Search Results (402)

The non-Newtonian Carreau fluid model is a suitable model for pseudoplastic fluids and can be used to characterize fluids not so different from biological fluids, such as the blood, and fluids involved in geological processes, such as lava and magma. These fluids are frequently conveyed by complex flow structures, which consist of a network of channels that allow the fluid to flow from one place (source or sink) to a variety of locations or vice versa. These flow networks are not randomly arranged but show self-similarity at different spatial scales. Our work focuses on the design of self-similar branched flow networks that look the same on any scale. The flow is incompressible and stationary with a viscosity following the Carreau model, which is important for the study of complex flow systems. The flow division ratios, the flow resistances at different scales, and the geometric size ratios for maximum flow access are studied, based on Computational Fluid Dynamics (CFD). A special emphasis is placed on investigating the possible incidence of flow asymmetry in these symmetric networks. Our results show that asymmetries may occur for both Newtonian and non-Newtonian fluids and shear-thinning fluids most affect performance results. The lowest flow resistance occurs when the diameters of the parent and daughter ducts are equal, and the more uniform distribution of flow resistance occurs for a ratio between the diameters of the parent and daughter ducts equal to 0.75. Resistances for non-Newtonian fluids are 4.8 to 5.6 times greater than for Newtonian fluids at Reynolds numbers of 100 and 250, respectively. For the design of engineering systems and the assessment of biological systems, it is recommended that the findings presented are taken into account. Full article

This study examines the flow behavior as well as the cuttings transport of non-Newtonian drilling fluid in the geometry of an eccentric annulus, accounting for what impacts drill pipe rotation might have on fluid velocity, as well as annular eccentricity on axial and tangential distributions of velocity. A two-phase Eulerian–Eulerian model was developed by using computational fluid dynamics to simulate drilling fluid flow and cuttings transport. The kinetic theory of granular flow was used to study the dynamics and interactions of cuttings transport. Non-Newtonian fluid properties were modeled using power law and Bingham plastic formulations. The simulation results demonstrated a marked improvement in efficiency, as much as 45%, in transport by increasing the fluid inlet velocity from 0.54 m/s to 2.76 m/s, reducing the amount of particle accumulation and changing axial and tangential velocity profiles dramatically, particularly at narrow annular gaps. At a 300 rpm rotation, the drill pipe brought on a spiral flow pattern, which penetrated tangential velocities in the narrow gap that had increased transport efficiency to almost 30% more. Shear-thinning behavior characterizes fluid of which the viscosity, at nearly 50% that of the central core low-shear regions, was closer to the wall high-shear regions. Fluid velocity and drill pipe rotation play a crucial role in optimizing cuttings transport. Higher fluid velocities with controlled drill pipe rotation enhance cuttings removal and prevent particle build-up, thereby giving very useful guidance on how to clean the wellbore efficiently in drilling operations. Full article

In this study, the influence of the presence of a Newtonian solvent on the flow of a Giesekus fluid in a plane channel or fracture is investigated with a focus on the determination of the flow rate for an assigned external pressure gradient. The pressure field is nonlinear due to the presence of the normal transverse stress component. As expected, the flow rate per unit width $Q^{\prime }$ is larger than for a Newtonian fluid and decreases as the solvent increases. It is strongly dependent on the viscosity ratio $\epsilon$ ($0\le \epsilon \le 1$), the dimensionless mobility parameter $\beta$($0\le \beta \le 1$) and the Deborah number $De$, the dimensionless driving pressure gradient. The degree of dependency is notably strong in the low range of $\epsilon$. Furthermore, $Q^{\prime }$ increases with $De$ and tends to a constant asymptotic value for large $De$, subject to the limitation of laminar flow. When the mobility factor $\beta$ is in the range $\left[0.5÷1\right]$, there is a minimum value of $\epsilon$ to obtain an assigned value of $De$. The ratio $U_N/U$ between Newtonian and actual mean velocity depends only on the product $\sqrt{\beta }De$, as for other non-Newtonian fluids. Full article

This study investigates the three-dimensional, steady, laminar boundary-layer equations of a non-Newtonian fluid over a flat plate in the absence of body forces. The classical boundary-layer theory, introduced by Prandtl in 1904, suggests that fluid flows past a solid surface can be divided into two regions: a thin boundary layer near the surface, where steep velocity gradients and significant frictional effects dominate, and the outer region, where friction is negligible. Within the boundary layer, the velocity increases sharply from zero at the surface to the freestream value at the outer edge. The boundary-layer approximation significantly simplifies the Navier–Stokes equations within the boundary layer, while outside this layer, the flow is considered inviscid, resulting in even simpler equations. The viscoelastic properties of the fluid are modeled using the Rivlin–Ericksen tensors. Lie group analysis is applied to reduce the resulting third-order nonlinear system of partial differential equations to a system of ordinary differential equations. Finally, we determine the admissible forms of the freestream velocities in the x- and z-directions. Full article

The Reynolds number (Re), introduced in the late 19th century, has become a fundamental parameter in a lot of scientific fields—the main one being fluid mechanics—as it allows for the determination of flow characteristics by distinguishing between laminar and turbulent regimes, or some intermediate stage. Reynolds’ 1895 paper, which decomposed velocity into average and fluctuating components, laid the foundation for modern turbulence modeling. Since then, the concept has been applied to various fields, including external flows—the science that studies friction—as well as wear, lubrication, and heat transfer. Literature research in recent times has explored new interpretations of Re, and despite its apparent simplicity, the precise prediction of Reynolds numbers remains a computational challenge, especially under conditions such as the study of multiphase flows, non-Newtonian fluids, highly turbulent flow conditions, flows on very small scales or nanofluids, flows with complex geometries, transient or non-stationary flows, and flows of fluids with variable properties. Reynolds’ work, which encompasses both scientific and engineering contributions, continues to influence research and applications in fluid dynamics. Full article

We investigate the topological degree for generalized monotone operators of class ${\left(S\right)}_{+}$ with compact set-valued perturbations. It is assumed that perturbations can be represented as the composition of a continuous single-valued mapping and an upper semicontinuous set-valued mapping with aspheric values. This allows us to extend the standard degree theory for convex-valued operators to set-valued mappings whose values can have complex geometry. Several theoretical aspects concerning the definition and main properties of the topological degree for such set-valued mappings are discussed. In particular, it is shown that the introduced degree has the homotopy invariance property and can be used as a convenient tool in checking the existence of solutions to corresponding operator inclusions. To illustrate the applicability of our approach to studying models of real processes, we consider an optimal feedback control problem for the steady-state internal flow of a generalized Newtonian fluid in a 3D (or 2D) bounded domain with a Lipschitz boundary. By using the proposed topological degree method, we prove the solvability of this problem in the weak formulation. Full article

Flexible fibers, such as biomass particles and glass fibers, are critical raw materials in the energy and composites industries. Assemblies of the fibers show strong interlocking, non-Newtonian and compressible flows, intermittent avalanches, and high energy dissipation rates due to their elongation and flexibility. Conventional mechanical theories developed for regular granular materials, such as dry sands and pharmaceutical powders, are often unsuitable for modeling flexible fibers, which exhibit more complex mechanical behaviors. This article provides a comprehensive review of the current state of research on the mechanics of flexible fiber assemblies, focusing on their behavior under compression, shear flow, and gas–fiber two-phase flow processes. Finally, the paper discusses open issues and future directions, highlighting the need for advancements in granular theories to better accommodate the unique characteristics of flexible fibers, and suggesting potential strategies for improving their handling in industrial applications. Full article

Every day, approximately 7 m³ of air flows through the lungs of an adult, which comes into contact with 80 m² of the lung surface. This air contains both natural and anthropogenic particles, which can deposit on the surface of the mucus lining the respiratory tract. The presence of particles in the mucus leads to changes in its rheology and, consequently, in its functions. Therefore, this research aimed to determine how a non-Newtonian fluid suspension will behave during flow, illustrating the movement of mucus during coughing. The model mucus was an aqueous solution of carboxymethylcellulose (CMC). The tested particles suspended in a non-Newtonian fluid were Arizona Fine Dust, diesel exhaust particles, polyethylene microparticles, and pine pollen. It was noticed that as the fluid viscosity increases, the number of Kelvin–Helmholtz instabilities increases. The fluid’s expansion angle at the output of the measuring cell decreased, and the values of parameters characterizing the aerosol generated at the outlet decrease for selected particles present in the fluid. The research shows that the deposition of particles from polluted air in the respiratory tract, although they do not enter the bloodstream, may affect the human body. Deposited particles can change the behavior of mucus, which may translate into its functions. Full article

Designing scaffolds similar to the structure of trabecular bone requires specialised algorithms. Existing scaffold designs for bone tissue engineering have repeated patterns that do not replicate the random stochastic porous structure of the internal architecture of bones. In this research, the Voronoi tessellation method is applied to create random porous biomimetic structures. A volume mesh created from the shape of a Zygoma fracture acts as a boundary for the generation of random seed points by point spacing to create Voronoi cells and Voronoi diagrams. The Voronoi lattices were obtained by adding strut thickness to the Voronoi diagrams. Gradient Voronoi scaffolds of pore sizes (19.8 µm to 923 µm) similar to the structure of the trabecular bone were designed. A Finite Element Method-based computational fluid dynamics (CFD) simulation was performed on all designed Voronoi scaffolds to predict the pressure drops and permeability of non-Newtonian blood flow behaviour using the power law material model. The predicted permeability (0.33 × 10⁻⁹ m² to 2.17 × 10⁻⁹ m²) values of the Voronoi scaffolds from the CFD simulation are comparable with the permeability of scaffolds and bone specimens from other research works. Full article

This investigation specifically aims to enhance the understanding of digestate flow and mixing behavior across typical temperatures in bioreactors in agricultural biogas plants, facilitating energy-efficient mixing. Experimental tests confirmed that digestate exhibits non-Newtonian characteristics, allowing its flow behavior to be captured by rheological models. This study validated that digestate rheology significantly varies with temperature, which influences flow resistance, mixing efficiency and overall energy requirements. Two rheological models—the Bingham and Ostwald models—were applied to characterize digestate behavior, with the Ostwald model emerging as the most effective for Computational Fluid Dynamic (CFD) simulations, given its balance between predictive accuracy and computational efficiency. Specifically, results suggest that, while three-parameter models, like the Herschel–Bulkley model, offer high precision, their computational intensity is less suitable for large-scale modeling where efficiency is paramount. The small increase in the accuracy of the shearing process description does not compensate for the significant increase in CFD calculation time. Higher temperatures were found to reduce flow resistance, which in turn enables increased flow rates and more extensive mixing zones. This enhanced mass transfer and mixing potential at elevated temperatures are especially pronounced in peripheral areas of the bioreactor, farthest from the agitators. By contributing a model for rheological behavior under realistic bioreactor conditions, this study supports the optimization of energy use in biogas production. These findings emphasize that temperature adjustments within bioreactors could serve as a reliable control strategy to maintain optimal production conditions while minimizing operational costs. Full article

Debris flows are a dynamic and hazardous geological phenomenon, as by definition, debris flows are rapid, gravity-driven flows of saturated materials that often contain a mixture of water, rock, soil, and organic matter. They are highly destructive and occur in steep channels, posing a significant threat to infrastructure and human life. The dynamics of debris flows are complex due to their non-Newtonian behaviour and varying sediment–water interactions, making accurate modelling essential for risk mitigation and emergency planning. This paper reports and discusses the results of numerical simulations of back analyses aimed at studying the reconstruction of a real rapid debris flow. The selected test case is the event that occurred on 12 and 16 March 2021 along the Rio Sonno channel, a tributary of the Liri River, following the landslide event of Rendinara (Municipality of Morino, Abruzzo Region, Italy). There are significant flow sources in the area, fed by a highly fractured carbonaceous aquifer that extends immediately upslope of the detachment zone. The continuous flow influences the saturation level in the fine-grained sediments and favours the triggering of the debris flow. This phenomenon was simulated using the commercial RAMMS code, and the rheological model selected was “Voellmy fluid friction”. The modelling approaches used in this research are valid tools to estimate the volumes of materials involved in the flow-feeding process and for the purpose of possible mitigation works (debris flow-type dams, weirs, flow diversion, etc.). Full article

Microchannels are widely used across various industries, including pharmaceuticals and biochemistry, automotive and aerospace, energy production, and many others, although they were originally developed for the computing and electronics sectors. The performance of microchannels is strongly affected by factors such as rarefaction and viscous dissipation. In the present paper, a numerical analysis of the performance of microchannels featuring rectangular, trapezoidal and double-trapezoidal cross-sections in the slip flow regime is presented. The fully developed laminar forced convection of a Newtonian fluid with constant properties is considered. The non-dimensional forms of governing equations are solved by setting slip velocity and uniform heat flux as boundary conditions. Model accuracy was established using the available scientific literature. The numerical results indicated that viscous dissipation effects led to a decrease in the average Nusselt number across all the microchannels examined in this study. The degree of reduction is influenced by the cross-section, aspect ratio and Knudsen number. The highest reductions in the average Nusselt number values were observed under continuum flow conditions for all the microchannels investigated. Full article

Due to their nature, using shear thickening fluids (STFs) in engineering applications has sparked an interest in developing energy-dissipating systems, such as damping devices or shock absorbers. The Rheinforce technology allows the design of customized energy dissipative composites by embedding microfluidic channels filled with STFs in a scaffold material. One of the reasons for using microfluidic channels is that their shape can be numerically optimized to control pressure drop (also known as rectifiers); thus, by controlling the pressure drop, it is possible to control the energy dissipated by the viscous effect. Upon impact, the fluid is forced to flow through the microchannel, experiencing the typical entry flow until it reaches the fully developed flow. It is well-known for Newtonian fluid that the entrance flow is responsible for a non-negligible percentage of the total pressure drop in the fluid; therefore, an analysis of the fluid flow at the entry region for STFs is of paramount importance for an accurate design of the Rheinforce composites. This analysis has been numerically performed before for shear-thickening fluids modeled by a power-law model; however, as this constitutive model represents a continuously growing viscosity between end-viscosity plateau values, it is not representative of the characteristic viscosity curve of shear-thickening fluids, which typically exhibit a three-region shape (thinning-thickening-thinning). For the first time, the influence of these three regions on the entry flow on an axisymmetric pipe is analyzed. Two-dimensional numerical simulations have been performed for four STFs consisting of four dispersions of fumed silica nanoparticles in polypropylene glycol varying concentrations (7.5–20 wt%). Full article

Investment casting is a widely utilized casting technique that offers superior dimensional accuracy and surface quality. In this method, the wax patterns are employed in the layer-by-layer formation of a shell mold. As is customary, the patterns were created through the injection of molten or semi-solid wax into the die. The quality of the final casting is affected by the quality of the wax pattern. Furthermore, the filling of the die with wax can be associated with die-filling challenges, such as the formation of weld lines and misruns. In this study, the injection filling of the fluidity probe die with RG20, S1235, and S1135 pattern waxes was simulated using ProCast software. The thermal properties of the waxes, including thermal conductivity, heat capacity, and density across a wide temperature range, were determined with the assistance of a laser flash analyzer, a differential scanning calorimeter, and a dynamic mechanical analyzer. A favorable comparison of the acquired properties with those reported in the literature was observed. The Carreau model, which corresponds to non-Newtonian flow, was employed, and the parameters in the Carreau viscosity equation were determined as functions of temperature. Utilizing the thermal data associated with the wax patterns and the simulation outcomes, the interfacial heat transfer coefficients between the wax and the die were ascertained, yielding a value of 275–475 W/m²K. A strong correlation was observed between the experimental and simulated filling percentages of the fluidity probe across a wide range of injection temperatures and pressures. The analysis of the simulated temperature, fraction solid, viscosity, and shear rate in the wax pattern revealed that viscosity is a crucial factor influencing the wax fluidity. It was demonstrated that waxes with an initial high viscosity exhibit a low shear rate, which subsequently increases the viscosity, thereby hindering the wax flow. Full article

Radical or partial nephrectomy, commonly used for the treatment of kidney tumors, is a surgical procedure with a risk of high blood loss. The primary aim of this study is to quantify blood loss and elucidate the redistribution of blood flux and pressure between the two kidneys and the abdominal aorta during renal resection. We have developed a robust research methodology that introduces a new lumped-parameter mathematical model, specifically focusing on the vasculature of both kidneys using a non-Newtonian Carreau fluid. This model, a first-order approximation, accounts for the variation in the total impedance of the vasculature when various vessels are severed in the diseased kidney (assumed to be the left in this work). The model offers near real-time estimations of the flow–pressure redistribution within the vascular network of the two kidneys and the downstream aorta for several radical or partial nephrectomy scenarios. Notably, our findings indicate that the downstream aorta receives an approximately 1.27 times higher percentage of the redistributed flow from the diseased kidney compared to that received by the healthy kidney, in nearly all examined cases. The implications of this study are significant, as they can inform the development of surgical protocols to minimize blood loss and can assist surgeons in evaluating the adequacy of the remaining kidney vasculature. Full article