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Due to the numerous practices of non-Newtonian fluids in technological and industrial fields, the attention towards such fluids increases incredibly. The highly nonlinear equations emerge in the modeling of the non-Newtonian fluids. The differential transform method is one of the analytical methods which is used to acquire the solution to these complicated nonlinear equations in the series form. The current analysis comprises the squeeze flow of non-Newtonian fluid in two dimensions. Two infinite parallel plates are considered in which the time-dependent fluid is squeezed. The heat transfer mechanism is deliberated with the significance of heat absorption/generation. The nonlinear setup of ordinary differential equations is acquired by practicing the appropriate similarity variables on the governing equations of the concerned flow mechanism. The nonlinear setup is analytically resolved with the help of an analytical differential transform method. For the authenticity of the differential transform method, the analytical outcomes are compared with the numerical results. Graphical illustrations of fluid temperature and velocity profiles relative to the pertinent parameters are briefly explicated numerically and analytically. The fluid velocity demonstrates the descending behavior and the temperature field exhibits the expanding nature relative to the squeezing parameter. [ABSTRACT FROM AUTHOR]

Background: Synovial fluid (SF) is often used for diagnostic and research purposes as it reflects the local inflammatory environment. Owing to its complex composition, especially the presence of hyaluronic acid, SF is usually viscous and non-homogeneous. The presence of high-molar-mass hyaluronan in this fluid gives it the required viscosity for its function as a lubricant. Viscosity is the greatest major hydraulic attribute of the SF in articular cartilage. Methods: Empirical modeling of previously published results was performed. In this study, we explored the flow of a non-Newtonian fluid that could be used to model the SF flow. Analyzing the flow in a simple geometry can help explain the model's efficacy and assess the SF models. By employing some viscosity data reported elsewhere, we summarized the dynamic viscosity values of normal human SF of the knee joints in terms of time after injecting hyaluronidase (HYAL) at 25°C. The suggested quadratic behavior was obtained through extrapolation. For accurate diagnosis or prediction, the comparison between three specific parameters (ai, t0, and ln η0) was made for normal and pathological cases under the same experimental conditions for treatment by addition of HYAL and for investigation of the rheological properties. A new model on the variation of viscosity on the SF of knee joints with time after injection of HYAL with respect to normal and postmortem samples at different velocity gradients was proposed using data previously reported elsewhere. Results: The rheological behavior of SF changes progressively over time from non-Newtonian to a Newtonian profile, where the viscosity has a limiting constant value (η0) independent of the gradient velocity at a unique characteristic time (t0 ≈ 8.5 h). The proposed three-parameter model with physical meaning offers insights into future pathological cases. The outcomes of this work are expected to offer new perspectives for diagnosis, criteria, and prediction of pathological case types through comparisons with new parameter values treated under the same experimental conditions as HYAL injection. This study also highlights the importance of HYAL treatment for better intra-assay precision. [ABSTRACT FROM AUTHOR]

We address the stability of stationary solutions to a class of 2D non-newtonian fluid equations, when the external force contains hereditary characteristics involving unbounded delays. Firstly, when the unbounded variable delay is driven by a continuously differential function, we establish the stability of nontrivial weak stationary solutions and the asymptotic stability of trivial stationary solution. Then when the general unbounded delay is continuous with respect to time, the stability of nontrivial strong stationary solutions is also obtained. Eventually, when the proportional delay is considered, the polynomial stability of trivial stationary solution is verified. [ABSTRACT FROM AUTHOR]

We have found that the unique particle properties of fly ash can be applied to the modification of shear thickening fluid. In this paper, rheological properties and microscopic thickening mechanism of fly ash/silicon-based shear thickening fluid (subsequently abbreviated as FA/SiO2-STF) are studied. Ultrasonic technology and mechanical stirring method were used to prepare FA/SiO2-STF with different mass fractions of fly ash, and then rheometer was used to carry out steady-state rheological testing for FA/SiO2-STF, and 4%FA/SiO2-STF dynamic rheological test and temperature sensitivity testing, respectively. The thickening mechanism of FA/SiO2-STF was analyzed by scanning electron microscope. The rheological test results show that the FA/SiO2-STF with 4% fly ash content exhibits remarkable shear thickening effect. Finally, the relationship between the viscosity and shear rate of FA/SiO2-STF is numerically described by a mathematical model, which can accurately reflect the viscosity thickening effect. [ABSTRACT FROM AUTHOR]

Magnetotactic bacteria (MTB) are promising candidates for use as biomicrorobots in biomedical applications due to their motility, self-propulsion, and the ability to direct their navigation with an applied magnetic field. When in the body, the MTB may encounter non-Newtonian fluids such as blood plasma or mucus. However, their motility and the effectiveness of directed navigation in non-Newtonian fluids has yet to be studied on a single-cell level. In this work, we investigate motility of Magnetospirillum magneticum AMB-1 in three concentrations of polyacrylamide (PAM) solution, a mucus-mimicking fluid. The swimming speeds increase from 44.0 ± 13.6 µm/s in 0 mg/mL of PAM to 52.73 ± 15.6 µm/s in 1 mg/mL then decreases to 24.51 ± 11.7 µm/s in 2 mg/mL and 21.23 ± 10.5 µm/s in 3 mg/mL. This trend of a speed increase in low polymer concentrations followed by a decrease in speed as the concentration increases past a threshold concentration is consistent with other studies of motile, flagellated bacteria. Past this threshold concentration of PAM, there is a higher percentage of cells with an overall trajectory angle deviating from the angle of the magnetic field lines. There is also less linearity in the trajectories and an increase in reversals of swimming direction. Altogether, we show that MTB can be directed in polymer concentrations mimicking biological mucus, demonstrating the influence of the medium viscosity on the linearity of their trajectories which alters the effective path that could be predefined in Newtonian fluids when transport is achieved by magnetotaxis. [ABSTRACT FROM AUTHOR]

The hydrotransport of settling particles using laminar flow as opposed to the more energy‐ and water‐intensive turbulent flow has remained a tentative option for industries due to the complexity in characterizing particle settling dynamics in opaque non‐Newtonian fluids under sheared conditions. To provide insight into this unknown physics, this study focused on viscoelastic shear‐thinning fluids and developed a semi‐empirical model to characterize the batch‐settling dynamics of dilute suspensions (<5 vol% solids concentration) experiencing a shear field. These suspensions consisted of spherical glass microparticles in aqueous xanthan gum solutions. Settling profiles were measured with Electrical Resistance Tomography (ERT) while a motorized belt generated a cross‐shear field. The data acquired by the ERT showed that introducing cross‐shear fields into such suspensions increased settling rates when compared with static settling contexts. Then, a semi‐empirical model describing the "acceleration phase" of the settling process was developed and validated at accuracies between 81% and 97%. [ABSTRACT FROM AUTHOR]

A semi-numeric study is presented to explore the nonlinear, radiative, mixed convective boundary layer flow of non-Newtonian Eyring-Powell fluid (EPF) over a porous stretching wedge in the existence of suction/injection, viscous dissipation, activated energy, and ohmic heating. The governing coupled partial differential equations (PDEs) in the flow regime are transformed into coupled ordinary differential equations (ODEs) under suitable boundary conditions (BCs). Computations are performed for variations of various pertinent parameters on velocity, temperature distribution, surface drag force, and heat transfer rate number. It is noted that with increasing Eyring Powell parameter velocity increases for stretching parameter greater than free stream velocity, but decreases when wedge stretches slowly than free stream velocity. An increase in the local non-Newtonian fluid parameter decreases velocity when the wedge stretches faster as compared to free stream velocity. However, velocity increases when the wedge stretches faster. Temperature velocity decreases for both cases of wedge stretches faster or slower as the local non-Newtonian fluid parameter increases. Similar behavior is seen in the case of Eyring Powell parameter. Increasing heat generation or absorption decreases the momentum as well as thermal boundary layer thickness. When the suction/injection parameter is enhanced the velocity shows a declines behavior for both the cases of stretching parameter as it increases. Temperature profiles decline as the mass transfer parameter is enhanced for both the case's velocity ratio parameters, respectively. Excellent agreement is achieved with the differential transform method and numerical result. [ABSTRACT FROM AUTHOR]

Process of transportation of heat in ferrofluids has innumerable applications in the fields of electronics and automobile industry. By tracing the materials, the ferrofluid got popularity among researchers and engineers, also most ferrofluids are non-Newtonian in nature so here the non-Newtonian fluid is under consideration. In this study, the influences of viscous dissipation and magnetic parameter in the flow of ferromagnetic Carraeu fluid for a stretching surface are examined. Suitable similarity transformations in the system that consists of nonlinear form of Partial Differential Equations (PDEs) are transformed into a system of nonlinear form of ODEs, then the resulting Ordinary Differential Equations (ODEs) are resolved by use of a mathematical technique known as bvp4c. Effects of ferromagnetic interaction factor, Curie temperature, viscous dissipation and material parameter are examined for temperature profile as well as velocity fields. Moreover, the variations in velocity and thermal gradients are analyzed and described with the help of graphs. An upsurge in the values of magnetic interaction parameter and Weissenberg number causes a decline in the velocity field while the thermal gradient shows opposite behavior. It is detected that the temperature of Carreau fluid intensifies for larger and  λ. [ABSTRACT FROM AUTHOR]

Poiseuille flows are considered as flows of Newtonian fluids through stationary pipes, with applications ranging from the pharmaceutical industries to manufacturing companies. These flows have been extensively studied in several works of literature due to their relevance in many spheres of life. However, the Poiseuille flow for non-Newtonian flows has not gained much attention, even though most fluids are non-Newtonian. Based on this, this study investigates the Poiseuille flow of the second-grade fluid. Second-grade fluids are viscoelastic non-Newtonian fluids that exhibit both shear-thinning and shear-thickening with applications found in several industrial applications such as pharmaceutical, cosmetics and polymer processing. The Poiseuille flow of second-grade fluid is formulated from the underlying Navier-Stokes' equations and the general assumptions of Poiseuille flow are invoked to reduce the equations to the regular ordinary differential equations. An analytical solution for the flow problem is sought using the method of separation of variables and the results are graphed to show the response of velocity and flow rate to the parameters of the flow. The outcomes show that velocity distribution reduces as the pipe radius increases and second-grade fluid has lower velocity than the Newtonian fluid. [ABSTRACT FROM AUTHOR]

The main idea of this investigation is to introduce an integrated intelligence approach that investigates the chemically reacting flow of non-Newtonian fluid with a backpropagation neural network (LMS-BPNN). The AI-based LMS-BPNN approach is utilized to obtain the optimal solution of an MHD flow of Eyring–Powell over a porous shrinking wedge with a heat source and nonlinear thermal radiation ( R d ). The partial differential equations (PDEs) that define flow problems are transformed into a system of ordinary differential equations (ODEs) through efficient similarity variables. The reference solution is obtained with the bvp4c function by changing parameters as displayed in Scenarios 1–7. The label data are divided into three portions, i.e., 80% for training, 10% for testing, and 10% for validation. The label data are used to obtain the approximate solution using the activation function in LMS-BPNN within the MATLAB built-in command 'nftool'. The consistency and uniformity of LMS-BPNN are supported by fitness curves based on the MSE, correlation index ( R ), regression analysis, and function fit. The best validation performance of LMS-BPNN is obtained at 462, 369, 642, 542, 215, 209, and 286 epochs with MSE values of 8.67 × 10−10, 1.64 × 10−9, 1.03 × 10−9, 302 9.35 × 10−10, 8.56 × 10−10, 1.08 × 10−9, and 6.97 × 10−10, respectively. It is noted that f ′ (η) , θ (η) , and ϕ (η) satisfy the boundary conditions asymptotically for Scenarios 1–7 with LMS-BPNN. The dual solutions for flow performance outcomes ( C f x , N u x , and S h x ) are investigated with LMS-BPNN. It is concluded that when the magnetohydrodynamics increase ( M = 0.01 ,   0.05 ,   0.1 ), then the solution bifurcates at different critical values, i.e., λ c = − 1.06329 , − 1.097 , − 1.17694 . The stability analysis is conducted using an LMS-BPNN approximation, involving the computation of eigenvalues for the flow problem. The deduction drawn is that the upper (first) branch solution remains stable, while the lower branch solution causes a disturbance in the flow and leads to instability. It is observed that the boundary layer thickness for the lower branch (second) solution is greater than the first solution. A comparison of numerical results and predicted solutions with LMS-BPNN is provided and they are found to be in good agreement. [ABSTRACT FROM AUTHOR]

In this computational study, we investigate the gravity and pressure-driven electroosmotic multiphase flow of third-grade fluid through steep microchannel by using the semi-analytical technique. A two-dimensional mathematical model is proposed here for the supercritical bi-phase flow with the suspension of the nanometallic particles. A special type of non-Newtonian fluid (third-grade) is selected as a base fluid. The governing equations for the current flow problem are obtained through Poisson–Boltzmann equations, continuity equations, and Cauchy's momentum equations. The Poisson–Boltzmann equation is simplified by using the Debye–Hückel approximation. The symbolic software MATHEMATICATM is used to obtain the closed-form expression of electric potential, fluid and particle velocities, pressure gradient, and volumetric flow rate, respectively. The computational results are discussed qualitatively under the impact of the physical parameters embedded in the study. The graphical plots of fluid and particle-phase velocities are generated against the different parameters used in this study by adopting the same software as discussed earlier. The electrokinetic forces are responsible for electroosmotic flow which is modeled through the Laplace and Poisson–Boltzmann equations. The externally applied potential and electrical double-layer potential is governed by the Laplace and Poisson–Boltzmann equations, respectively. [ABSTRACT FROM AUTHOR]

Shear-thinning fluids have been widely used in microfluidic systems, but their internal flow mechanism is still unclear. Therefore, in this paper, molecular dynamics simulations are used to study the laminar flow of shear-thinning fluid in a microchannel. We validated the feasibility of our simulation method by evaluating the mean square displacement and Reynolds number of the solution layers. The results show that the change rule of the fluid system's velocity profile and interaction energy can reflect the shear-thinning characteristics of the fluids. The velocity profile resembles a top-hat shape, intensifying as the fluid's power law index decreases. The interaction energy between the wall and the fluid decreases gradually with increasing velocity, and a high concentration of non-Newtonian fluid reaches a plateau sooner. Moreover, the velocity profile of the fluid is related to the molecule number density distribution and their values are inversely proportional. By analyzing the radial distribution function, we found that the hydrogen bonds between solute and water molecules weaken with the increase in velocity. This observation offers an explanation for the shear-thinning phenomenon of the non-Newtonian flow from a micro perspective. [ABSTRACT FROM AUTHOR]

This paper studies a non-autonomous incompressible non-Newtonian fluid with delay in a 2D unbounded domain. The existence of pullback $ \mathcal{D} $ attractor with $ \mathbb{H}^2 $ regularity is obtained and its relationship with the pullback $ \mathcal{D} $ attractor with $ \mathbb{L}^2 $ regularity obtained in [25] is also shown. This fact exhibits the pullback smoothing effect of the fluid with delays. [ABSTRACT FROM AUTHOR]

This paper describes a theoretical framework and computational methods of a thin layer coating of a non-Newtonian polymeric material while it moves through a tiny space among two inverted rollers. Order of magnitude is accustomed to clarify the nondimensional forms of the governing equations. Semi-analytical solutions of pressure gradient, velocity profile and rate of the flow are acquired via optimal homotopy asymptotic method (OHAM). The graphical representation depicts the physical quantities of the effects of velocity profile ratio k and Weissenberg number We. It is observed that by increasing the values of k and We, velocity profile decreases while pressure distribution increases. [ABSTRACT FROM AUTHOR]

The study focuses on the flow characteristics with geometrical considerations utilizing electrical-conduct Non-Newtonian Fluid. The tubular concentric annulus is the geometry selected for the investigation. The electric-conductive Non-Newtonian Fluid is a character-wise two-constant Bingham model used in this study. The study also utilized geometry, the magnetohydrodynamic (MHD) effect, and the hall current. The employed system had the inner tube spinning and the outer tube stationary. Prandtl's assumptions of boundary layer principles are applied to solve the governing equations using the finite difference method for various fluid flow parameters, the Gauss-Elimination method to compute the results, and the MHD field and geometrical factors with hall current. This paper discusses fluid flow properties such as axial, radial, tangential velocities, and pressure distribution. Further, the mentioned above flow properties impact the heat transfer effect. This research details how flow parameters in the concentric tube flow process affect the development of heat transfer effects in the MHD field and hall current. [Display omitted] • The development of MHD flow and heat transport have been studied computationally. • The impact of Hall current and Magnetic effect on the flow field has been considered. • This work refers to the non-Newtonian fluid as a two-constant yield stress fluid model. • The heat transfer impact has been calculated using the fluid flow properties. • This work has been done using a variety of fluid and geometric factors. [ABSTRACT FROM AUTHOR]

This paper uses the Volume of Fluid (VOF) method to simulate a double Co-Flow microfluidic device that can produce double emulsions in both Newtonian (water) and non-Newtonian fluids. The simulation is 2D axisymmetric and involves three phases. A model is evaluated in this study to examine how the size and double emulsion's generation rate are impacted by factors such as phase velocity, viscosities, interfacial tension, and the rheological properties of non-Newtonian fluids. The model predicted the process of emulsification successfully in dripping and jetting regimes and predicted the impacts of phase velocity on the dimension and frequency of compound droplets. Increasing the flow rate of the inner phase causes the inner droplets to grow, while the outer droplet dimensions remain mostly unchanged. Vice versa, an increase in outer phase flow rate reduces compound droplet size. However, when the middle phase's flow rate is enhanced, the size of detached droplets in the inner and outer phases undergoes opposite changes, i.e., decreasing and increasing, respectively. The results showed that in non-Newtonian fluids, smaller droplets are formed compared to water, and the diameter of the double emulsions formed decreases with the rise in the viscosity at zero shear rate of the non-Newtonian fluid. • Double emulsion formation is studied in both Newtonian and non-Newtonian ambient fluids. • By adjusting phase flow rates in Newtonian and non-Newtonian fluids, the double emulsion characteristics can be readily tuned. • The results showed that in non-Newtonian fluids, smaller droplets are formed compared to Newtonian fluid. [ABSTRACT FROM AUTHOR]

We have generalized, in the current study, the results of research presented earlier with the aim of obtaining an approximate solution for the creeping, plane-parallel flow of viscoplastic non-Newtonian fluid where the focus is on the study of rivulet fluid flows on an inclined surface. Namely, profiles of velocity of flow have been considered to be given in the same form as previously (i.e., Gaussian-like, non-stationary solutions) but with a novel type of pressure field p. The latter has been chosen for solutions correlated explicitly with the critical maximal non-zero level of stress τs in the shared plane layer of rivulet flow, when it begins to move as viscous flow (therefore, we have considered here the purely non-Newtonian case of viscoplastic flow). Correlating phenomena such as the above stem from the equations of motion of viscoplastic non-Newtonian fluid considered along with the continuity equation. We have obtained a governing sub-system of two partial differential equations of the first order for two functions, p and τs. As a result, a set of new semi-analytical solutions are presented and graphically plotted. [ABSTRACT FROM AUTHOR]

As a pivotal prospective clean energy source, the secure and efficient extraction of natural gas hydrate has emerged as a forefront concern within the global oil drilling industry in recent years. In this study, a self-developed multiphase pump adapted to "gas-liquid-solid" three-phase mixing is used to extract natural gas hydrate slurries which have non-Newtonian characteristics. Prior research on pumps has primarily focused on water, introducing a significant disparity in handling slurries containing hydrates. This paper investigates the hydraulic performance and flow field variations of a multiphase pump using three different concentrations of Herschel-Bulkley non-Newtonian fluids that exhibit rheological properties similar to natural gas hydrate slurries. Additionally, a viscous Newtonian fluid with seawater as the liquid phase medium is studied for comparison. The results show that the shear-thinning properties of the non-Newtonian fluid improve the efficiency of the pump. However, excessive concentration negatively affects the hydraulic properties. The flow field characteristics such as apparent viscosity and turbulent kinetic energy are closely related to the pump structure and fluid properties. Compared with viscous Newtonian fluid, the non-Newtonian fluid's also have a greater effect on the distribution of gas-solid phases. [Display omitted] • Paper analyzes 'gas-liquid-solid' multiphase pump for transporting non-Newtonian fluids in gas hydrate exploitation, using experimental and numerical methods. • Non-Newtonian fluids enhance multiphase pump efficiency but concentrated ones may harm transportation efficiency. • Study compares internal flow in multiphase pump, analyzing viscosity, turbulent energy, and pressure during non-Newtonian and viscous Newtonian fluid transport. • Paper examines multiphase pump's hydraulic performance and internal flow with varying speeds during non-Newtonian fluid transport. [ABSTRACT FROM AUTHOR]

In this paper, we consider the first boundary value problem for a class of steady non-Newtonian micropolar fluid equations with heat convection in the three-dimensional smooth and bounded domain Ω. By using the fixed-point theorem and introducing a family of penalized problems, under the condition that the external force term and the vortex viscosity coefficient are appropriately small, the existence and uniqueness of strong solutions of the problem are obtained. [ABSTRACT FROM AUTHOR]

The hyperconcentrated fluid flow occurs as a result of heavy rainfall, during which a large amount of sediments from the upstream basin is washed away and suddenly increases the flow concentration of the alluvial channels. The stresses exerted by this type of fluid on the bed and body of the stream/river and related structures such as dam lead to the failure them and cause many human and financial losses. One of the important topics in the simulation of dam break caused by non-Newtonian fluid flow is the modeling of frictional stresses. In this research, after collecting several relationships to model the coefficient of friction loss of non-Newtonian fluid, a two-dimensional model was developed based on the numerical solution of shallow water equations in curvilinear coordinates to simulate hyperconcentrated flow. The results of the validation of the model were presented by comparing the measurement data of the suddenly complete dam break caused by the non-Newtonian fluid flow in the form of graphs, which all emphasize the accuracy of the developed model. It was also shown that for a suddenly complete dam break, with an increase in fluid volume concentration from 13.8 to 36.4%, the flow depth at the failure site increases by 18.8%. Next, asymmetric two-dimensional partial dam break of non-Newtonian fluid was simulated and compared with the results of Newtonian fluid. The results showed that the maximum flow velocity in the center of the fracture wall for the non-Newtonian fluid with a concentration of 32.2% is less than half of the maximum velocity of the Newtonian fluid. [ABSTRACT FROM AUTHOR]

In the current landscape of natural gas hydrate extraction, the lifting pump assumes a pivotal role as the essential equipment for conveying subsea fluidized hydrate slurry to the wellhead. The inherent shear-thinning characteristics of natural gas hydrate slurry, compounded by the complex multiphase flow conditions of the "gas-liquid-solid" system, present significant challenges to the operational efficiency and stability of the lifting pump. Consequently, this study adopts a hybrid approach, combining experimental and numerical simulations, to comparatively investigate the impact of non-Newtonian and viscous Newtonian fluids on the hydraulic performance, vortex structure evolution, and induced pressure fluctuations in a multiphase pump. Concurrently, a comparative analysis is conducted on the influence of these two fluid types on the distribution patterns of the "gas-solid" two-phase system. The research findings indicate that the apparent viscosity variations are more pronounced in the diffuser region compared to the impeller region. Under non-Newtonian fluid conditions, two separation vortices emerge at the trailing edge of the diffuser, as opposed to a single separation vortex in the viscous Newtonian fluid, with the latter exhibiting a smaller vortex structure scale. Moreover, the shear-thinning characteristics intensify the interaction between the separated vortex and the mainstream, resulting in an exacerbation of pressure fluctuations. In contrast to the viscous Newtonian fluid, the rotor–stator interaction and shear-thinning characteristics play a predominant role in pressure fluctuations, with shear-thinning attributes giving rise to low-frequency pressure fluctuations. Additionally, shear-thinning characteristics significantly influence the distribution behavior of the gas-solid two-phase flow. [ABSTRACT FROM AUTHOR]

We consider the micro- and the macro-scale to investigate the motion of single grains in a dilute suspension under shear flow and Poiseuille flow to analyze effects like shear-wall migration and rolling of grains as observed in physical experiments. To be able to simulate the behavior of fresh concrete or mud flow, as realistically as possible, we are taking into account a non-Newtonian Bingham–Papanastasiou rheology for the carrier fluid. Due to a surface coupled approach, Smoothed Particle Hydrodynamics (SPH) gives the opportunity to consider both, the motion of a solid particle, by tracking its center of mass and also surface points, and the interaction and influence on the near field of the velocity field in the fluid phase. We show an independence of the motion of solid grains from the surrounding carrier fluid. While the macroscopic flow reaches a stationary flow field quite fast, the motion of the solid grains still oscillates between parts of the fluid that flow with different velocities and does not show a stable steady state. Providing a comparison between the motion in a Newtonian and a non-Newtonian fluid, we point out the differences and thus the importance of the choice of the material model for the carrier fluid in numerical simulations. • SPH simulations of suspensions with Newtonian or non-Newtonian carrier fluid. • Detailed analysis of the motion of solid grains in a suspension on different scales. • Focus on the analysis of the near velocity field at the surface of solid grains. [Display omitted] [ABSTRACT FROM AUTHOR]

A study has been made of the flow of a non-Newtonian polymer medium in a plane channel and of heat transfer in it with boundary conditions of the first kind for small Reynolds numbers and a large Péclet number with the Ellis rheological model with a viscosity dependent on the temperature, pressure, and degree of chemical conversion of the medium. Consideration was given to the flow of a high-viscosity medium with chemical reactions leading to an abrupt increase in its viscosity for whose mathematical description the authors used a model that included the kinetic chemical-reaction equation and the energy equation with a dissipative term. Significant influence of various factors on the formation and rate of growth of the solidified wall layer in such flow has been shown. The problem has been solved numerically by the finite-diff erence method according to the iterative scheme. [ABSTRACT FROM AUTHOR]

This study aims to analyze the forces acting on the organs from the bolus during swallowing, excluding direct organ contact forces. We simulated the swallowing process of healthy individuals ingesting thickened non-Newtonian foods using a swallowing simulator based on the moving-particle simulation method. The force vectors acting on the organs and the bolus shape were extracted at each time interval. A twodimensional graph matrix was developed to visualize the temporal and spatial relationships between force and time for comprehensive interpretation and discussion. The graph matrix revealed that the bolus originated from tongue movement and was transferred between the oral cavity and pharynx, with coordinated movements of each organ occurring in pairs with balanced forces of the tongue and other organs. Information on the organ forces may offer a novel perspective for interpreting conventional mechanical indicators such as high-resolution manometry or tongue-pressure measurements. [ABSTRACT FROM AUTHOR]

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The present paper analyzes the Rabinowitsch fluid (RF) behavior on a pivoted curved slider with surface roughness (SR) with the aid of the perturbation technique. In order to account for the random roughness of the bearing surfaces, a stochastic random variable with a nonzero mean, variance, and skewness was taken into consideration. The averaged Reynolds equation (RE) was developed using a stochastic random variable. The load carrying capacity (LCC) and centre of pressure (COP) were obtained by solving the relevant stochastically averaged RE with appropriate boundary conditions. Bearing performance was observed to suffer as a result of transverse SR; nevertheless, the bearing system's efficiency can be increased in the case of negatively-skewed SR. It was demonstrated that, unlike a traditional lubricant, the bearing can withstand a LCC even in the absence of flow. The outcomes of the current paper can be helpful in various modern mathematical physics engineering applications. [ABSTRACT FROM AUTHOR]

Due to friction vibration dampers' inability to effectively dampen low loads during high-frequency dewatering, drum washing machines vibrated intensively. In order to address this problem, in this paper, a novel type of low-cost non-Newtonian fluid damper is proposed and investigated based on the non-Newtonian fluid shear thinning properties' effect on vibration suppression during the high-frequency dewatering process of the washing machine. In contrast to other commonly used dampers, the homemade non-Newtonian fluid damper significantly suppresses the growth trend of the apparent elastic coefficient at high frequencies. A systematic investigation of damper structural parameters reveals that smaller gap height, higher piston head number, and more viscous fluid viscosity are adequate for vibration suppression and noise reduction. These results demonstrate that the non-Newtonian fluid damper can produce an excellent vibration-damping effect for the entire washing process of the washing machine, especially for the high-frequency dewatering process. The acceleration attenuation ratio can reach up to 83.49%, the energy attenuation is up to 98.44%, and the noise reduction is up to 10.38 dB. [ABSTRACT FROM AUTHOR]

Multilayer fluid models play a crucial role in comprehending fluid-fluid and fluid-nanoparticle interactions within the petroleum industry, geophysics, and plasma physics due to their diverse industrial applications. The current research aims to investigate the impact of a heat source/sink on a non-Newtonian hybrid nanofluid that saturates a porous medium positioned between a transparent viscous fluid filling a vertical channel. The model governing nonlinear coupled differential equations are nondimensionalized using appropriate fundamental quantities. Subsequently, the regular perturbation method is employed to solve the transformed dimensionless governing equations. Upon comparing the data, it is evident that current results closely align with the previously published findings. The parameter Q2 causes an increase in both θs(ζ) and θt(ζ) across all three regions. Increasing Casson parameter leads to a decrease in θt(ζ). [ABSTRACT FROM AUTHOR]

This work attempted to conduct an experimental study which demonstrates the effect of the initial concentration of solute on the apparent viscosity of ice slurry in a horizontal circular pipe. The study was conducted on ice slurry based on propylene glycol, varying from 5 to 24% with different ice mass fractions varying from 5 to 25%. During the experiments, the initial concentration of the propylene glycol, ice concentration, and flow rate was modified as parameters. The flow tests were performed on laminar flows. The results of the investigation revealed that the ice slurry behaved like a non-Newtonian fluid, while it sometimes behaved like a Newtonian fluid. The rheological behavior of the ice slurry is reflected by its viscosity. For the shear-thickening behavior, the apparent viscosity increases with increasing the shear rate, and for the shear-thinning behavior, the viscosity decreases with increasing the shear rate, while for the Newtonian behavior, the viscosity remains almost constant. Then it was revealed that the viscosity of the mixture became too high for low shear rates at high ice mass fractions by increasing the concentration of the solute. The power law was used to establish a relationship between the apparent viscosity and the indexes of flow and consistency of ice slurry. [ABSTRACT FROM AUTHOR]

The undesirable presence of the gas bubbles negatively affects the expected properties (strength, molding and etc.) of a liquid polymer in some industrial products. Therefore, the development of the degassing methods is becoming an important industrial issue. The vibration is one of the most effective degassing approaches but still little researches have published in order to improve this method characters. The current study has investigated the rheological and thermophysical properties of a non-Newtonian polymer liquid in the bubble removal process to find the optimum properties of vibration. Therefore, a mathematical correlation has attained between the vibration and a non-Newtonian fluid properties. Also, the results show that in a viscoplastic fluid, the vibrational deflation ratio is slightly sensitive to the yield stress and by increasing the fluid surface tension from 0.03 to 0.07 N/m, the vibration bubble-desalination ratio increases by 10.6 times. As well as decreasing the fluid stability index from 0.30 to 0.50 results the increase in the bubbling ratio by 14.47%. However, by increasing the flow index from 0.30 to 0.50, due to the decrease in fluid thinning property, the final bubble velocity decreases by 48.27%. [ABSTRACT FROM AUTHOR]

We consider the Cauchy problem for coupled system of Vlasov and non-Newtonian fluid equations. We establish local well-posedness of the strong solutions, provided that the initial data are regular enough. [ABSTRACT FROM AUTHOR]

In this paper, we study the flow of a non-Newtonian fluid through a thin three-dimensional domain with an oscillating boundary. Starting from a nonlinear coupled system describing a non-isothermal regime of the flow, we rigorously derive three different effective models, depending on the period of the boundary roughness. We employ a homogenization technique based on the adaption of the unfolding method and deduce the roughness-induced effects on the fluid flow. [ABSTRACT FROM AUTHOR]

This paper numerically investigates mixed convective heat transfer in a vented square cavity incorporated with a baffle that is subjected to external non‐Newtonian fluids (NNFs). Adiabatic conditions are imposed on the top and bottom walls, while cold temperature conditions are applied to the right and left solid boundaries. Heated NNF enters the cavity through the inlet and goes out through the outlet at three different locations, and it passes on a vertical baffle fixed at the base placed at different lengths. To examine the impact of the inlet and outlet positions, three different shapes of the outlet port located on the right wall and the inlet port on the left bottom wall were investigated. The impacts of Reynolds number (Re) of 100 ≤ Re ≤ 1000, Richardson number (Ri) of 0.1 ≤ Ri ≤ 3, power law index (n) of 0.6 ≤ n ≤ 1.4, length of baffle (Lb) of 0.2 ≤ Lb ≤ 0.6 and the outlet hole positions (S) of 0≤S≤0.9 $0\le S\le 0.9$ on the thermal and flow distributions in the cavity are taken into consideration in this paper. The results demonstrated that the flow's intensity and heat transfer increase with improvement in the Re and n at any baffle length. When the Ri increased from 0.1 to 3, Nuavg $N{u}_{\mathrm{avg}}$ increased by 23.3% at n=0.6 $n=0.6$, and 13.8% at n=1.2 $n=1.2$. Also, the Ri increment results in the augmentation of the average heat transfer. [ABSTRACT FROM AUTHOR]

Non-Newtonian fluid flow in pipe bends is inevitable in industrial applications. Previous researchers have extensively explored Newtonian flow through curved ducts. However, the non-Newtonian counterpart gets little attention. We study the turbulent flow of shear-dependent fluids obeying the Power-Law model in a pipe manifold containing an in-plane double bend. Ostwald-de Waele's power law is used to model the fluid's rheology. We utilize computational fluid dynamics (CFD) to solve Reynolds-averaged Navier-Stokes (RANS) equations with the k-ε turbulence model. We validate our numerical results with previous experimental results. The in-plane double bend perturbs the flow in the pipe manifold to develop a Prandtl's secondary flow of the first kind. A fully developed flow at the bend upstream is disturbed due to the bend's curvature and regains its fully developed characteristics upon a certain downstream length after the exit of the bend. We study the rheological characteristics of the secondary flow within the bend and the evolution of fluid flow at the bend downstream. We demonstrate that the centrifugal force-dominated secondary flow increases with a decrease of the non-Newtonian power-law index. We capture the camel'sback-shaped velocity profiles within the bend due to accelerating-decelerating flow. The study reveals that the average flow velocity increases along the bend with a corresponding pressure head loss. We quantify this velocity rise by a newly introduced non-dimensional number, viz. enhancement ratio. The double bend's enhancement ratio decreases with an increase in n. [ABSTRACT FROM AUTHOR]

In this paper, we show that a weak solution for unsteady flows of 3D shear‐thinning fluids is strong under certain integrability assumptions about two components of the vorticity. In particular, if two components of the vorticity belong to the marginal critical space L1(0,T;BMO)$$ {L}^1\left(0,T; BMO\right) $$, then the solution is strong. [ABSTRACT FROM AUTHOR]

The work at hand studies thin-film flow instabilities in a non-Newtonian second-grade fluid moving over a stretching sheet. The analysis considers the free surface evolution equation of the thin second-grade viscoelastic fluid model based on the long-wave approximation method. We undertook a linear stability analysis using a normal mode approach and obtained expressions for the linear time growth rate, linear phase speed, and critical wavenumber, which illustrates the linear stability structure of the flow system. Furthermore, the multi-scale analysis of the fluid's weakly non-linear stability characteristics reveals the presence of subcritical instability in the linear stability zone. The study shows that the varying flow parameters affect the threshold amplitude, which influences the stable and unstable zones in the subcritical region. The outcomes show a stabilizing effect spanning the range of non-dimensional parameters, such as the second-grade parameter ranging from 0 to 100 in values, the surface tension parameter ranging from 0 to 100 in values, and the modified Froude number from 0 to 100 in values. [ABSTRACT FROM AUTHOR]

The variation of the classical viscous fingering instability is studied numerically in this work. An investigation of the viscous fingering phenomenon of immiscible displacement in the Hele–Shaw cell (HSC), where the displaced fluid is a shear-thinning fluid, was carried out numerically using the volume of fluid (VOF) method by adding a minor depth gradient or altering the geometry of the top plate in the HSC. The findings demonstrate how the presence of depth gradients can change the stability of the interface and offer a chance to regulate and adapt the fingering instability in response to the viscous fingering properties of air driving non-Newtonian fluids under various depth gradients. The relative breadth will shrink under the influence of the depth gradient, and the negative consequences of the gradient will be increasingly noticeable. Specifically, under different power-law indices, we found that with the enhancement of shear-thinning characteristics (lower power-law exponent n) in both positive and negative depth gradients, the fingers that protrude from the viscous fingers become shorter and thicker, resulting in higher displacement efficiency. Additionally, several modifications were performed to the upper plate's design, and the findings revealed that the shape had no effect on the viscous fingering and only had an impact on the longitudinal amplitude. Based on the aforementioned traits, we may alter the HSC's form or depth gradient to provide high-quality and effective work. [ABSTRACT FROM AUTHOR]

We present a Graphic Processing Units (GPU) implementation of non-Newtonian Hele-Shaw flow that models the displacement of Herschel-Bulkley fluids along narrow eccentric annuli. This flow is characteristic of many long-thin flows that require extensive calculation due to an inherent nonlinearity in the constitutive law. A common method of dealing with such flows is via an augmented Lagrangian algorithm, which is often painfully slow. Here we show that such algorithms, although involving slow iterations, can often be accelerated via parallel implementation on GPUs. Indeed, such algorithms explicitly solve the nonlinear aspects only locally on each mesh cell (or node), which makes them ideal candidates for GPUs. Combined with other advances, the optimized GPU implementation takes ≈ 2.5 % of the time of the original algorithm. [ABSTRACT FROM AUTHOR]

The measurement capabilities of a newly developed in‐situ rheometric device based on a single passive acoustic emission sensor and machine learning algorithms were investigated. Two surfactant structured fluids demonstrating complex non‐Newtonian rheology (Power‐law and Herschel‐Bulkley models) were examined. Furthermore, a static evaluation on the laboratory scale in comparison to dynamic processing on the pilot scale was conducted. The results indicate that the machine learning algorithms of this technology can identify, in > 90 % of scenarios, the correct type of rheology or the manufacturing process step across both scales. This identification is based on solving a classification problem using quadratic support vector machine learning algorithms, which have proven to deliver the most robust predictions across a choice of 24 different algorithms tested. Additionally, a new format of in situ rheology display was introduced, referred to as RRF™ factor. [ABSTRACT FROM AUTHOR]

Because of the ease with which oxide films form on its surfaces, stainless steel has strong corrosion resistance and excellent processing performance. Electrochemical machining (ECM) is a flexible process that can create microstructures on stainless steel (SS304); however, with traditional masked ECM, the efficiency and accuracy of microstructure machining are low. Proposed here is the use of a non-Newtonian fluid [polyacrylamide (PAM)] as the electrolyte. To date, there have been few papers on the electrochemical dissolution behavior of stainless-steel micromachining with a non-Newtonian fluid as the electrolyte. The aims of the study reported here were to investigate the electrochemical properties of SS304 with PAM and PAM–NaOH as electrolytes, and to explain their electrochemical corrosion mechanisms. The effects of different electrolytes were compared, and the polarization curves of SS304 in PAM and PAM–NaOH electrolyte solutions with different components were analyzed and compared with that in NaNO3 electrolyte. Then, the effects of the main processing parameters (pulse voltage, frequency, and duty ratio) on the machining performance were investigated in detail. A microhole array was obtained with a good quality comprising an average diameter of 330.11 µm, an average depth of 16.13 µm, and a depth-to-diameter ratio of 0.048. Using PAM to process microstructures on stainless-steel surfaces was shown to be feasible, and experiments indicated that the mixed electrolyte (PAM–NaOH) had not only the physical characteristics of a non-Newtonian fluid but also the advantages of a traditional electrolyte to dissolve processing products, and it effectively improved the processing accuracy of masked ECM for SS304. [ABSTRACT FROM AUTHOR]

Blood is a shear-thinning non-Newtonian fluid in which the viscosity reduces with the shear rate. When simulating arterial flow, it is well established that the non-Newtonian nature is important in the smallest vessels; however, there is no consistent view as to whether it is required in larger arteries, such as the carotid. Here, we investigate the importance of incorporating a non-Newtonian model when applying a plaque deposition model which is based on near-wall local haemodynamic markers: the time-averaged near wall velocity and the ratio of the oscillatory shear index to the wall shear stress. In both cases the plaque deposition was similar between the Newtonian and non-Newtonian simulations, with the observed differences being no more significant than the differences between the selected markers. More significant differences were observed in the haemodynamic properties in the stenosed region, the most significant being that lower levels of near-wall reverse flow were observed for a non-Newtonian fluid. [ABSTRACT FROM AUTHOR]

In most of practical situation multiple slips (velocity, temperature and concentration) has importance in manufacturing, medicinal, imaging processes and design of materials. In view of this, the present work considered the multiple slips on Magneto hydrodynamic (MHD) dissipative non-Newtonian fluid (Casson fluid) above a curved type of a stretching surface are studied. Multiple slips with Casson fluid have significance in controlling the blood flow distribution in human and animal bodies. The R–K fourth-order via shooting technique is used to convert the nonlinear governing equations. The impact of governing parameters is shown and explored graphically. The present investigation explores the multiple slip effects in governing equations under the influence of the magnetic field; the fluid's temperature and velocity have reverse characteristics. In a few unique situations, the current findings have been in reasonable agreement with the current results. As opposed to when viscous dissipation is absent, the temperature distribution is higher when viscous dissipation is present. It helps us to decide depending on the industrial and manufacturing processes, whether dissipation has to be applied or not. The stretching parameter enhances the Skin friction coefficient and rate of heat transfer, while decreases the rate of mass transfer. Also, the fluid's temperature decreases because an increase in Casson fluid parameter enhances the plastic dynamic viscosity, which creates resistance in the fluid motion. [ABSTRACT FROM AUTHOR]

This article concerns the dynamic transitions of a non‐Newtonian horizontal fluid layer with thermal and solute diffusion and in the presence of vertical magnetic field. First, a linear stability analysis is performed by deriving the principle of exchange of stability condition, which shows the system loses stability when the thermal Rayleigh number exceeds a threshold. Second, we consider the transition induced by real eigenvalues and complex eigenvalues, respectively, and two nonlinear transition theorems along with several transition numbers determining the transition types are obtained via the method of center manifold reduction. Finally, rigorous numerical computations are performed to offer examples of possible transition types. Our results show that both continuous and jump transitions can occur for certain parameters when the diffusivities from big to small are thermal, solute concentration and magnetic diffusion, but only continuous transition induced by real eigenvalues is observed when the diffusivities from big to small is the opposite of the previous case. [ABSTRACT FROM AUTHOR]

The control mechanism of the pressure drop and bubble size has a guiding significance for selecting the micropump, the pressure resistance design, and the precise control of the microfluidics. In this study, single-phase flows and gas-non-Newtonian fluid two-phase flows are studied in a microchannel containing curved structures. Sodium carboxymethyl cellulose solutions are used as the non-Newtonian fluids; water and nitrogen are used as Newtonian fluid and gas phases, respectively. The pressure drop and the bubble length are measured. The influences of operating conditions are discussed. The non-Newtonian properties of the solutions are found to affect the parameters measured significantly. The experimental results are compared with the existing models, and the fanning friction factor is used to evaluate the pressure drop. The two-phase flow pressure drop can be predicted by the Lockhart-Martinelli method with a newly developed C-coefficient as a function of the fluid characteristic parameters and microchannel structure parameters. The new correlation for two-phase pressure drop prediction has an error within 18%, smaller than existing models. A new prediction method for the dimensionless bubble length containing the two-phase friction multiplier is also given with an error of 16%. [Display omitted] • A novel microchannel containing curved structures was studied experimentally. • Empirical models for predicting pressure drop and bubble length were developed and compared with existing models. • The prediction accuracy of the pressure drop was improved by considering structural and non-Newtonian fluid parameters. • The prediction accuracy of the bubble length was improved by considering the influence of pressure drop. [ABSTRACT FROM AUTHOR]

Multi-layer fabrics are commonly used in ballistics shields with a lower bulletproof class to protect against pistol and revolver bullets. In order to additionally limit the dynamic deflection of the samples, layers reinforced with additional materials, including non-Newtonian fluids compacted by shear, are additionally used. Performing a wide range of tests in each case can be very problematic; therefore, there are many calculation methods that allow, with better or worse results, mapping of the behavior of the material in the case of impact loads. The search for simplified methods is very important in order to simplify the complexity of numerical fabric models while maintaining the accuracy of the results obtained. In this article, multi-layer composites were tested. Two samples were included in the elements subjected to shelling. In the first sample, the outer layers consisted of aramid fabrics in a laminate with a thermoplastic polymer matrix. The middle layer contained a non-Newtonian shear-thickening fluid enclosed in hexagonal (honeycomb) cells. The fluid was produced using polypropylene glycol and colloidal silica powder with a diameter of 14 µm in the proportions of 60/40. The backing plate was made using a 12-layer composite made of Twaron® para-aramid fabrics with a DCPD matrix—not yet used in a wide range of ballistics. Then, numerical simulations were carried out in the Abaqus/Explicit dynamic analysis. The Johnson–Cook constitutive strength model was used to describe the behavior of elastic–plastic materials constituting the elements of the projectiles. For the non-Newtonian fluid, a Up-Us EOS was used. The inner layers of the fabric were treated as an orthotropic material. Complete homogenization of the sample layers was carried out, thanks to which each layer was treated as a homogeneous continuum. As a parameter of fracture mechanics for shield components, the strain criterion was used with the smooth particles hydrodynamics method (SPH). Then, the results of simulations were compared with the results of the ballistic test for both samples placed next to each other, which resulted in the formation of a multi-layer composite in one ballistic test subjected to impact loads during firing with a 9 × 19 mm Parabellum FMJ projectile with an initial velocity of 370 ± 10 m/s. The results of numerical tests are very similar to the ballistic tests, which indicates the correct mapping of the process and the correct conduct of layer homogenization. The applied proportions of the components in the non-Newtonian fluid allowed a reduction in the deflection compared to previous studies. Additionally, the proposal to use a DCPD matrix allowed to obtain a much lower deflection value compared to other materials, which is a novelty in the field of production of ballistic shields. [ABSTRACT FROM AUTHOR]

This study compared the behavior of food boluses describing Newtonian and non-Newtonian fluids through a validated human swallowing simulator based on moving particle simulation. The simulation was qualitatively and quantitatively validated through comparisons with videofluorography images. The positions and configurations of the food boluses and normalized brightness of the simulated and videofluorography images during every timestep were similar, and we thought that the simulator can be used to study the mechanism of food bolus behavior. The validated swallowing simulator results show that the key factors for the optimal design of the thickener are the control of the bolus inflow velocity, which is influenced by rheological and tribological properties, prevention of small splash particles, and bolus discharge flow rate from the epiglottis to the esophagus. In addition, we propose an evaluation index for the degree of bolus coherence based on the bolus flow rate and velocity. [ABSTRACT FROM AUTHOR]

Two‐phase flow involving non‐Newtonian fluids in fractured media is of vital importance in many natural processes and subsurface engineering applications, such as rock grouting, groundwater remediation, and enhanced oil recovery. Yet, how the displacement dynamics is impacted by the non‐Newtonian rheology remains an open question. Here, we conduct primary drainage experiments in which a shear‐thinning Xanthan gum solution displaces a silicone oil in a transparent rough fracture for a wide range of shear‐thinning property (controlled by polymer concentration) and flow rates. We first evaluate the effects of shear‐thinning property on displacement efficiency. Based on qualitative and quantitative analyses of the observed fluid morphologies, we present an experimental phase diagram of the obtained displacement patterns. We characterize a novel displacement pattern where the fluid‐fluid interface changes from stable (plug flow) to unstable (fingering) as the fracture aperture, averaged over the transverse direction, varies along the mean flow direction. We demonstrate that the existence of this mixed displacement pattern can be explained by local viscosity heterogeneity induced by the coupling of the shear‐thinning behavior and the spatial variability of apertures. Finally, we propose a theoretical model elucidating the mechanisms behind the flow regime transitions. The interface stability criterion predicted by this model exhibits good agreement with the experimental measurements, and stresses the potentially important role of fluid rheology, coupled to aperture variability, in immiscible displacements in rough fractures. These findings provide new insights into the dynamics of immiscible two‐phase flows with non‐Newtonian effects, and has potential implications for the aforementioned engineering applications. Key Points: We conduct drainage experiments in which a shear‐thinning fluid displaces a Newtonian fluid in a transparent rough fractureWe present an experimental phase diagram of displacement patterns in the space of flow rate and shear‐thinning rheological propertyWe propose a theoretical model of stability criterion and elucidate the mechanisms behind the flow regime transitions [ABSTRACT FROM AUTHOR]

In the present work, a modified numerical model was developed to simulate the water flow during a dam break with the mud layer transfer of different heights, consisting of three phases (water, air, and a phase for deposition). To carry out a numerical simulation of this process, a mathematical model based on the VOF (volume of fluid) method was modified, taking into account the movement of the water-free surface, which is carried out by the movement of water flow based on the Newtonian fluid model, and the movement of mud impurities is based on the non-Newtonian fluid model. Validation of the constructed model for the influence of three-dimensional features of the flow on morphological changes is carried out by a modified mathematical model and compared with the results of calculation for two-dimensional (2D) and three-dimensional (3D) models. The proposed method for modeling is applied on a real complex terrain, which was based on the Kargalinka – a river in Almaty and the Almaty region of Kazakhstan, the right tributary of the Kaskelen River. Simulation analysis is carried out for cases with different deposit heights. All results of the numerical simulation can be visually viewed using graphs and illustrations. [ABSTRACT FROM AUTHOR]