CN102207441B - Automatic detection method of static contact angle and dynamic contact angle - Google Patents

Abstract

The invention discloses an automatic high-accuracy droplet calculation method of dynamic and static contact angles. The method of the invention is realized by obtaining the droplet edge of a shot clear drop image with a level set method and judging whether the image is a static contact angle, an advancing angle or a receding angle. For a static contact angle image, if the droplet is large in size, an ellipse fitting method should be employed, while if the droplet size and the contact angle are both small, a circle fitting algorithm is chosen. If to calculate an advancing angle, a circle fitting or ellipse fitting algorithm is chosen. If to calculate a receding angle, a polynomial fitting algorithm is employed. By obtaining the tangent of a curve resulting from fitting at a droplet marginal point corresponding to a triplet, two contact angles respectively on the left and right are then obtained. The average of the two contact angles is a final contact angle. According to the method of the invention, dynamic and static contact angles can be calculated rapidly and automatically, with high rate of accuracy.

Description

The automatic testing method of a kind of static contact angle and dynamic contact angle

Technical field

The present invention relates to static contact angle and dynamic contact angle automatic algorithms that a kind of hydrophobic nature detects, belong to the material properties test field.

Background technology

Porcelain and glass insulator consist of insulation by hydrophilic material, have less surface resistance in the wet situation of dirt, cause pollution flashover voltage low.Silicon rubber has hydrophobic nature, migration of hydrophobicity, still has very high surface resistance under dirty wet environment, thereby has higher pollution flashover voltage.Composite insulator and room temperature vulcanization (RoomTemperature Vulcanization, RTV) silicone rubber coating is made of silastic material, and they have stronger anti-soil and dodge ability, have a wide range of applications in the electric system external insulation.Hydrophobic nature is the key characteristic of silastic material, and silastic surface easily suffers immersion, corona, stains in atmospheric environment, so the forfeiture of its hydrophobic nature and the research of recovery characteristics have great importance in these situations.

The hydrophobic nature characterizing method of silicon rubber mainly contains water spray rating scale method and contact angle method, the former is by spraying water to silastic surface, then judge the surface hydrophobicity situation according to size, shape and the distribution of the globule, it is less demanding to test condition, but the subjectivity of judging is slightly large, mainly for the composite insulator at scene or the RTV coating on porcelain and the glass insulator.Contact angle method is by dripping deionized water to silastic surface, then judge the hydrophobic nature of material according to the angle (contact angle) of gas, liquid, solid triplet place drop edge tangent line and solid-liquid interface, this method is slightly high to conditional request, but the sign to the material hydrophobic nature is more careful, is usually used in the smooth silastic material of rule.For common static contact angle method in the research of silastic material hydrophobic nature, the method required image is less at present, and it is comparatively convenient to process, and has obtained good effect when the material surface smoother is smooth.Immersion, corona, stain rear material surface and become coarse, solute precipitation is arranged, triplet maintained static when this moment, contact angle changed in certain variation range, that is to say that there is hysteresis phenomenon in the contact angle measurement, static contact angle is often bigger than normal and near advancing angle, its test result and surface hydrophobicity situation may not be very identical during beginning.Consider that the drop of certain volume is on the surface of coarse material, if increase a small amount of drop then along with the increase drop floorage of drop remains unchanged and contact angle increases gradually with microsyringe, until the floorage that droplet size increases above drop after the critical value becomes large, contact angle reduces to some extent, and the Maximum Contact angle that obtains in this process is advancing angle θ _AIf extract a small amount of drop then along with the minimizing drop floorage of drop also remains unchanged and contact angle reduces gradually with microsyringe, until reducing, droplet size surpasses the then floorage minimizing of drop of critical value, contact angle increases, and the minimal contact angle that obtains in this process is receding angle θ _RCan suppress to a certain extent the factor interference that measurement causes to contact angle such as coarse, solute precipitation based on the dynamic Contact horn cupping of advancing angle/receding angle.

Dynamic Contact angular measurement hour hands need to be taken many images to a test point could obtain accurately advancing angle and receding angle, if all choose then match then workload is excessive of marginal point by naked eyes; And the edge that affects the globule that is subject to needle tubing is not circular or oval completely, only has the suitable edge of selection to carry out match and could obtain accurately contact angle, and this has proposed certain requirement to the tester.Cause the multiplication of workload and computing time.

Summary of the invention

For solving the problem that exists in the existing contact angle computing method, the invention provides static contact angle and the dynamic contact angle automatic algorithms used when a kind of material hydrophobic nature detects, it is characterized in that, comprising:

Obtain globule image with digital camera or the shooting of CCD camera combining image capture card;

Obtain globule edge in the described image based on the movable contour model of level set;

Judge static contact angle, advancing angle image or receding angle image according to circle, ellipse fitting, single order polynomial expression and second order polynomial match for the size of excluding near the drop edge errors needle tubing;

Adopt circle fitting process or ellipse fitting algorithm to calculate static contact angle or advancing angle;

Adopt single order and second order polynomial fitting algorithm to calculate receding angle.

Described judgement image is static contact angle, advancing angle image or receding angle image: namely near the drop edge after excluding the needle tubing, if the error of fitting of circle fitting algorithm and ellipse fitting algorithm is less than single order and second order polynomial error of fitting then be static contact angle or advancing angle image; If the error of fitting of circle fitting algorithm and ellipse fitting algorithm is greater than single order and second order polynomial error of fitting then be the receding angle image.

Calculate static contact angle or advancing angle, select to treat the edge of match less than critical value according to error of fitting, with the match of oval algorithm elder generation, when gained contact angle during greater than eccentricity correspondence contact angle, corresponding contact angle is final contact angle, otherwise selects circle fitting algorithm to calculate contact angle.

Calculate receding angle, select to treat the edge of match according to error of fitting less than critical value, select respectively single order and second order polynomial match, if latter's error is greater than the former 1.5 times, then selecting the former gained contact angle is final contact angle, is final contact angle otherwise select latter's gained contact angle.

Described various fitting algorithm obtains error of fitting and treats the match part less than critical value and the longest drop edge conduct, and this edge comprises gas, near the drop edge of solid, liquid boundary line at gas, more than the solid, liquid boundary line.

Beneficial effect of the present invention has:

(1) adopt movable contour model to obtain drop edge, antijamming capability is strong

Because the disturbing factor that the globule image that hydrophobic nature measures exists is a lot, the globule edge that conventional boundary operator obtains is easy to be interfered, and the marginal point that obtains is not convenient for subsequent treatment not according to arranged sequentially.Level Set Method is based on finding the solution partial differential equation, utilize better image information, can obtain the drop edge of global optimum, insensitive to initial profile, therefore under various interference, all can comparatively accurately obtain the edge of the globule, for the accurate calculating of follow-up contact angle is laid a good foundation.

(2) can fully automatically calculate sound attitude contact angle

Comparison automatic decision according to circle match, ellipse fitting error and fitting of a polynomial error size is that static contact angle, advancing angle calculate or receding angle calculates, and the present invention need not to know in advance that pending image is static contact angle image or dynamic contact angle image.Drop image during for static contact angle, should select the whole edge of this drop to carry out match, should select to carry out match near near the drop edge the triplet for the dynamic contact angle image, more good utilisation drop edge information accurately obtains contact angle like this.The present invention selects to treat the edge of match according to the size adaptation of error of fitting, the longest match edge for the treatment of when namely selecting error of fitting less than critical value, and accuracy is higher like this.The present invention both need not to know that pending image belonged to static contact angle image or dynamic contact angle image, also need not to obtain in advance simultaneously drop edge information.

(3) accuracy of computation is high

During for the drop image of static contact angle and advancing angle because the present invention selects the higher circle fitting algorithm of accuracy or ellipse fitting algorithm automatically according to the relation of eccentricity and contact angle, the present invention is according to the adaptively selected linear fit of error of fitting or second order polynomial match when calculating receding angle, accuracy that like this can the calculating of Effective Raise sound attitude contact angle.

Description of drawings

Below in conjunction with accompanying drawing the present invention is elaborated:

Fig. 1 is the process flow diagram according to the embodiment of the invention;

Fig. 2 is the process flow diagram according to the circle fitting algorithm of the embodiment of the invention;

Fig. 3 is the process flow diagram according to the ellipse fitting algorithm of the embodiment of the invention;

Fig. 4 selects figure according to the circle of the embodiment of the invention and ellipse fitting algorithm.

Embodiment

Referring to accompanying drawing 1, use step of the present invention and be:

(1) adopt digital camera or CCD camera combining image capture card that the globule on the material is taken pictures, camera plane is perpendicular to material plane;

(2) gained globule image is adopted based on level set method acquisition globule edge;

(3) carry out match according to circle, ellipse fitting and fitting of a polynomial near drop edge excluding needle tubing, size according to errors is judged as static contact angle, advancing angle image or receding angle image, if the former is static contact angle or advancing angle image less than latter; Otherwise be the receding angle image;

(4) when calculating static contact angle or advancing angle, select circle fitting process or ellipse fitting method, select to treat the edge of match less than critical value according to error of fitting, with the first match of oval algorithm, when the gained contact angle during greater than the corresponding contact angle of eccentricity corresponding contact angle be final contact angle, otherwise select circle fitting algorithm to calculate contact angle.Select to treat the edge of match when calculating receding angle less than critical value according to error of fitting, select respectively single order and second order polynomial match, if consider that latter's error is greater than the former 1.5 times, then selecting the former gained contact angle is final contact angle, is final contact angle otherwise select latter's gained contact angle.

Following Haminlton-Jacobi equation is followed in the evolution of level set function curved surface.

F represents the Evolution Rates of each point on the curve in the formula, and direction is along the normal to a curve direction, and is usually relevant with image gradient and curvature;

Be level set function

Gradient on two dimensional surface; Different F expression formula correspondences different image partition methods.

The energy function of Chan-Vese model is expressed as follows:

$E(c_1,c_2,C)=\mathrm{\μL}\left(C\right)+\mathrm{vA}\left(C\right)+{\mathrm{\λ}}_1\underset{I\left(C\right)}{\∫}{|u_0-c_1|}^2\mathrm{dxdy}+{\mathrm{\λ}}_2\underset{O\left(C\right)}{\∫}{|u_0-c_2|}^2\mathrm{dxdy}---\left(2\right)$

A in the formula (C) is the interior zone area of curve C; μ, v 〉=0, λ ₁, λ ₂＞0 is weight coefficient; I (C) and O (C) are respectively the inside and outside zone of C; c ₁, c ₂Be respectively the average of I (C) and O (C) epigraph gray scale.

With

Be defined as follows:

In the formula

Be level set function.

Energy function is expressed as

The minimization of energy function will obtain Euler-Lagrange equation, and the gradient that obtains level set function after the conversion is as follows:

Formula (6) is through after calculating

Be the edge of gained image.

Obtain in the image behind the drop edge curve at the usage level collection, if static contact angle image, this moment, the needle tubing of microsyringe was not inserted in the drop, the edge of drop is circle or oval in the gained image, consider and do not satisfy circular in the drop image border when not being very large when droplet size, use is based on the fitting algorithm of circle, along with ellipse fitting algorithm is selected at its edge of increase of droplet size closer to ellipse.If dynamic contact angle image, because the needle tubing of microsyringe is inserted in the globule, the edge of drop can not satisfy circle or elliptic equation fully, near the drop edge of triplet (gas-liquid-solid three-state boundary line) is close to circle or oval when measuring advancing angle, relation according to eccentricity and contact angle is selected circle match or ellipse fitting algorithm, then according to error less than the critical value the longest adaptively selected match drop edge for the treatment of, obtain final contact angle according to the match curve obtained.If drop edge is generally close to polynomial curve near the measurement receding angle, triplet, the match edge finally obtain contact angle behind the match acquisition curvilinear equation according to error of fitting less than critical value the longest adaptively selected treating.

-based on round approximating method

If the array that the globule marginal point that obtains is horizontal, ordinate forms is X (n), n=1 ..., 2i-1,2i ... 2N, wherein X (2i-1), X (2i) are respectively horizontal stroke, the ordinate that i is ordered; The central coordinate of circle of place, globule edge circle is [X ₀, Y ₀], radius is R, then defines the error that n orders as follows:

$e_n=\sqrt{{(X(2n-1)-X_0)}^2+{(X\left(2n\right)-Y_0)}^2}-R---\left(7\right)$

Then have a total error to be defined as:

$E=\frac{1}{2}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{e}_n^2---\left(8\right)$

X in the formula ₀, Y ₀, R is unknown variable.The Levenberg-Marquardt algorithm has obtained computing velocity near the second order local derviation with the calculated amount of single order local derviation, is very suitable for the non-linear least square problem, therefore selects the method.

If e=[e ₁, e ₂..., e _N] ^TBe the error column vector; W is the column vector that the nonlinear multielement function variable forms, W=[X ₀, Y ₀, R] ^TJ is Jacobian matrix,

w _jBe j element among the W; I is 3 dimension unit matrix.The variable element iterative formula is as follows:

W(k+1)＝W(k)-(J(k) ^TJ(k)+λI) ^-1J(k) ^Te(k) (9)

K is iterations in the formula; λ adjusts according to the comparative result of twice error of calculation in front and back, if error increase then λ=λ * 10, λ=λ if error reduces * 0.1, its Initial value choice 0.1 effect is pretty good.

For the match of static contact angle, Jacobian matrix is calculated as follows:

$J_{i,1}=\frac{{\∂e}_i}{\∂X_O}=\frac{-(X(2n-1)-X_O)}{\sqrt{{(X(2n-1)-X_O)}^2+{(X\left(2n\right)-Y_O)}^2}}---\left(10\right)$

$J_{i,2}=\frac{{\∂e}_i}{\∂Y_O}=\frac{-(X\left(2n\right)-Y_O)}{\sqrt{{(X(2n-1)-X_O)}^2+{(X\left(2n\right)-Y_O)}^2}}---\left(11\right)$

$J_{i,3}=\frac{{\∂e}_i}{\∂R}=-1---\left(12\right)$

N is the sequence number of globule marginal point in the formula.

Because the gap of initial solution and optimum solution will have a strong impact on speed of convergence, even computational accuracy.The boundary line of gas-liquid-solid three-state is called triplet, and it corresponds to the point of ordinate minimum in the globule edge at image, and each point of left and right side is established sequence number and is respectively j, k.Because of the usually distribution around 90 ° of contact angle of the silastic surface globule, based on the hypothesis of semicircle, the initial center of circle that algorithm uses and radius use following strategy to obtain:

X ₀＝(X(2j-1)+X(2k-1))/2；Y ₀＝(X(2j)+X(2k))/2 (13)

$R=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\sqrt{{(X(2i-1)-X_0)}^2+{(X\left(2i\right)-Y_0)}^2}---\left(14\right)$

Can obtain fast the initial value of the center of circle and radius according to the method, and this value to depart from exact value usually little, measured result shows that this mode can ensure accuracy and the real-time of measuring.

If edge, the globule left and right sides and surface level intersecting point coordinate are respectively (x ₁, y ₁), (x ₂, y ₂), the central coordinate of circle that match obtains is [X ₀, Y ₀], then left and right sides slope is calculated as follows:

k ₁＝-(x ₁-X ₀)/(y ₁-Y ₀)；k ₂＝-(x ₂-X ₀)/(y ₂-Y ₀) (15)

K in the formula ₁And k ₂Be respectively that triplet place circular arc is upper left, the slope of right tangent.Arranged on left and right sides contact angle computing formula is as follows.

θ ₁＝atan(k ₁)×180/π，k ₁≥0；θ ₁＝180+atan(k ₁)×180/π，k ₁＜0；

θ ₂＝180-atan(k ₂)×180/π，k ₂≥0；θ ₂＝-atan(k ₂)×180/π，k ₂＜0 (16)

θ in the formula ₁And θ ₂Be respectively the contact angle of arranged on left and right sides, the span of atan function is-pi/2～pi/2.

The contact angle θ of the globule is calculated as follows:

θ＝(θ ₁+θ ₂)/2 (17)

The unit of θ is ° in the formula.

The Levenberg-Marquardt algorithm improves degree of accuracy by iteration, and the situation of judgement convergence has a significant effect to degree of accuracy and the real-time of algorithm.Algorithm determines whether stopping to calculate according to the situation of change of gained contact angle before and after the iteration.Continuous three result of calculations often can fine sign convergence situation in the Levenberg-Marquardt algorithm iteration process.Therefore, convergence criterion is as follows: the gained contact angle is respectively A after establishing N, N+1, N+2 iteration _N, A _N+1, A _N+2If satisfy

| A _N-A _N+1|≤C ₁With | A _N+1-A _N+2|≤C ₂(18)

Then iteration stops, wherein C ₁, C ₂Be respectively the critical value of setting, the present invention is chosen as 0.5 ° and 0.01 °, can suitably adjust according to actual conditions when specifically using, and the standard deviation of using under normal circumstances this criterion to calculate the gained contact angle only is about 0.5 °.Algorithm flow chart as shown in Figure 2.

-based on the approximating method of ellipse

The circle fitting algorithm error increases when droplet size is larger, should select elliptic equation that drop edge is carried out match.Conventional least square fitting calculated amount is large, and the real-time that contact angle calculates will be affected, and select a kind of algorithm of direct calculating elliptic parameter.Oval general equation can be expressed as:

F(m，n)＝n·m＝ax ²+bxy+cy ²+dx+ey+f＝0 (19)

X, y represent respectively horizontal stroke, ordinate, m=[a, b, c, d, e, f in the following formula] ^T, n=[x ², xy, y ², x, y, 1].If n _i=[x _i ², x _iy _i, y _i ², x _i, y _i, 1], B=[n ₁ ^T, n ₂ ^T..., n _N ^T] ^T, F (m, n _i) be referred to as Plane-point (x _i, y _i) to the algebraic distance of curve F (m, n)=0.When all discrete data point algebraic distance quadratic sums of ellipse fitting hour can solve corresponding quafric curve, this belongs to the non-linear least square problem, and conventional least-squares algorithm such as Levenberg-Marquardt algorithm calculated amount and programing work amount are all larger.For the observation data that N is ordered, fitting criterion is:

$E_{\min }=\min \left(\underset{i=1}{\overset{N}{\mathrm{\Σ}}}F{(m,n_i)}^2\right)---\left(20\right)$

Must limit b for formula (20) ²The result of-4ac＜0 guarantee match is oval, otherwise fitting result might be para-curve or hyperbolic curve but not ellipse.Because of b ²-4ac＜0 is not an equation restrictive condition, can not ensure solution owing to the Kuhn-Tucker condition when actual finding the solution, therefore introduce restrictive condition b ²-4ac=-1 is expressed as with matrix form:

m ^TCm＝1 (21)

In the formula $C=\left[\begin{array}{cccccc}0& 0& 2& 0& 0& 0\\ 0& -1& 0& 0& 0& 0\\ 2& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right].$

Formula (20) is equivalent to

E _min＝min(|Bm| ²) (22)

Because B is known quantity, amount to be asked is m in the formula (22), and the key of problem is carried out optimizing to m exactly.

Introducing Lagrange operator and differentiate gets:

2B ^TBm-2λCm＝0 (23)

Make S=B ^TB, formula (23) is rewritten as:

Sm＝λCm (24)

For formula (24), can solve by the method for generalized eigenvalue and generalized eigenvector 6 groups of characteristic of correspondence value λ _iAnd u _iFor the condition restriction Matrix C, its eigenwert is [2 ,-1,2,0,0,0], an eigenwert is only arranged for just.Only generalized eigenvalue λ ∈ R is only arranged ⁺With generalized eigenvector u as the ellipse fitting solution.For any k ∈ R ⁺, should make (λ, ku) to satisfy formula (21), i.e. k ²u ^TCu=1, then:

k＝[1/(u ^TCu)] ^1/2＝[1/(u ^TSu)] ^1/2 (25)

The unique solution of m:

$\hat{m}=\mathrm{ku}---\left(26\right)$

The information such as oval center, major axis, minor axis, the anglec of rotation can be obtained according to the gained solution, then contact angle can be obtained according to the tangent line situation.

Algorithm flow chart as shown in Figure 3.Be respectively L if obtain oval long and short semiaxis according to the m that finds the solution _LAnd L _S, the center is (X ₀, Y ₀), the angle of inclination is θ ₀Radian; Then ellipse is gone up point (x ₁, y ₁) expression formula is as follows:

x＝L _Lcosθ；y＝L _Ssinθ； (27)

x ₁＝xcosθ ₀-ysinθ ₀+X ₀；

y ₁＝xsinθ ₀+ycosθ ₀+Y ₀；

Left and right sides triplet corresponding point are respectively (X on the drop edge _L, Y _L) and (X _R, Y _R), consider that sample may not be in the state of complete level, it is as follows that contact angle calculates thinking, obtains first the θ in formula (27) corresponding to left and right sides triplet corresponding point, is designated as θ _L1And θ _R1, angle (A) obtains the phase place of plural A, and the span of function is-π～π.Be calculated as follows:

X _L1＝(X _L-X ₀)cosθ ₀+(Y _L-Y ₀)sinθ ₀；

Y _L1＝-(X _L-X ₀)sinθ ₀+(Y _L-Y ₀)cosθ ₀；

X _R1＝(X _R-X ₀)cosθ ₀+(Y _R-Y ₀)sinθ ₀；

Y _R1＝-(X _R-X ₀)sinθ ₀+(Y _R-Y ₀)cosθ ₀；

θ _L1＝angle(Y _L1/L _Sj+X _L1/L _L)；

θ _R1＝angle(Y _R1/L _Sj+X _R1/L _L).

According to θ _L1And θ _R1And oval tilt angle theta ₀The contact angle that can get the drop left and right sides when not considering the surface inclination is respectively θ _L2And θ _R2, unit is °, shown in (28).

$\left\{\begin{array}{c}{\mathrm{\&theta;}}_{L2}=\frac{180}{\mathrm{\&pi;}}[a\tan \left(\frac{-L_S}{L_L\tan {\mathrm{\&theta;}}_{L1}}\right)+{\mathrm{\&theta;}}_0],Y_{L1}\&GreaterEqual;0\\ {\mathrm{\&theta;}}_{L2}=\frac{180}{\mathrm{\&pi;}}[\mathrm{\&pi;}+a\tan \left(\frac{-L_S}{L_L\tan {\mathrm{\&theta;}}_{L1}}\right)+{\mathrm{\&theta;}}_0],Y_{L1}<0\\ {\mathrm{\&theta;}}_{R2}=\frac{180}{\mathrm{\&pi;}}[a\tan \left(\frac{L_S}{L_L\tan {\mathrm{\&theta;}}_{R1}}\right)+{\mathrm{\&theta;}}_0],Y_{R1}\&GreaterEqual;0\\ {\mathrm{\&theta;}}_{R2}=\frac{180}{\mathrm{\&pi;}}[\mathrm{\&pi;}+a\tan \left(\frac{L_S}{L_L\tan {\mathrm{\&theta;}}_{R1}}\right)+{\mathrm{\&theta;}}_0],Y_{R1}<0\end{array}\right.---\left(28\right)$

If obtaining the surface slope according to left and right sides triplet corresponding point is k ₁, then left and right sides contact angle and final contact angle are respectively θ _L, θ _RAnd θ, shown in (29), (30), unit is °.

$\left\{\begin{array}{c}{\mathrm{\&theta;}}_L={\mathrm{\&theta;}}_{L2}-180a\tan \left(k_1\right)/\mathrm{\&pi;}\\ {\mathrm{\&theta;}}_R={\mathrm{\&theta;}}_{R2}+180a\tan \left(k_1\right)/\mathrm{\&pi;}\end{array}\right.---\left(29\right)$

θ＝(θ _L+θ _R)/2 (30)

-polynomial fitting method

Polynomial fitting method is selected several points by near drop edge triplet, and it is carried out fitting of a polynomial, then obtains the tangent line at triplet place and then obtains contact angle.If obtain the arranged on left and right sides polynomial expression according to match be

And left and right sides triplet place coordinate is (X _L, Y _L), (X _R, Y _R), then be respectively according to the tangent slope of its correspondence of polynomial expression on drop

If obtaining the surface slope according to left and right sides triplet place is k ₁, then about 2 side joint feelers be

$\left\{\begin{array}{c}{\mathrm{\&theta;}}_L=\frac{180}{\mathrm{\&pi;}}[a\tan k_L-a\tan k_1],Y_{L1}\&GreaterEqual;0\\ {\mathrm{\&theta;}}_L=\frac{180}{\mathrm{\&pi;}}[\mathrm{\&pi;}+a\tan k_L-a\tan k_1],Y_{L1}<0\\ {\mathrm{\&theta;}}_R=\frac{180}{\mathrm{\&pi;}}[a\tan k_R+a\tan k_1],Y_{R1}\&GreaterEqual;0\\ {\mathrm{\&theta;}}_R=\frac{180}{\mathrm{\&pi;}}[\mathrm{\&pi;}+a\tan k_R+a\tan k_1],Y_{R1}<0\end{array}\right.$

The final contact angle of drop

θ＝(θ _L+θ _R)/2 (31)

-edge and algorithm adaptively selected

Near needle tubing the edge, whole drop edge can better be expressed with circle or ellipse fitting algorithm when image is static contact angle image or advancing angle image; When image be the receding angle image then near needle tubing the edge, whole drop edge can better be expressed with single order or second order polynomial fitting algorithm.Therefore, the size of drop edge error is judged as static contact angle, advancing angle image or receding angle image near the needle tubing for excluding according to circle, ellipse fitting and fitting of a polynomial, if the former is static contact angle or advancing angle image less than the latter image; Otherwise be the receding angle image.When globule small volume, then its edge is not rounded in globule inside when needle tubing, the edge that obtains can be got final product with the equation of a circle match.When needle tubing is inserted in the globule, it is influential near the globule edge the needle tubing, globule edge no longer satisfies circular, but near the globule edge effect when measuring advancing angle the triplet is very little, if the match edge selects suitable then error of fitting is less, error of fitting becomes large if the edge is selected excessive, if though the edge selects too small then error of fitting is little, but match obtains curve may not be near the true edge of the globule, can select as much as possible the match point for the treatment of during less than critical value in error.Matched curve can be circle or polynomial expression, and therefore this matched curve selected circle or ellipse fitting that better effects is arranged relatively close to circle or oval when contact angle camber line large, that treat match was longer when measuring advancing angle.Concrete criterion can be with reference to the accompanying drawings 4 be judged when measuring static contact angle and advancing angle, selects ellipse fitting algorithm when contact angle is greater than the critical angle of correspondence when eccentricity is determined otherwise selects circle fitting algorithm.Contact angle is less when measuring receding angle, and camber line treats that match is partly relatively close to the low order polynomial expression more in short-term, so the time select fitting of a polynomial, polynomial expression is generally selected second order or single order according to actual conditions, if consider that latter's error is greater than the former 1.5 times, then select the former, otherwise select the latter.

The above is the preferred embodiments of the present invention only, is not limited to the present invention, and for a person skilled in the art, the present invention can have various modifications and variations.Within the spirit and principles in the present invention all, any modification of doing, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (2)

1. the automatic testing method of a static contact angle and dynamic contact angle is characterized in that, comprising:

Obtain globule image with digital camera or the shooting of CCD camera combining image capture card;

Obtain globule edge in the described image based on the movable contour model of level set;

For excluding near the drop edge needle tubing, judge static contact angle, advancing angle image or receding angle image according to the size of errors according to circle, ellipse fitting, single order polynomial expression and second order polynomial match;

Described judgement image is static contact angle, advancing angle image or receding angle image: namely near the drop edge after excluding the needle tubing, if the error of fitting of circle fitting algorithm and ellipse fitting algorithm is less than single order and second order polynomial error of fitting then be static contact angle or advancing angle image; If the error of fitting of circle fitting algorithm and ellipse fitting algorithm is greater than single order and second order polynomial error of fitting then be the receding angle image;

Adopt circle fitting process or ellipse fitting algorithm to calculate static contact angle or advancing angle;

Adopt single order and second order polynomial fitting algorithm to calculate receding angle;

When calculating receding angle, select to treat the edge of match less than critical value according to error of fitting, select respectively single order and second order polynomial match, if latter's error is greater than the former 1.5 times, then selecting the former gained contact angle is final contact angle, is final contact angle otherwise select latter's gained contact angle.

2. the method for claim 1, it is characterized in that, described various fitting algorithm obtains error of fitting and treats the match part less than critical value and the longest drop edge conduct, and this edge comprises gas, near the drop edge of solid, liquid boundary line at gas, more than the solid, liquid boundary line.

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