating layer on a substrate and a method for obtaining a drying rate distribution of a coating layer on a substrate.

Conventionally, as a method for measuring the drying rate of a coating layer on a substrate, a method using mass change (for example, Non-Patent Document 1 below) and a method for analyzing the composition of the coating layer (film) (for example, the following Non-Patent Document) 2) is known. However, the non-patent document 1 has no application example for a wet thickness of 400 μm or less and a hot air wind speed of 3 m or more, and may be greatly separated from the current practical drying conditions. Moreover, the thing of the nonpatent literature 2 may be remarkably inferior in measurement accuracy. In order to overcome these drawbacks, a technique that utilizes changes in the surface temperature of the substrate and the coating layer has recently been proposed (for example, Non-Patent Document 3 below).
Okazaki, et al .; Journal of Chemical Engineering of Japan, 7 (2), pp99-106 (1974)) (Gehrmann, D. and W. Kast; Proceedings of 1st. Internatioal Symposium on Drying, pp.239-246, August1978, Montreal, Canada Sullivan, DA; Journal of Paint Technology, 47 (610), pp. 60-67 (1975) Kan, D. et al .; Proceeding of International Workshop on Process Intensification in Fluid and Particle Engineering, P326, Oct. 2006, Kobe, Japan

  The non-patent document 3 using the surface temperature change of the substrate and the coating layer does not take into account the temperature dependence of the evaporation enthalpy of the wet component in the coating layer and the sensible heat of the evaporated vapor in the coating layer. Therefore, it is considered inappropriate to apply the wet component alone to an organic solvent or a case where the hot air temperature greatly exceeds 373K.

  Therefore, an object of the present invention is to provide a method for estimating the drying rate of a coating layer on a substrate, which can be applied to a case where the wet component in the coating layer alone is an organic solvent or a case where the hot air temperature greatly exceeds 373 K, and this estimation. A method for obtaining a drying rate distribution using data obtained from the method.

Means and effects for solving the problems

[1] A method for estimating a drying rate of a coating layer on a substrate in the present invention includes a substrate, a coating layer coated on the surface of the substrate, and a heat insulating material provided on the back surface of the substrate. When the following (a ₁ ) or the following (a ₂ ) is performed on the surface of the coating layer in the member, the steps of substituting values corresponding to the parameters of the following formulas (1) to (3), Substituting the film heat transfer coefficient h _s on the surface of the coating layer obtained by Equation (1) into the following Equation (2) to obtain the mass w _w1 of the water in the coating layer after t ₁ second, Substituting the film heat transfer coefficient h _s of the coating layer surface obtained in (1) into the following formula (3) to obtain a mass change Δw _w of moisture in the coating layer in Δt seconds, and the w _w1 and Applying Δw _w to the following equation (4) to estimate the drying rate of the coating layer.
(A ₁ ) Hot air heating (a ₂ ) One or more of radiant heating, induction heating, or current heating, and hot air heating

According to the above configuration, even when the wet component in the coating layer is an organic solvent alone or when the hot air temperature greatly exceeds 373K, the substrate, the coating layer coated on the surface of the substrate, and the substrate The drying rate of the coating layer on the base material when the above (a ₁ ) or (a ₂ ) is performed on the surface of the coating layer in a member provided with a heat insulating material provided on the back surface of the substrate is estimated. it can.

[2] A method for estimating a drying rate of a coating layer on a substrate in the present invention includes a substrate, a coating layer coated on the surface of the substrate, and a heat transfer material provided on the back surface of the substrate. Substituting values corresponding to the parameters of the following formulas (5) to (7) when the following (b ₁ ) or the following (b ₂ ) is performed on the surface of the coating layer in the member: Substituting the film heat transfer coefficient h _s of the coating layer surface obtained by the following formula (5) into the following formula (6), and obtaining the mass w _w1 of the water in the coating layer after t ₁ second; Substituting the film heat transfer coefficient h _s on the surface of the coating layer obtained by Equation (5) into the following Equation (7) to obtain a mass change Δw _w of moisture in the coating layer during Δt seconds, and w _w1 And Δw _w is applied to the following equation (8) to estimate the drying rate of the coating layer.
(B ₁ ) Hot air heating (b ₂ ) Any one or more of radiant heating, induction heating, or current heating, and hot air heating

According to the above configuration, even when the wet component in the coating layer is an organic solvent alone or when the hot air temperature greatly exceeds 373K, the substrate, the coating layer coated on the surface of the substrate, and the substrate The drying speed of the coating layer on the substrate when the above (b ₁ ) or (b ₂ ) is performed on the surface of the coating layer in the member provided with the heat transfer material provided on the back surface of Can be estimated.

[3] A method for estimating a drying rate of a coating layer on a substrate in the present invention includes a substrate and a coating layer coated on the surface of the substrate, and a member whose back surface is in contact with the atmosphere. When hot air heating is performed on the front surface of the coating layer and the back surface of the base material, the values corresponding to the parameters of the following formulas (9) to (11) are substituted, and the following formula (9) is obtained. Substrate heat transfer coefficient h _s on the surface of the coating layer was substituted into the following formula (10) to obtain the mass w _w1 of water in the coating layer after t ₁ second, and the following formula (9) Substituting the film heat transfer coefficient h _s on the surface of the coating layer into the following formula (11) to obtain a mass change Δw _w of moisture in the coating layer in Δt seconds, and calculating the _{w w1} and the Δw _w by the following formula (12) and a step of estimating the drying rate of the coating layer.

  According to the above configuration, even when the wet component in the coating layer is an organic solvent alone or when the hot air temperature greatly exceeds 373K, the substrate and the coating layer coated on the surface of the substrate are provided, It is possible to estimate the drying rate of the coating layer on the substrate when hot air heating is performed on the surface of the coating layer and the back surface of the substrate in the member whose back surface of the substrate is in contact with the atmosphere.

[4] A method for estimating a drying rate of a coating layer on a base material in the present invention includes a base material and a coating layer applied to the surface of the base material, and the back surface of the base material is in contact with the atmosphere. When the following (c ₁ ) or the following (c ₂ ) is performed on the surface of the coating layer and the back surface of the base material, values corresponding to the parameters of the following formulas (13) to (15) are substituted. Step of substituting the film heat transfer coefficient h _s of the coating layer surface obtained by the following formula (13) into the following formula (14) to obtain the mass w _w1 of the water in the coating layer after t ₁ second And substituting the film heat transfer coefficient h _s of the coating layer surface obtained by the following formula (13) into the following formula (15) to obtain a mass change Δw _w of moisture in the coating layer in Δt seconds; Applying the w _w1 and the Δw _w to the following equation (16) to estimate the drying rate of the coating layer; have.
(C ₁ ) Hot air heating (c ₂ ) Any one or more of radiant heating, induction heating, or current heating, and hot air heating

According to the above configuration, when the wet component in the coating layer is an organic solvent alone or when the hot air temperature greatly exceeds 373 K, the substrate includes a coating layer coated on the surface of the substrate, and the base Drying of the coating layer on the substrate when the following (c ₁ ) or the following (c ₂ ) is performed on the surface of the coating layer and the back surface of the substrate in the member whose back surface of the material is in contact with the atmosphere Speed can be estimated.

  Further, in the method for estimating the drying rate of the coating layer on the substrate of [1] to [4] above, (ii) when there are a plurality of wet components in the coating layer, (ii) external drying conditions such as hot air temperature are When changing a plurality of times in a constant or stepwise manner, (iii) batch type (when the substrate having the coating layer formed on the surface is stationary) or continuous method (for example, a plurality of coating layers having the coating layer formed on the surface) Even when the base material is sequentially conveyed so as to flow in the manufacturing process), the parameters in each formula are obtained by measurement or calculation, and applied to each formula, thereby drying the coating layer on the base material. The speed can be estimated with the same or higher accuracy as before. Moreover, even if it uses the thin base material or the thick base material, the drying rate estimation method of the coating layer on the base material of said [1]-[4] is applicable. Moreover, in the said nonpatent literature 1-3, although it was limited to examination with respect to the system of drying required time 20 minutes or more, according to the drying rate estimation method of the coating layer on the base material of said [1]-[4]. This is useful because it can be applied to the case where the drying time is short of 5 minutes or less.

In the present specification, R: drying rate (kg-water / (m ² -material · s), A: surface area of coating layer (m ² ), t _F : drying end time (s), w _w : Mass of moisture in the coating layer (kg), w _w0 : mass of initial moisture in the coating layer (kg), w _wF : mass of moisture after completion of drying in the coating layer (kg), w _d : dry Mass of coating layer (kg), w _b : Mass of base material (kg), T _as : Temperature of hot air on coating layer surface (K), T _s : Surface temperature of coating layer (K), T _s0 : Coating layer Initial surface temperature (K), T _sF : surface temperature after completion of drying of coating layer (K), T _r : upper surface temperature of heat transfer material (K), T _rF : upper surface temperature of heat transfer material after completion of drying _{(K), T ab:} temperature of hot air in the substrate rear surface (K), _{T b:} the back surface temperature of the substrate _{(K), T bF:} behind the drying after the end of the substrate Temperature _{(K), T m = (} T s + T b) / 2: average temperature of the substrate and the coating layer _{(K), T m0:} initial average temperature of the substrate and the coating layer _{(K), T mF:} Average temperature (K) after completion of drying of substrate and coating layer, c _w : constant pressure specific heat capacity of water (liquid) (J / (kg · K)), c _Gw : constant pressure specific heat capacity of water (steam) ( J / (kg · K)), c _d : specific heat capacity of dried coating layer (J / (kg · K)), c _b : specific heat capacity of substrate (J / (kg · K)), h _s : The film heat transfer coefficient on the surface of the coating layer, h _b : the film heat transfer coefficient on the back surface of the base material, h _r : the heat transfer coefficient derived from the contact resistance between the base material and the heat transfer material, Δh _w0 : at T _s0 Evaporation enthalpy of water (liquid), Q: Energy generated by radiant heating, induction heating, or current heating.

[5] The method for obtaining the drying rate distribution of the coating layer on the substrate of the present invention is the method for estimating the drying rate of the coating layer according to any one of claims 1 to 4 over the entire surface of the coating layer. A drying rate estimation step for estimating the drying rate by using, and a step of obtaining a drying rate distribution of the coating layer from the drying rate obtained in the drying rate estimation step.

  According to the above configuration, it is possible to obtain the drying rate distribution of the coating layer on the substrate with higher accuracy and more easily than in the past.

  In addition, the program of the present invention can cause a computer to execute the methods [1] to [4] or the method [5]. The recording medium of the present invention stores any of the programs of the present invention.

<First Embodiment>
Next, a first embodiment of the present invention will be described.

  FIG. 1 shows hot air heating on the surface of a coating layer 2 in a member including a substrate 1, a coating layer 2 coated on the surface of the substrate 1, and a heat insulating material 3 provided on the back surface of the substrate 1. It is a conceptual diagram which shows the state which is performed and the temperature of the surface of the application layer 2 is measured with the radiation thermometer 4. FIG. In many cases, hot air is used in combination with radiant heat transfer, such as infrared rays, microwaves, and high frequencies, and induction heating or current heating for metal substrates. Consider the case.

  The substrate 1 is a thin polymer film, paper, glass plate, metal plate or the like, and the coating layer 2 is an aqueous solution containing one or more components. The substrate 1 having the coating layer 2 on the surface may be referred to as a wet material. Although the heat insulating material 3 insulates the back surface of the base material 1, it cannot insulate completely. However, in this embodiment, it treats as what is completely insulated.

(Principle in the method for estimating the drying rate of the coating layer on the substrate according to this embodiment)
Even if internal heating is used in combination with a thin substrate or a substrate with high thermal conductivity, the assumption of uniform material temperature is approximated only when internal heating is not used in a thin layer with a thickness of several millimeters. (Non-Patent Document 3). The energy balance in the coating layer 2 of FIG. The enthalpy of liquid water and solid at the initial surface temperature _TSO of the coating layer was shown as a reference, and the temperature dependence of the evaporation enthalpy was considered. Moreover, the case where evaporating water vapor | steam rose to hot air temperature was considered. When the wet substance is water, the energy required for increasing the temperature of the evaporated water vapor is often ignored, but the evaporation enthalpy of the organic solvent is about 1/3 of water. From this, even in the case of water, when the hot air temperature greatly exceeds 373K, or when the wet substance is an organic solvent, the energy required for increasing the temperature of the evaporated vapor should be considered.

Here, c _w and c _Gw are constant-pressure specific heat capacities of liquid water and water vapor, and the average values between 273K and 373K are 4.18 × 10 ³ (J / (kg · K)) and 1.88 × 10 respectively. ³ (J / (kg · K)) (the same applies to modifications and other embodiments described later). T _as is the hot air temperature and is a constant value. T _s is the surface temperature of the coating layer, and approximates the average temperature T _m = T _s between the surface temperature of the coating layer and the back surface temperature of the substrate. Δh _w0 is the enthalpy of water evaporation at T _s0 , and is represented by Δh _w0 = 3.177 × 10 ⁶ −2.47 × 10 ³ T _s0 (J / kg-water) (in the first embodiment described later) The same applies to the modified example.) A dry material mass average moisture content _{x m = w w / w d} . Then, after the drying of the coating layer 2, the above formula (17) becomes the following formula (18).

Here, Q _F and T _sF are the generated energy after the completion of drying and the coating layer surface temperature. However, when a thick substrate or a substrate with poor thermal conductivity is used, the temperature distribution in the substrate is not uniform for a while from the start of the experiment. t = 0 from the period not uniform up to t _1, when the subsequent it uniform period, the following formula representing the enthalpy balance of the former period (19), the above equation (17) from t = 0 obtained by integrating up to t _1.

Here, w _w0 and w _w1 are the moisture masses at the start of drying and at t = t ₁ , respectively. On the other hand, the enthalpy balance of t = _{t 1} after the time period is given by the formula (17) was obtained by the integration from t = _{t 1} to _{t F} the following formula (20).

Here, w _wF is the moisture mass at the end of drying. The enthalpy balance of the entire drying period is given by the sum of the above formula (18) and the above formula (19). The following equation (2) obtained by modifying the above equation (18), the following equation (3) obtained by modifying the above equation (17), the following equation (4), and 0 ≧ t ≧ t _F And a drying rate of t ₁ ≧ t ≧ t _F is obtained. However, as will be described later, h _s needs to be obtained. Note that the data of 0 ≧ t ≧ t _F is specifically data obtained as follows. That is, Δw _w is added to w _w1 to obtain w _w and R after t + Δt seconds. Then, using this obtained w _w , Δw _w for the next Δt seconds is obtained. By adding this to the w _{w of} t + Δt, w _w and R after t + 2Δt seconds are obtained. By repeating this, data of 0 ≧ t ≧ t _F is obtained. The same applies to the following embodiments and modifications.

Note that Δw <0 must be satisfied except in a high humidity condition where the average temperature of the substrate 1 and the coating layer 2 is equal to or lower than the wet bulb temperature of the hot air condition. The above formulas (1) to (4) and (17) to (20) are obtained by adding the internal heating effect, the temperature dependence of the evaporation enthalpy, and the sensible heat effect of the evaporated vapor to the technique of Non-Patent Document 3. Corresponds to the case. Further, the steady-state material temperature T * _sF is measured as Q _F = 0 after completion of the drying experiment, and this value is _{satisfied as} the hot air temperature _Tas . This is a measure to prevent the hot air temperature after the drying experiment and the measurement error of the dry material temperature from becoming the heat transfer rate from the hot air to the material, leading to a decrease in the measurement accuracy of the drying rate. . Considering this point, the following formula (1) for obtaining h _s is obtained from the above formulas (18) to (20). _Then, h _{s, w w1,} by applying the [Delta] w _w, to obtain the drying rate R from the above equation (4).

In addition, when the initial temperature distribution is uniform and the single-sided surface temperature of a flat plate having a thickness L is increased stepwise at t = 0 and kept constant, the flat plate average temperature increases to 95% of the rising temperature. The time t ′ ₁ required for is given by 1.21 L ² / α in the absence of internal heating (Crank, J; The Mathematics of Diffusion, p. 59, Oxford University Press, England 1975). Here, α is the thermal diffusivity of the flat plate. Therefore, it is approximated as a drying period t ₁ = t ′ ₁ where the assumption of uniform temperature between the coating layer and the substrate is not established. This approximation is safe because the internal heating effect promotes uniform temperature.

(Configuration of apparatus in this embodiment)
Next, the configuration of an apparatus for executing the method for obtaining the drying rate estimation of the coating layer on the substrate and the drying rate distribution of the coating layer on the substrate according to the first embodiment of the present invention will be described. FIG. 2 shows the hardware configuration of an apparatus (computer) that executes the method for estimating the drying rate of the coating layer on the substrate and obtaining the drying rate distribution of the coating layer on the substrate according to the first embodiment of the present invention. FIG. FIG. 3 is a flowchart of the drying rate estimation process for the coating layer on the substrate according to the present embodiment.

  As shown in FIG. 1, the computer 100 includes a main body 110, a keyboard 111 as an input device, and a display unit 112 such as a monitor, and is connected to a network 109.

  The main body 110 includes a CPU 101 that performs control operations according to a preset program, a ROM 102 that stores various control commands (commands) and the like for transmission to each unit, and the like. RAM 103 in which various commands are set by being called from, a system bus 104 that connects each unit so as to communicate, a keyboard controller (KBC) 105 that controls the interface of the keyboard 111, and a display that controls the interface of the display unit 112 Controller 106 of unit 112, storage and reading unit 107 that can store the data and can read the stored data, and network interface controller (NIC) 108 for connection to network 109 There.

  A control device (not shown) that can transmit the measurement value of the radiation thermometer 4 of FIG. 1 is connected to the network 109, and the measurement value of the radiation thermometer is stored in the storage and reading unit 107 or displayed. It can be displayed on the section 112.

  The storage and reading unit 107 is, for example, a hard disk drive, and is installed with a program that executes the processing of the flowchart shown in FIG. At the time of execution, it is loaded into the RAM 103 and executed under the control of the CPU 101. Although not shown, the storage and reading unit 107 may be connected to another device such as a magnetic drive or an optical drive, and a program for executing the processing of the flowchart shown in FIG. May be configured such that data is read from a recording medium (such as a floppy (registered trademark) disk or CD-ROM) stored in the memory and installed in the storage and reading unit 107.

  Next, the process of the flowchart shown in FIG. 3 will be described. First, necessary parameter values in the above formulas (1) to (3) are input (step S1). Note that the values recorded in advance in the storage and reading unit 107 and the values measured immediately before are automatically input, but this may be manual input from the keyboard 111. In addition, the necessary parameter values can be obtained by the methods described in the above-mentioned non-patent documents or the methods already known.

Next, the calculation of obtaining w _w1 is performed by substituting h _s obtained by the above equation (1) into the above equation (2) (step S2). Subsequently, h _s obtained by the above equation (1) is substituted into the above equation (3), and calculation for obtaining Δw _w is performed (step S3).

By applying the w _w1 and Δw _w obtained in this way, calculation for estimating the drying rate of the coating layer 2 from the above equation (4) is performed (step S4).

  Further, whether to estimate the drying speed at other positions of the coating layer 2 is input (step S5). When further estimation is made (step S5: YES), the process returns to step S1. When not estimating (step S5: NO), the process which outputs a result (data) to the display part 112 is performed (step S6), and it complete | finishes. In step S6, the result (data) may be stored in the storage and reading unit 107, and a process for obtaining a drying speed distribution from the obtained result may be performed.

Instead of step 5, a predetermined portion of the coating layer 2 may be designated from the beginning, and the drying speed may be estimated for all of the portions. Further, if the substrate 1 is being conveyed in a continuous manner, instead of step 5, from the beginning, the same plurality of positions in the conveying direction are measured at regular time intervals, and the drying speed in the conveying direction of the coating layer 2 is determined. It is good also as processing so that it may estimate continuously. However, in this case, if the drying speed changes, the final moisture content w _wF also changes, so that it is practical only when w _{wF ≈0} .

According to this embodiment having the above-described configuration, even when the wet component in the coating layer is an organic solvent alone or when the hot air temperature greatly exceeds 373K, the coating layer applied to the surface of the substrate 1 and the substrate 1 2 and the surface of the coating layer 2 in the member provided with the heat insulating material 3 provided on the back surface of the base material, (a ₁ ) hot air heating, (a ₂ ) radiation heating, induction heating, or current heating Any one or more of the above and the drying rate of the coating layer 2 on the substrate 1 when hot air heating is performed can be estimated.

  Also, (i) when there are a plurality of wet components in the coating layer 2, (ii) when the external drying conditions such as hot air temperature change a plurality of times in a constant or stepwise manner, (iii) a batch type (the coating layer 2 on the surface Or a continuous method (for example, a plurality of base materials 1 having a coating layer 1 formed on the surface thereof are sequentially conveyed so as to flow in the manufacturing process). However, the drying speed of the coating layer on the substrate 1 can be estimated with the same or higher accuracy as before by determining the parameters in each formula from measurement or calculation and applying the parameters to each formula. Moreover, even if it uses the thin base material or the thick base material, the drying rate estimation method of the application layer 2 on the base material 1 which concerns on this embodiment is applicable. Moreover, in the said nonpatent literature 1-3, although it was limited to the examination with respect to the system of drying required time 20 minutes or more, according to the drying rate estimation method of the coating layer on the base material concerning this embodiment, it is 5 minutes or less. This is useful because it can be applied to cases having a short drying time.

<Modification of First Embodiment>
Next, a modification of the first embodiment of the present invention will be described. This modification considers the case where heat is transferred from the back surface of the substrate (including incomplete heat insulation) instead of complete heat insulation as in the first embodiment.

(Principle in the method for estimating the drying rate of the coating layer on the substrate according to this modification)
Heat is transferred from the back surface of the substrate (including incomplete heat insulation) (assuming that the heat insulating material in FIG. 1 transfers heat or that the heat insulating material in FIG. 1 is a heat transfer material) Except for, basically the same as the first embodiment. Therefore, the description of the portions may be omitted as in the first embodiment.

  Similarly to the first embodiment, when the energy balance in the coating layer is considered, the following equation (21) is obtained. And after completion | finish of drying, following formula (22) is materialized from the following formula (21).

Next, similarly to the first embodiment, when considering a case where a thick base material or a base material with poor thermal conductivity is used, the temperature distribution in the base material is not uniform for a while from the start of the experiment. Therefore, as in the first embodiment, the above equation (21) is integrated from t = 0 to _{t 1,} when obtaining the enthalpy balance from t = 0 to _{t 1,} the table as the following equation (23) Is done. Further, the enthalpy balance of t = _{t 1} after the time period is given by the formula (21) was obtained by the integration from t = _{t 1} to _{t F} the following formula (24).

The following equation (6) obtained by modifying the above equation (23), the following equation (7) obtained by modifying the above equation (21), the following equation (8), and 0 ≧ t ≧ by using the t _F data, drying rate of _{t 1} ≧ _t ≧ _{t F} is obtained. However, as will be described later, h _s needs to be obtained.

Here, similarly to the first embodiment, Δw <0 must be satisfied except in a high humidity condition where the average temperature of the substrate 1 and the coating layer 2 is equal to or lower than the wet bulb temperature of the hot air condition. The hot air temperature T _as is _satisfied by measuring the steady-state material temperature T * _sF by completely insulating the bottom surface of the substrate after the drying experiment and setting Q _F = 0. The measured value is used for the heat transfer plate upper surface temperature _Tr . From the above equations (22), (23) and (24), the following equation (5) for obtaining h _s can be obtained. h _r is obtained by substituting h _s into the above equation (22). Then, h _r , h _s , w _w1 , and Δw _w are applied to obtain the drying speed R from the above formula (8).

Also here, as in the first embodiment, when the single-sided surface temperature of a flat plate having a uniform initial temperature distribution and a thickness of L is increased stepwise at t = 0 to maintain a constant value, the flat plate average temperature is The time t ′ ₁ required to rise to 95% of the rising temperature is given by 1.21 L ² / α when there is no internal heating. Here, α is the thermal diffusivity of the flat plate. Therefore, it is approximated as a drying period t ₁ = t ′ ₁ where the assumption of uniform temperature between the coating layer and the substrate is not established. This approximation is safe because the internal heating effect promotes uniform temperature. Furthermore, when the surface temperature of both surfaces of a flat plate having a uniform initial temperature distribution and a thickness L is increased stepwise at t = 0, t ′ ₁ = 1.21 (L / 2) ² / α, This approximation is also safe for conduction heat transfer.

(Configuration of apparatus in this modification)
Although it is substantially the same as 1st Embodiment, it replaces with Formula (1), (2), (3), and in Formula (5), (6), (7) in the processing routine of the drying rate estimation of FIG. Are different in that they are used in order.

  According to this modification of the above configuration, even if a heat transfer material or a heat insulating material that can only be incompletely insulated is provided on the back surface of the base material 1, the same effects as those of the first embodiment can be obtained.

Second Embodiment
Next, a second embodiment of the present invention will be described. FIG. 4 shows a base material 21, a synthetic rubber ring 25 placed on the surface of the base material 21, a coating layer 22 applied to the inside of the ring 25 on the surface of the base material 21, and the base material 21 and the ring 25. The surface of the coating layer 22 and the base material in a member provided with a heat insulating material 23 provided in a ring shape on the side peripheral surfaces of the base material 21 and the ring 25 and a support plate 26 that supports the heat insulating material 23 It is a conceptual diagram which shows the state which hot-air heating is performed to the back surface of 21, and the temperature of the surface of the coating layer 22 and the back surface of the base material 21 is measured with the radiation thermometers 24a and 24b. Therefore, this embodiment considers the case where hot air heating is performed not only on the surface side of the coating layer as in the first embodiment but also on the back surface of the substrate. Note that description of the same parts as in the first embodiment may be omitted.

  The base material 21 is a polymer film, paper, a glass plate, a metal plate, or the like, and the coating layer 22 is an aqueous solution containing one or more components. Here, the coating layer 22 is sufficiently thicker than the thickness of the substrate 21, but may be as thick as the substrate as in the first embodiment.

(Principle in the method for estimating the drying rate of the coating layer on the substrate according to this embodiment)
In the case where both the front surface of the coating layer 22 and the back surface of the base material 21 are dried with hot air as in the present embodiment, the convection heat transfer area is twice the dry area. The energy balance in double-sided hot air drying is shown in (25) below. The coating layer surface temperature is T _s , the substrate bottom surface temperature is T _b , the average temperature of the substrate 21 and the coating layer 22 is T _m = (T _s + T _b ) / 2, and evaporation is approximated as occurring at T _s. did. The energy balance is shown based on the enthalpy of liquid water and solid at the initial average temperature T _m0 (= T _s0 ) of the base material 21 and the coating layer 22, and the case where the evaporated water vapor rises to the hot air temperature was considered. It is assumed that the base material 21 and the coating layer 22 are stationary in a horizontal plane. Here, Δh _w0 is the evaporation enthalpy of water at T _s0 , and is represented by Δh _w0 = 3.177 × 10 ⁶ −2.47 × 10 ³ T _m0 (J / kg-water) (described later) The same applies to the modified example.) Further, after the drying is completed, the following formula (26) is established from the following formula (25).

Next, similarly to the first embodiment, when considering a case where a thick base material or a base material with poor thermal conductivity is used, the temperature distribution in the base material is not uniform for a while from the start of the experiment. Therefore, as in the first embodiment, the above equation (25) is integrated from t = 0 to _{t 1,} when obtaining the enthalpy balance from t = 0 to _{t 1,} the table as the following equation (27) Is done. Further, the enthalpy balance of t = _{t 1} after the time period is given by the formula (25) was obtained by the integration from t = _{t 1} to _{t F} the following formula (28).

Similarly to the first embodiment, the following formula (10) obtained by modifying the above formula (27), the following formula (11) obtained by modifying the above formula (28), and the following formula (12) ) And 0 ≧ t ≧ t _F data, a drying rate of t ₁ ≧ t ≧ t _F is obtained. However, as will be described later, h _s needs to be obtained.

Here, similarly to the first embodiment, Δw <0 must be satisfied except in a high humidity condition where the average temperature of the base material 21 and the coating layer 22 is equal to or lower than the wet bulb temperature of the hot air condition. After the drying experiment, the steady material temperature measured by insulating the bottom surface of the dry substrate 21 is regarded _{as the} upper hot air temperature T _as , and the steady material temperature measured while insulating the coating layer 22 surface is regarded as the lower hot air temperature T _ab. . This is because the hot air temperature after the drying experiment and the measurement error of the average temperature of the base material 21 and the coating layer 22 become the heat transfer rate from the hot air to the base material 21 and the coating layer 22, and the measurement accuracy of the drying speed is reduced. It is a device to prevent it because it causes. From the above equations (26), (27), and (28), the following equation (9) for obtaining h _s can be obtained. h _b is obtained by substituting h _s into the above equation (26). _{Then, h b, h s, w} w1, by applying the [Delta] w _w, to obtain the drying rate R from the above equation (12).

In the drying experiment of a substrate having a coating layer having a long drying time or a thin layer, when a material having a large layer thickness and a small effective thermal conductivity is targeted, a thickness having a short drying time is required. As in the case of a substrate with a small coating layer, it is necessary to study the coating layer immediately after the start of drying and the drying period during which the assumption of uniform temperature between the coating layer and the substrate due to unsteady heat transfer in the substrate is not valid. It is. The time required for the average temperature of the flat plate to rise to 95% of the rising temperature when the surface temperature of both surfaces of the flat plate having a uniform initial temperature distribution and a thickness of 2 L is increased stepwise at t = 0 and kept constant. t ′ ₁ is given by 1.21 L ² / α, as in the first embodiment. Therefore, as in the first embodiment, the drying period t ₁ ≈t ′ _{1 in} which the assumption that the average temperature of the base material 21 and the coating layer 22 is uniform cannot be established.

(Configuration of apparatus in this modification)
Although it is substantially the same as 1st Embodiment, it replaces with Formula (1), (2), (3) in the processing routine of drying speed estimation of FIG. 3, Formula (9), (10), (11) Are different in that they are used in order.

  According to this embodiment having the above-described configuration, even when the front surface of the coating layer 22 and the back surface of the substrate 21 are heated with hot air at the same time, the same effects as those of the first embodiment can be obtained.

<Modification of Second Embodiment>
Next, a modification of the second embodiment will be described. In the second embodiment, only hot air heating is considered. However, in this modification, radiant heat transfer such as infrared rays, microwaves, and high frequencies, induction heating and electric current heating for a metal substrate are used for hot air heating. Consider a combination. Note that description of the same parts as in the first embodiment may be omitted.

(Principle in the method for estimating the drying rate of the coating layer on the substrate according to this modification)
Similarly to the second embodiment, the energy balance is represented by the following formula (29). Here, Q is energy generated by radiation or induction / energization. Incidentally, assuming an average uniform temperature of the substrate and the coating layer was approximated by the coating layer surface temperature T _s. Energy balance, shown as reference enthalpy possessed by the liquid water and solids in T _s0, evaporated water vapor is considered a case in which rises to the hot air temperature. Further, after the drying, the following formula (30) is established from the following formula (29).

Next, similarly to the first embodiment, when considering a case where a thick base material or a base material with poor thermal conductivity is used, the temperature distribution in the base material is not uniform for a while from the start of the experiment. Therefore, as in the first embodiment, the above equation (29) is integrated from t = 0 to _{t 1,} when obtaining the enthalpy balance from t = 0 to _{t 1,} the table as the following equation (31) Is done. Further, the enthalpy balance of t = _{t 1} after the time period is given by the formula (29) was obtained by the integration from t = _{t 1} to _{t F} the following formula (232).

The following equation (14) obtained by modifying the above equation (31), the following equation (15) obtained by modifying the above equation (32), the following equation (16), and 0 ≧ t ≧ by using the t _F data, drying rate of _{t 1} ≧ _t ≧ _{t F} is obtained. However, as will be described later, h _s needs to be obtained.

Here, similarly to the first embodiment, Δw <0 must be satisfied except in a high humidity condition where the average temperature of the base material and the coating layer is equal to or lower than the wet bulb temperature of the hot air condition. After the drying experiment is completed, the bottom surface (back surface of the base material) of the dry base material and the coating layer is completely insulated, and the steady material temperature measured with Q _F = 0 is the hot air temperature T _as above, and the coating layer surface is insulated. The steady material temperature measured with Q _F = 0 is considered as the lower hot air temperature _Tab . This is because the hot air temperature after the drying experiment and the measurement error of the temperature of the coating layer and the base material become the heat transfer rate from the hot air to the base material and the coating layer, which causes a decrease in the measurement accuracy of the drying speed. It is a device to prevent it. From the above equations (30), (31), (32), the following equation (5) for obtaining h _s can be obtained. h _b is obtained by substituting h _s into the above equation (30). _{Then, h b, h s, w} w1, by applying the [Delta] w _w, to obtain the drying rate R from the above equation (16).

In addition, even in a drying experiment of a substrate having a coating layer that requires a long drying time or a thin layer, when a material having a large layer thickness and a small effective thermal conductivity is targeted, a thickness having a short drying time is required. As in the case of small coating layers and substrates, it is necessary to examine the coating layer immediately after the start of drying and the drying period during which the assumption of uniform temperature of the coating layer and substrate due to unsteady heat transfer in the substrate does not hold. . The time required for the average temperature of the flat plate to rise to 95% of the rising temperature when the surface temperature of both surfaces of the flat plate having a uniform initial temperature distribution and a thickness of 2 L is increased stepwise at t = 0 and kept constant. t ′ ₁ is given by 1.21 L ² / α, as in the first embodiment. Therefore, as in the first embodiment, the drying period t ₁ ≈t ′ _{1 in} which the assumption of uniform average temperature between the base material and the coating layer is not valid can be approximated. This approximation is safe because the internal heating effect promotes uniform temperature.

(Configuration of apparatus in this modification)
Although it is substantially the same as 1st Embodiment, it replaces with Formula (1), (2), (3) in the process routine of drying speed estimation of FIG. 3, Formula (13), (14), (15) Are different in that they are used in order.

  According to this embodiment having the above-described configuration, the same effect as that of the first embodiment is obtained not only when the front surface of the coating layer and the back surface of the base material are heated simultaneously with hot air, but also when internal heating is performed. Can be obtained.

(Example 1)
Using the method of the first embodiment, experimental equipment in the same state as in FIG. 1 was prepared, and an experiment for estimating the drying rate of the coating layer on the substrate was performed. This will be specifically described below.

  On the surface of a polyester film (thickness: 100 μm) as a base material, a commercial synthetic paste (initial water content of about 7 kg-water / kg-PVA) mainly composed of an aqueous polyvinyl alcohol (PVA) solution as a coating layer has a diameter of Plate coating was performed so as to form a circle of 80 mm (three types of thicknesses of 156 μm, 246 μm, and 377 μm were prepared), and three types of experimental samples were prepared. And about each sample, the back surface of the polyester film was heat-insulated with polystyrene foam, and the following convection drying experiment was conducted in which hot air was allowed to flow only on the top surface.

  The temperature change data on the sample surface was automatically measured with a radiation thermometer (radiation thermometer IT-550F, manufactured by HORIBA, Ltd., resolution 0.1K) every 1 s. Hot air generated by an electric hot air generator (TSK-10 manufactured by Takezuna Seisakusho Co., Ltd.) was rectified by a wire mesh and then supplied from above the sample. The hot air temperature in the vicinity of the sample was 60 to 65 ° C., and the hot air speed was about 2.4 m / s. When a 1 mmφ sheathed thermocouple (K type) was placed under the substrate having a dry coating layer after the drying experiment was completed and the temperature measured with a digital thermometer was compared with the measured temperature of the radiation thermometer, the emissivity was set to 0. Since the values almost coincided with 99, the temperature was measured using this value throughout the entire experiment of this example.

  The results obtained by experiments are shown as points in FIG. As can be seen from FIG. 5, the temperature rising period until the surface temperature from 150 to 320 s reached the wet bulb temperature and then the hot air temperature was observed from 240 to 550 s. The amount of evaporated water at this time was 0.13 to 0.31 g. The drying curves obtained by applying these data and the values of known parameters to the above formulas (1) to (3) are shown as lines in FIG. The drying rate curve is shown in FIG.

In calculating the drying curve and the drying rate curve, the specific heat capacity of water c _w = 4180 J / (kg · K), the specific heat capacity of PVA c _d = 1500 J / (kg · K), and the specific heat capacity c of the polyester film _b = 1680 J / (kg · K) and approximated to a constant. Further, as described above, the hot air temperature T _as was regarded as being equal to the final material surface temperature T _sF, and the back surface of the base material was approximated to complete thermal insulation. The obtained film heat transfer coefficient was h _s = 61 to 65 W / (m ² · K). Further, the final material temperature T _sF = hot air temperature T _as = 60.4 to 62.5 ° C. at this time. The obtained h _s is not an inappropriate value for a vertical flow with a wind speed of 2.4 m / s.

  Therefore, it can be seen from the results of this example that the effects of the first embodiment have been verified.

In this example, a synthetic film having a thickness of 157 μm, 246 μm, and 377 μm was formed on a polyester film substrate having a thickness of 100 μm, and a drying experiment was performed. The polyester film substrate and the entire synthetic film were made of synthetic resin and water. When approximated with a resin having a minimum α, t ₁ ≈1.21 L ² /α=0.7 to 2.5 s is obtained. Approximately equal to the average moisture content x _m is the initial moisture content of this time, the drying rate curve at time of this value since it is effective. This is one of the points that were not considered in the prior art. Here, α = λ / (c _p ρ) is defined, and approximate values for representative substances are shown below. The same applies to the embodiments described later.

Water (α = 1.4 × 10 ⁻⁷ m ² / s, λ = 0.6 W / (m · K), c _p = 4200 J / (kg · K), ρ = 1000 kg / m ³ ), acrylic resin ( α = 1.1 × 10 ⁻⁷ m ² / s, λ = 0.2 W / (m · K), c _p = 1500 J / (kg · K), ρ = 1200 kg / m ³ ), glass (α = 3 .4 × 10 ⁻⁷ m ² / s, λ = 0.6 W / (m · K), c _p = 700 J / (kg · K), ρ = 2500 kg / m ³ ), glass fine particle packed bed (α = 4) .4 × 10 ⁻⁷ m ² / s, λ = 0.2 W / (m · K), c _p = 350 J / (kg · K), ρ = 1300 kg / m ³ ), iron (α = 2.5 × 10 ⁻⁵ m ² / s, λ = 80 W / (m · K), c _p = 400 J / (kg · K), ρ = 7900 kg / m ³ ), paper (α = 5.6 × 10 ⁻⁸ m ²⁾ / S, λ = 0 _{06W / (m · K),} c p = 1200J / (kg · K), ρ = 900kg / m 3)

(Example 2)
Next, using the method of the second embodiment, experimental equipment in the same state as in FIG. 4 was prepared, and an experiment for estimating the drying rate of the coating layer on the substrate was performed. This will be specifically described below.

Glass fine particles (particle size 37-63 μm, Tokyo Glass Instrument Co., Ltd. No. 0.05) were mixed with distilled water, and this was used as a coating layer on a glass plate (thickness 1.8 mm) as a substrate. A predetermined initial liquid phase ratio φ ₀ = 0.50 (m ³ −water / m ³ −) was applied to a synthetic rubber ring having an inner diameter of 66 mm bonded (two types having a height of 3.0 mm and 5.0 mm). void), porosity ε = 0.39 to 0.42 (m ³ -void / m ³ -layer), and two types of experimental samples were prepared. And like FIG. 4, only the side surface of each sample was heat-insulated with the polystyrene foam, and the double-sided drying experiment which flows the same hot air on the coating layer surface and a base material back surface was implemented. At this time, similarly to FIG. 4, the samples prepared as described above were placed on a laminated wooden support plate having a thickness of 3 mm with a circular hole having a diameter of 66 mm, and the following experiment was performed.

In this example, the surface side hot air temperature T _as = 321K (when the coating layer thickness is 5 mm), 321K (when the coating layer thickness is 3 mm), and the back surface side hot air temperature T _ab = 319K of the base material. The experiment was conducted as 318K (when the coating layer thickness was 3 mm) (when the coating layer thickness was 5 mm). Further, h _s obtained by the above formula (7) was 51 W / (m ² · K) (when the coating layer thickness was 5 mm) and 51 W / (m ² · K) (when the coating layer thickness was 3 mm). It was. The obtained h _s is not an inappropriate value for a vertical flow having a wind speed of 2.5 m / s.

  The sample surface temperature change data and the glass plate back surface temperature change data were manually measured with a radiation thermometer (CT-30 manufactured by Kos Co., Ltd., resolution 0.1 K) every minute. Hot air generated by an electric hot air generator (TSK-10 manufactured by Takezuna Seisakusho Co., Ltd.) was rectified by a wire mesh, and then supplied from the vertical direction of the sample. The hot air temperature in the vicinity of the sample was 319K to 323K, the hot air speed was about 2.5 m / s, and a separate hot air generator was used in the vertical direction. Under the present circumstances, in order to verify the validity of the drying rate measured by the temperature change method, the time-dependent change data of the average moisture content were measured by the mass change method every 10 minutes.

  Separately, a 1 mmφ thermistor sensor (MC-T100, manufactured by Sato Keiki Seisakusyo Co., Ltd.) is embedded in a dry material layer in which the side surface of the coating layer and the back surface of the substrate are thermally insulated, and under the same conditions as in the drying experiment. The temperature measured with a digital thermometer (SK-1250MC manufactured by Sato Keiki Seisakusho Co., Ltd.) was compared with the measured temperature of the radiation thermometer, and the emissivity was 0.91. Since the values agreed with each other, the temperature was measured using this value throughout the entire experiment of this example.

  First, FIG. 7 shows the results of two types of temperature data on the front surface of the coating layer (thickness 5 mm) and the back surface of the base material obtained by experiment as described above. As can be seen from FIG. 7, there is a considerable difference between the two temperatures, the approximation of the uniform material temperature does not hold, and the two temperatures intersect in the vicinity of 1500 s. Since the evaporation area is smaller than the heat transfer area, the surface temperature is higher than the wet bulb temperature even during the constant rate drying period. Then, the material was completely dried around 2500 s in the middle of the temperature of the hot air asymptotic to the hot air temperature. Thereafter, the material was dried up to 3000 s, and the temperature rising period of the material was observed. Thus, a typical non-hydrophilic porous flat plate drying behavior was obtained. The amount of evaporated water was 3.4 g.

  Next, FIG. 8 shows the results of two types of temperature data on the front surface of the coating layer (thickness 3 mm) and the back surface of the base material obtained by experiment as described above. As can be seen from FIG. 8, the same result as in the case of 5 mm was obtained. The amount of evaporated water was 2.0 g.

Moreover, the drying curve in the case of the coating layer thickness 5mm calculated | required using said Formula (5) and (6) and the case of a coating layer thickness 3mm is shown as a continuous line in FIG.7 and FIG.8. In the calculations of the above formulas (5) and (6), the water specific heat capacity c _w = 4200 J / (kg · K), the dry material specific heat capacity c _d = 480 J / (kg · K), and the container specific heat capacity c _b = 800 J / (kg · K) and approximated to a constant. It is a result when the data of a dry material temperature rising period are not included. This handling is limited to non-hydrophilic materials, and in a substrate having a coating layer, water evaporation generally continues until the end of drying. The film heat transfer coefficient on the back side of the substrate was h _b = 32 W / (m ² · K) (application layer thickness 5 mm), 29 W / (m ² · K) (application layer thickness 3 mm). Further, the final surface temperature T _sF = _321K (application layer thickness 5 mm), 320K (application layer thickness 3 mm) of the coating layer at this time, the final back surface temperature T _bF = _320K (application layer thickness 5 mm) of the substrate, It became 320K (coating layer thickness 3 mm). The fact that h _b was smaller than h _s despite the fact that the wind speed was almost the same on the upper and lower surfaces is thought to be the result of the increase in the film thickness due to the influence of the plate thickness for supporting the sample. . As a result, the change in the measured moisture content by the mass change method could be accurately reproduced.

  Therefore, it can be seen from the results of this example that the effects of the second embodiment have been verified.

  In addition, FIGS. 9 and 10 show drying rate curves in the case where the coating layer thickness is 5 mm and the coating layer thickness is 3 mm in this example. It is obvious that this embodiment, which is effective for a much thicker material compared to a thin substrate coated with a thin coating layer, is also effective for a thin substrate coated with a thin coating layer. .

In this example, a glass particle slurry layer having a thickness of 5 mm or 3 mm was formed on a glass plate having a thickness of 1.8 mm, and a double-sided drying experiment was performed. The entire wet material was filled with glass, glass fine particles, and the smallest in water. If approximated by water indicating α, t ₁ ≈1.21 L ² / α = 99 s (application layer thickness 5 mm) or 49 s (application layer thickness 3 mm) is obtained. The average water content _{x m} at this time = 0.13 (coating layer thickness of 5 mm, 3 mm both) is. Therefore, the drying rate curves in FIGS. 7 and 8 are effective at x _m of 0.13 or less.

(Example 3)
Next, using the method of the modification of the second embodiment, the experimental equipment shown in FIG. 11 was prepared, and an experiment for estimating the drying rate of the coating layer on the substrate was performed. This will be specifically described below.

  As shown in FIG. 11, a commercially available acrylic emulsion water-based paint is applied at a thickness of about 120 to 130 μm on the surface of a substrate 31 of a glass plate (thickness 1.8 mm) to form a coating layer 32, and a sample is prepared. Produced. The heat insulating material 36 (styrofoam plate) having a thickness of about 5 mm is used as a sample supporting plate, and this is cut into the size of the base material 31, and the sample is set so that the coated surface of the base material 31 coincides with the upper surface of the heat insulating material 36. Then, a double-sided hot air drying experiment in which the same hot air was passed through the upper and lower surfaces was performed as follows.

The temperature change data on the coated surface and the bottom surface of the glass plate were manually measured every 10 to 30 seconds with a radiation thermometer (Radio Thermometer IT-550F, manufactured by Horiba, Ltd., resolution 0.1K). Hot air generated by an electric hot air generator (TSK-10 manufactured by Takezuna Seisakusho Co., Ltd.) was rectified by a wire mesh, and then supplied from the vertical direction of the sample. By using separate hot air generators in the vertical direction, the hot air temperatures near the coated surface and the back surface of the substrate were set to 60 ° C. and 40 ° C. or 40 ° C. and 60 ° C., respectively. The hot air velocity was about 2 m / s in both directions. After completion of the drying experiment, the sample surface temperature obtained by covering the back surface of the substrate with a heat insulating material was adopted as the upper surface direction hot air temperature, and the sample bottom surface temperature obtained by covering the sample surface was adopted as the lower surface direction hot air temperature. Separately, a dry sample was placed on a heat insulating material with a 1 mmφ thermocouple (K type) embedded in the surface, and a steady heat transfer experiment was performed under hot air under the same conditions as the drying experiment. When the temperature measured with a digital thermometer (SK-1250MC manufactured by Sato Keiki Seisakusho Co., Ltd.) and the measurement temperature of the radiation thermometer were compared, the emissivity was 0.85 on the coated surface and 0.70 on the glass surface. Since the values sometimes coincided with each other, the temperature was measured using this value throughout the experiment of this example. Incidentally, the desired hot air temperature of 60 ° C. to the surface side hot air temperature T _{as =} 331K (the surface of the coating layer of the coated layer in this case - if desired hot air temperature of 40 ° C. to the substrate back surface (hereinafter, a 60 ° C. -40 ° C. )) 313K (desired hot air temperature 40 ° C. to the surface of the coating layer−desired hot air temperature 60 ° C. to the back of the substrate (hereinafter referred to as 40 ° C.-60 ° C.))) bottom hot air temperature T _ab = It was 312K (60 ° C-40 ° C), 333K (40 ° C-60 ° C). Moreover, when the desired hot air temperature to the surface of the coating layer is 60 ° C.—the desired hot air temperature to the back surface of the substrate is 40 ° C., the desired hot air temperature to the surface of the coating layer is 40 ° C.—to the back surface of the substrate. Both were about 50 μm when the desired hot air temperature was 60 ° C.

  The results in the case of 60 ° C. to 40 ° C. obtained as a result of the experiment are shown in FIG. As can be seen from FIG. 12, the coating surface temperature> the bottom surface temperature in the material preheating period and the constant rate drying period, but the uniform material temperature was approximated in the decreasing rate drying period. The amount of evaporated water was 0.24 g.

  Moreover, the result in the case of 40 to 60 degreeC is shown in FIG. The coating surface temperature was less than the bottom surface temperature during the material preheating period and the constant rate drying period, but the uniform material temperature was approximated during the reduced rate drying period. The amount of evaporated water was 0.27 g.

The coating layer and the base material are approximated to an average uniform temperature, and only the change in the surface temperature of the coating layer is used, and the surface side film heat transfer coefficient h of the coating layer determined as Q = 0 in the above equation (13). _s is 41 W / (m ² · K) (60 ° C. to 40 ° C.), 34 W / (m ² · K) (40 ° C. to 60 ° C.), and the bottom side film heat transfer coefficient h _b is 46 W / (m ² · K) (60 ° C.-40 ° C.) and 34 W / (m ² · K) (40 ° C.-60 ° C.).

Next, the drying curves and drying speed curves obtained using the above formulas (14) and (15) are shown in FIGS. 12, 13, 14 (only for the surface of the coating layer), and FIG. 15 (the surface of the coating layer). And for the back side of the substrate). In this case, the specific heat capacity of water c _w = 4180 J / (kg · K), the specific heat capacity of dry material c _d = 1460 J / (kg · K), and the specific heat capacity of the container c _b = 800 J / (kg · K) are constants. And approximated. Actually, there is a difference between the surface temperature of the coating layer and the back surface temperature of the substrate between the preheating period and the constant rate drying period. Therefore, the surface side film heat transfer coefficient h _s of the coating layer obtained by the equation (9) of the second embodiment using both temperature changes is 41 W / (m ² · K) (60 ° C.-40 ° C.), 33 W. / (M ² · K) (40 ° C-60 ° C), bottom side film heat transfer coefficient h _b is 47 W / (m ² · K) (60 ° C-40 ° C), 36 W / (m ² · K) (40 ° C-60 ° C). From these, it can be seen that the results of Example 2 and this example are in good agreement.

In addition, although the heat transfer coefficient (= thermal conductivity / thickness) of the glass plate which is a base material used in the present example was about 330 W / (m ² · K), it was 2000 for a plastic film having a thickness of 100 to 30 μm. Up to 7000 W / (m ² · K), an iron plate with a thickness of 1 mm reaches 80000 W / (m ² · K), and a much smaller temperature difference can be expected compared to a glass plate, and the temperature change on the back side of the substrate is measured. When this is difficult, it is considered that the approximate analysis method based only on the temperature change of the evaporation surface in this embodiment is effective.

  Therefore, it can be seen from the results of this example that the effects of the modification of the second embodiment have been verified.

In this example, a double-sided drying experiment was performed by forming a 120-130 μm thick aqueous coating film on a 1.8 mm thick glass plate. If the entire wet material is approximated by an acrylic resin that exhibits the minimum α in glass, acrylic resin, and water, t ₁ ≈1.21 L ² / α = 10 s is obtained. The average moisture content x _{m at} this time is = 1.15. Therefore, the drying curves and drying speed curves in FIGS. 12 to 15 are effective at x _m of 1.15 or less.

  The present invention can be changed in design without departing from the scope of the claims, and is not limited to the above-described embodiments and examples.

  Since the present invention can quantitatively estimate the drying unevenness of the dryer, it can be applied to the optimization of the drying conditions of the dryer and the improvement of the dryer.

It is a schematic block diagram used for demonstrating the experimental installation of 1st Embodiment of this invention. It is a schematic block diagram of the apparatus which performs the method of 1st Embodiment of this invention. It is a flowchart which shows the processing routine of the calculation which concerns on 1st Embodiment of this invention. It is sectional drawing used for demonstrating the experimental installation of 2nd Embodiment of this invention. It is a graph which shows the experimental result of Example 1 of this invention, Comprising: It is a graph which shows the relationship between drying time and the surface temperature of an application layer, and the relationship between drying time and the average moisture content of an application layer. It is a graph which shows the experimental result of Example 1 of this invention, Comprising: It is a graph which shows the relationship between the average moisture content of a coating layer, and a drying rate. It is a graph which shows the experimental result of Example 2 of this invention, Comprising: It is a graph which shows the relationship between drying time and the average moisture content of a coating layer (thickness 5mm), and the relationship between drying time and the temperature of a sample. . It is a graph which shows the experimental result of Example 2 of this invention, Comprising: It is a graph which shows the relationship between drying time and the average moisture content of a coating layer (thickness 3mm), and the relationship between drying time and the temperature of a sample. . It is a graph which shows the experimental result of Example 2 of this invention, Comprising: It is a graph which shows the relationship between the average moisture content of a coating layer (thickness 5mm), and a drying rate. It is a graph which shows the experimental result of Example 2 of this invention, Comprising: It is a graph which shows the relationship between the average moisture content of a coating layer (thickness 3mm), and a drying rate. It is a schematic block diagram used for demonstrating the experimental installation of Example 3 of this invention. It is a graph which shows the experimental result of Example 3 of this invention, Comprising: The relationship between the drying time of 60 degreeC-40 degreeC and the temperature of a coating layer surface and a base material back surface, and the drying time of 60 degreeC-40 degreeC, and application | coating It is a graph which shows the relationship with the average moisture content of a layer. It is a graph which shows the experimental result of Example 3 of this invention, Comprising: The relationship between the drying time of 40 degreeC-60 degreeC and the temperature of a coating layer surface and a substrate back surface, and the drying time of 40 degreeC-60 degreeC and application | coating It is a graph which shows the relationship with the average moisture content of a layer. It is a graph which shows the experimental result of Example 3 of this invention which considered only the temperature of the coating layer surface, Comprising: The relationship between the average moisture content of a coating layer of 60 degreeC-40 degreeC and 40 degreeC-60 degreeC and a drying rate is shown. It is a graph to show. It is a graph which shows the experimental result of Example 3 of this invention which considered the temperature of the coating layer surface and the back surface of a base material, Comprising: The average moisture content and drying rate of a coating layer of 60 to 40 degreeC and 40 to 60 degreeC It is a graph which shows the relationship.

Explanation of symbols

1, 21, 31 Base material 2, 22, 32 Coating layer 3, 23, 36 Insulating material 4, 24a, 24b Radiation thermometer 25 Ring 26 Support plate 100 Computer 104 System bus 105 Keyboard controller 106 Display controller 107 Recording and Reading unit 109 Network 110 Main body 111 Keyboard 112 Display unit

Claims (9)

On the surface of the coating layer in a member comprising a substrate, a coating layer coated on the surface of the substrate, and a heat insulating material provided on the back surface of the substrate, the following (a ₁ ) or (a ₂ ), a process of substituting values corresponding to the parameters of the following formulas (1) to (3),
Substituting the film heat transfer coefficient h _s of the coating layer surface obtained by the following formula (1) into the following formula (2), and obtaining the mass w _w1 of the water in the coating layer after t ₁ second;
Substituting the film heat transfer coefficient h _s of the coating layer surface obtained by the following formula (1) into the following formula (3) to obtain a mass change Δw _w of moisture in the coating layer in Δt seconds;
Applying the w _w1 and the Δw _w to the following equation (4) to estimate the drying rate of the coating layer, and a method for estimating the drying rate of the coating layer on the substrate .
(A ₁ ) Hot air heating (a ₂ ) One or more of radiant heating, induction heating, or current heating, and hot air heating

Here, R: drying rate (kg-water / (m ² -material · s), A: surface area (m ² ) of coating layer, t _F : drying end time (s), w _w : moisture in coating layer Mass (kg), w _w0 : initial mass of moisture in the coating layer (kg), w _wF : mass of moisture after completion of drying in the coating layer (kg), w _d : mass of the dried coating layer (kg) ), W _b : mass of the substrate (kg), T _as : temperature of hot air on the coating layer surface (K), T _s : surface temperature of the coating layer (K), T _s0 : initial surface temperature of the coating layer (K) ), T _sF : Surface temperature after drying of coating layer (K), c _w : Constant pressure specific heat capacity of water (liquid) (J / (kg · K)), c _Gw : Constant pressure specific heat capacity of water (steam) (J / (kg · K) ), c d: dry heat capacity of the coating layer (J / (kg · K) ), c b: specific heat capacity of the substrate (J / (kg · K) ) Delta] h _w0: enthalpy of vaporization of water at _{T s0} (liquid), Q: radiant heating, induction heating, or generating energy by conduction heating, it is. On the surface of the coating layer in a member comprising a substrate, a coating layer coated on the surface of the substrate, and a heat transfer material provided on the back surface of the substrate, the following (b ₁ ) or ( if b ₂₎ was performed, and a step of substituting the respective values to the parameters of the following formula (5) to (7),
Substituting the film heat transfer coefficient h _s of the coating layer surface obtained by the following formula (5) into the following formula (6) to obtain the mass w _w1 of the water in the coating layer after t ₁ second;
Substituting the film heat transfer coefficient h _s of the coating layer surface obtained by the following formula (5) into the following formula (7) to obtain a mass change Δw _w of moisture in the coating layer in Δt seconds;
Applying the w _w1 and the Δw _w to the following equation (8) to estimate the drying rate of the coating layer, and a method for estimating the drying rate of the coating layer on the substrate .
(B ₁ ) Hot air heating (b ₂ ) Any one or more of radiant heating, induction heating, or current heating, and hot air heating

Here, R: drying rate (kg-water / (m ² -material · s), A: surface area (m ² ) of coating layer, t _F : drying end time (s), w _w : moisture in coating layer Mass (kg), w _wF : mass of moisture after drying in the coating layer (kg), w _w0 : mass of initial moisture in the coating layer (kg), w _d : mass of dry coating layer (kg) ), W _b : mass of base material (kg), T _as : temperature of hot air on the coating layer surface (K), T _s : surface temperature of coating layer (K), T _r : top surface temperature of heat transfer material (K) ), T _rF : upper surface temperature (K) of the heat transfer material after completion of drying, T _s0 : initial surface temperature (K) of the coating layer, T _sF : surface temperature (K) after completion of drying of the coating layer, c _w : water constant pressure specific heat capacity of the (liquid) (J / (kg · K )), c Gw: water constant pressure specific heat capacity of the (vapor) (J / (kg · K )), c d: dry coating Specific heat capacity of the layer (J / (kg · K) ), c b: specific heat capacity of the substrate (J / (kg · K) ), h r: heat transfer resulting from the contact resistance between the substrate and the heat transfer member Coefficient, Δh _w0 : Evaporation enthalpy of water (liquid) at T _s0 , Q: Energy generated by radiation heating, induction heating, or current heating. When a hot air heating is performed on the surface of the coating layer and the back surface of the base material in a member having a base material and a coating layer applied to the surface of the base material, the back surface of the base material being in contact with the atmosphere Substituting values corresponding to the parameters of the following formulas (9) to (11),
Substituting the film heat transfer coefficient h _s of the coating layer surface obtained by the following formula (9) into the following formula (10) to obtain a mass w _w1 of water in the coating layer after t ₁ second;
Substituting the film heat transfer coefficient h _s of the coating layer surface obtained by the following formula (9) into the following formula (11) to obtain a mass change Δw _w of moisture in the coating layer in Δt seconds;
Applying the w _w1 and the Δw _w to the following equation (12) to estimate the drying rate of the coating layer, and a method for estimating the drying rate of the coating layer on the substrate .

Here, R: drying rate (kg-water / (m ² -material · s), A: surface area (m ² ) of coating layer, t _F : drying end time (s), w _w : moisture in coating layer Mass (kg), w _wF : mass of moisture after drying in the coating layer (kg), w _w0 : mass of initial moisture in the coating layer (kg), w _d : mass of dry coating layer (kg) ), W _b : mass of the substrate (kg), T _as : temperature of hot air on the surface of the coating layer (K), T _ab : temperature of hot air on the back surface of the substrate (K), T _s : surface temperature of the coating layer ( K), T _s0 : Initial surface temperature (K) of coating layer, T _sF : Surface temperature after finishing drying of coating layer (K), T _b : Back surface temperature (K) of substrate, T _bF : After finishing drying backside temperature of the substrate _{(K), T m = (} T s + T b) / 2: average temperature of the substrate and the coating layer _{(K), T m0:} substrate and the coating layer Initial average temperature _{(K), T mF:} drying after completion of the average temperature of the substrate and the coating layer (K), _{c w:} water constant pressure specific heat capacity of the (liquid) (J / (kg · K )), c _Gw : constant pressure specific heat capacity of water (steam) (J / (kg · K)), c _d : specific heat capacity of dried coating layer (J / (kg · K)), c _b : specific heat capacity of substrate (J / (Kg · K)), h _b : film heat transfer coefficient on the back of the substrate, Δh _w0 : evaporation enthalpy of water (liquid) at T _s0 . The following (c ₁ ) is provided on the surface of the coating layer and the back surface of the base material in a member comprising a base material and a coating layer applied to the surface of the base material, the back surface of the base material being in contact with the atmosphere. Or, when the following (c ₂ ) is performed, a step of substituting values corresponding to the parameters of the following formulas (13) to (15),
Substituting the film heat transfer coefficient h _s of the coating layer surface obtained by the following formula (13) into the following formula (14) to obtain the mass w _w1 of the water in the coating layer after t ₁ second;
Substituting the film heat transfer coefficient h _s of the coating layer surface obtained by the following formula (13) into the following formula (15) to obtain a mass change Δw _w of moisture in the coating layer in Δt seconds;
Applying the w _w1 and the Δw _w to the following equation (16) to estimate the drying rate of the coating layer, and a method for estimating the drying rate of the coating layer on the substrate .
(C ₁ ) Hot air heating (c ₂ ) Any one or more of radiant heating, induction heating, or current heating, and hot air heating

Here, R: drying rate (kg-water / (m ² -material · s), A: surface area (m ² ) of coating layer, t _F : drying end time (s), w _w : moisture in coating layer Mass (kg), w _wF : mass of moisture after drying in the coating layer (kg), w _w0 : mass of initial moisture in the coating layer (kg), w _d : mass of dry coating layer (kg) ), W _b : mass of the substrate (kg), T _as : temperature of hot air on the surface of the coating layer (K), T _ab : temperature of hot air on the back surface of the substrate (K), T _s : surface temperature of the coating layer ( K), T _s0 : initial surface temperature (K) of coating layer, T _sF : surface temperature after finishing drying of coating layer (K), c _w : constant pressure specific heat capacity of water (liquid) (J / (kg · K) _{)), c Gw:} water (pressure specific heat capacity of steam) (J / (kg · K )), c d: specific heat capacity of dry coating layer (J / (kg · K) ) c _b: specific heat capacity of the substrate (J / (kg · K) ), Δh w0: enthalpy of vaporization of water at _{T s0} (liquid), Q: radiant heating, induction heating, or energy in, is generated by electrical heating . A drying rate estimation step for estimating a drying rate using the drying rate estimation method for a coating layer according to any one of claims 1 to 4, over the entire surface of the coating layer,
And obtaining a drying rate distribution of the coating layer from the drying rate obtained in the drying rate estimating step.   A program for causing a computer to execute the drying rate estimation method according to any one of claims 1 to 4.   A program for causing a computer to execute the method for obtaining a drying speed distribution according to claim 5.   A computer-readable recording medium storing the program according to claim 6.   A computer-readable recording medium storing the program according to claim 7.

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