Showing papers on "Herschel–Bulkley fluid published in 2022"

Two-phase flow of couple stress fluid thermally effected slip boundary conditions: Numerical analysis with variable liquids properties

Abstract: The study of multiphase flows has earned much attention from researchers due to its numerous applications in mechanics and industry such as sewage management, synthetic fabrication, electricity generation, and medication processes. In the present work, we examined the Poiseuille flow of a couple stress fluid between parallel plates in presence of velocity and temperature slip boundary conditions. The effects of thermal conductivity and thermal radiations, variable viscosity, and non-uniform magnetic field on velocity and temperature fields in the existence of hafnium nanoparticles are also investigated. The temperature-dependent viscosity model, namely, Vogel’s model is utilized. The non-linear system of equations is solved numerically by using the shooting technique due to its fast convergence and prosperity to initial approximation. It is examined that the velocity slip parameter speeds up the flow rate of fluid but decelerated the temperature field while the temperature slip parameter upsurges the temperature of the fluid. It is also investigated that the concentration of nanoparticles enhanced both the velocity and temperature of the fluid. Further, the comparison of Newtonian and non-Newtonian (Couple stress fluid) is expressed with the help of graphs. To check the validation of results, a comparison with previous literature is also presented.

Numerical simulation of pressure profile of mining backfill fly-ash slurry in an L-shaped pipe using a validated Herschel-Bulkley model

Abstract: The study of pressure loss along pipelines during slurry transportation has become a core research concern. However, the simulation research on non-Newtonian flows in mining backfill operations is limited. In this study, a validated Herschel-Bulkley model is deployed to simulate and quantify the pressure evolution and flow characteristics of backfilling slurry inside an L-shaped pipe, showing that both the total and dynamic pressures decrease gradually from the central region to the layers close to the pipe walls. Through a numerical analysis, this paper introduces an unprecedented pressure loss calculation formula simultaneously taking into consideration, both the pipe diameter and the slurry flow velocity.

Effect of magnetic field on newtonian fluid sandwiched between non-newtonian fluids through porous cylindrical shells

Abstract: The present work deals with the influence of magnetic field on Newtonian fluid sandwiched between two porous cylindrical pipes which are filled with micropolar fluids. Fluid motion is occurring along the z*-axis and an applied magnetic field is taken in the direction perpendicular to the direction of fluid motion. On applying appropriate boundary conditions, velocity profiles, microrotations, flow rate, and shear stresses are obtained for the corresponding fluid regions. The graphs for volumetric flow rate and fluid velocity are plotted and discussed for different values of micropolar parameter, couple stress parameter, porosity, viscosity ratio parameter, Hartmann number, conductivity ratio parameters, and Darcy numbers.

Channel flows of shear-thinning fluids that mimic the mechanical response of a Bingham fluid

Abstract: The linear stability of channel flows driven by pressure drops is carried out for fluids that exhibit a yield stress, the mechanical response of which is prescribed by the Bingham constitutive relation or two of its regularizations: the model due to Allouche and co-workers that is usually referred to as the “simple model”, and Papanastasiou model. Despite the fact that these two regularized models provide a good approximation of the steady Poiseuille flow of a Bingham fluid, they fail to predict the stability characteristics of the exact Bingham model. The critical thresholds for the onset of turbulence predicted by using the simple and Papanastasiou models are essentially the same, but they differ significantly from that of the exact Bingham model. This discrepancy is shown to be due to the absence of energy dissipation in the rigid core of a Bingham fluid. • We investigate the 1D motion of Bingham fluid. • We also study the 1D flow for constitutive models that approximate the Bingham model. • We study the linear stability of the Bingham and regularized flows. • We show that the critical conditions of the regularized models do not converge to those of the Bingham fluid. • We prove that if one does not consider the unyielded part of the flow convergence is obtained.

Channel flows of shear-thinning fluids that mimic the mechanical response of a Bingham fluid

Abstract: The linear stability of channel flows driven by pressure drops is carried out for fluids that exhibit a yield stress, the mechanical response of which is prescribed by the Bingham constitutive relation or two of its regularizations: the model due to Allouche and co-workers that is usually referred to as the “simple model”, and Papanastasiou model. Despite the fact that these two regularized models provide a good approximation of the steady Poiseuille flow of a Bingham fluid, they fail to predict the stability characteristics of the exact Bingham model. The critical thresholds for the onset of turbulence predicted by using the simple and Papanastasiou models are essentially the same, but they differ significantly from that of the exact Bingham model. This discrepancy is shown to be due to the absence of energy dissipation in the rigid core of a Bingham fluid.

Solute dispersion in non-Newtonian fluids flow through small blood vessels: A varying viscosity approach

Abstract: Present work concerns the combined effect of Jeffrey fluid parameter and varying nature of viscosity on the solute dispersion in non-Newtonian fluids flow through small blood vessels. The generalized dispersion model of Sankarasubramanian and Gill (1973) has been considered. The objective of the present work is to understand the solute dispersion in non-Newtonian fluids flow through microvessels with absorbing walls under varying viscosity assumption. For more realistic modeling of blood flow in microvessels, Jeffrey and Herschel–Bulkley fluids model have been considered for a comparative study due to its low shear rate flow in small blood vessels such as arterioles, venules and capillaries. The whole solute dispersion analysis has been done for two alternative non-Newtonian fluids (Herschel–Bulkley and Jeffrey fluids) owing to their physiological importance. The present model has been validated by reducing it to previously studied specific cases of Newtonian, Bingham-plastic and Power-law fluids with constant/varying viscosities. It is perceived that the mean concentration, convection and axial dispersion coefficients are significantly affected by varying viscosity and Jeffrey fluid parameters. A noteworthy observation is that an increase in ratio of relaxation to retardation times (Jeffrey fluid parameter) enhanced the values of the transport coefficients. The outcome of the present study shows the diffusion of drugs to the physiological system through small blood vessels is significantly affected by the varying nature of viscosity and Jeffrey fluid parameters.

Rheological impact of Sutterby fluid in isothermal forward roll coating process: a theoretical study

Abstract: In this paper, the incompressible and isothermal flow of Sutterby fluid is investigated during the forward roll coating process. The mass and momentum equations are non-dimensionalized and simplified using lubrication approximation theory (LAT). Perturbative results are obtained for the velocity, pressure gradient, flow rate, and shear stress, while coating thickness, maximum pressure, separating point, roll separating force and roll-transmitted power are found by Simpson’s 3/8 rule. Outcomes exhibit that velocity, pressure gradient and coating thickness are substantially influenced by the non-Newtonian fluid parameter, which may increase the coating efficiency. Also, power input and roll separating force is directly proportional to the non-Newtonian parameter.

Different methods for determining the yield stress of ferrofluids

Abstract: The yield stress of ferrofluids has been a hot topic in their rheological studies, and it is still controversial which method could obtain the more accurate yield stress value. In this work, we used varieties of methods to obtain the yield stress of the ferrofluid, including steady shear and oscillatory shear. We obtained the static yield stress and dynamic yield stress of the ferrofluid by Herschel–Bulkley fitting of the flow curves measured by the controlled shear rate mode and the controlled shear stress mode, and found that at any magnetic field strength, the static yield stress was always significantly greater than the dynamic yield stress. We then performed oscillatory shear of the ferrofluid and determined the yield stress using three methods, where the yield stress value corresponding to the intersection of the storage modulus G′ and the loss modulus G″ is similar to the static yield stress value fitted by H-B at low magnetic field strength. The power law function and shear stress as a function of shear strain consistently gave the maximum value of the yield stress. Ultimately, we believe that which method is ultimately chosen depends on the practical application conditions of interest.

From breakup to coiling and buckling regimes in buoyant viscoplastic injections

Abstract: Abstract We study the injection flow of a heavy viscoplastic fluid into a light Newtonian fluid, via modelling and experiments. The injection is carried out downward, via an eccentric inner pipe inside a vertical closed-end outer pipe. This configuration results in a core viscoplastic fluid surrounded by an annular Newtonian fluid. The flow is structured and mixing is negligible. As the injection rate increases in a typical experiment, we observe three distinct flow regimes, associated with the core fluid behaviour, namely the breakup, coiling and buckling (bulging) regimes. In the breakup regime, the core fluid is yielded due to the extension caused by buoyancy, while in the buckling regime the yielding occurs due to the compression promoted by the pressure and the interfacial shear stress applied by the upward flow of the annular fluid. For the coiling regime, the core fluid remains largely unyielded until it exhibits a coiling behaviour. We develop a lubrication approximation model, using the Herschel–Bulkley constitutive equation, with dimensionless flow parameters including the Bingham number, the power-law index, the buoyancy number, the viscosity ratio, the diameter ratio, the eccentricity and the aspect ratio. Based on a reasonable prediction to the yielding onset, the model allows us to classify the flow regimes versus an elegant combination of the dimensionless numbers.

Experimental study on the entry of solid spheres into Newtonian and non-Newtonian fluids

Abstract: This study experimentally investigates the entry of hydrophobic/hydrophilic spheres into Newtonian and Boger fluids. By considering solution of 82% glycerin and 18% water and solution of 80% glycerin, 20% water and 100 ppm polyacrylamide, Newtonian and Boger fluids are made, respectively. It has been tried that liquids' surface tension, density, and viscosity are almost the same. Thus, all dimensionless numbers are approximately the same at a similar impact velocity except for the elasticity number. A PcoDimaxS highspeed camera captures the spheres' trajectory from the impact to the end of the path. Regarding the range of released height ([Formula: see text]), the impact velocities are approximately in the range of [Formula: see text]. The role of fluid elasticity in combination with the sphere surface wettability on the air cavity formation/evolution/collapse is mainly studied. Also, the kinetics of the sphere motion (velocity, acceleration, and hydrodynamic force coefficient) is studied. The results show that air drawn due to the sphere's impact with the Newtonian liquid is more, and the pinch-off takes place later. Also, shedding bubbles are cusped-shaped in the Boger fluid, while in the Newtonian fluid, they are elliptical. In addition, the most significant impact of surface wettability is observed in the Newtonian fluid. Finally, the results reveal that the sphere in the Newtonian fluid can move faster and travel a longer distance in a specific time interval. The differences observed are closely related to the viscoelastic fluid's elasticity property and extensional viscosity.

Locomotion with a wavy cylindrical filament in a yield-stress fluid

Abstract: Abstract A yield stress is added to Taylor's (1952, Proc. Royal Soc. A, 211, 225-239) model of a microscopic organism with a wavy cylindrical tail swimming through a viscous fluid. Viscoplastic slender-body theory is employed for the task, generalising existing results for Bingham fluid to the Herschel–Bulkley constitutive model. Numerical solutions are provided over a range of the two key parameters of the problem: the wave amplitude relative to the wavelength, and a Bingham number which describes the strength of the yield stress. Numerical solutions are supplemented with discussions of various limits of the problem in which analytical progress is possible. If the wave amplitude is sufficiently small, the yield stress of the material inevitably dominates the flow; the resulting ‘plastic locomotion’ results in swimming speeds that depend strongly on the swimming gait, and can, in some cases, even be negative. Conversely, when the yield stress is large, swimming becomes possible at the wave speed, with the swimmer sliding or burrowing along its centreline with a relatively high efficiency.

Stability criteria and convective mass transfer from the falling spherical drops, part <scp>II</scp> : <scp>Herschel–Bulkley</scp> fluids

Abstract: The combined effects of yield stress, shear-thinning, and shear-thickening fluid behaviour are investigated when a drop is falling in a Herschel–Bulkley fluid. The constitutive relation for Herschel–Bulkley fluids is regularized using the Papanastasiou regularization method. The governing partial differential equations for mass, momentum, and species transport are solved spanning a wide range of dimensionless numbers as Reynolds number, 1 ≤ Re ≤ 150; Schmidt number (10); Bingham number, 0 ≤ Bn ≤ 50; viscosity ratio (0.1 and 10); and power-law index, 0.4 ≤ n ≤ 1.6. The velocity field and mass transfer characteristics are expressed using streamlines, velocity contours, concentration contours, and sheared and un-sheared regions, while the surface averaged gross engineering quantities are described as a drag coefficient, yield-stress parameter, and Sherwood number. All else being equal, sheared regions in shear-thinning fluids are observed to be larger with respect to the shear-thickening fluids at finite Reynolds numbers. In the fully plastic flow limit, the yield stress effects dominate in the flow field, and therefore, the critical yield-stress parameter is observed to be independent of shear-thinning and shear-thickening fluid behaviours. However, in the viscoplastic limit (finite Bingham number), shear-thinning fluid always requires a larger value of yield stress to be static in the fluid with reference to shear-thickening fluids. The new set of dimensionless parameters are defined based on the effective viscosity scales, and the predictive correlations are put forward for both drag coefficient and Sherwood number.

Fractal Analysis of a Non-Newtonian Fluid Flow in a Rough-Walled Pipe

Abstract: The fully developed laminar flow of a viscous non-Newtonian fluid in a rough-walled pipe is considered. The fluid rheology is described by the power–law model (covering shear thinning, Newtonian, and shear thickening fluids). The rough surface of the pipe is considered to be fractal, and the surface roughness is measured using surface fractal dimensions. The main focus of this study lies in the theoretical investigation of the influence of the pipe surface roughness on the velocity profile and the Darcy friction factor of an incompressible non-Newtonian fluid. The plotted results demonstrate that shear thinning fluids are the most sensitive to the surface roughness compared with Newtonian and shear thickening fluids. For a particular value of the surface fractal dimension, there exists an intersection point where shear thinning, Newtonian, and shear thickening fluids behave the same way regarding the amplitude of the velocity profile and the friction factor. This approach has a variety of potential applications, for instance fluid dynamics in hydrology, blood flow in the cardiovascular system, and many industrial applications.

Modeling of Electrorheological Fluids

Abstract: In the absence of the electric field, a suspension called electrorheological (ER) fluid exhibits rheological properties similar to those of Newtonian fluids, but in the presence of an external electric field, the suspension changes to a Bingham fluid (yield flow) state exhibiting a pronounced yield stress which increases with the electric field strength. To evaluate the yield stress values from the ER flow measurements, a suitable constitutive equation is required. Different rheological models are compared to distinguish between a static yield stress from a dynamic yield stress and to describe the flow behavior. In addition, a master curve describing the apparent viscosity as a function of the shear rate was obtained by appropriate scaling of both axes. A new scaling function for the normalized yield stress versus the applied electric field strengths demonstrates its capability of modeling the yield stress behavior of ER fluids through the full range of electric fields.

Analysis of a Two-Fluid Taylor–Couette Flow with One Non-Newtonian Fluid

Abstract: Abstract We study the dynamic behaviour of two viscous fluid films confined between two concentric cylinders rotating at a small relative velocity. It is assumed that the fluids are immiscible and that the volume of the outer fluid film is large compared to the volume of the inner one. Moreover, while the outer fluid is considered to have constant viscosity, the rheological behaviour of the inner thin film is determined by a strain-dependent power-law. Starting from a Navier–Stokes system, we formally derive evolution equations for the interface separating the two fluids. Two competing effects drive the dynamics of the interface, namely the surface tension and the shear stresses induced by the rotation of the cylinders. When the two effects are comparable, the solutions behave, for large times, as in the Newtonian regime. We also study the regime in which the surface tension effects dominate the stresses induced by the rotation of the cylinders. In this case, we prove local existence of positive weak solutions both for shear-thinning and shear-thickening fluids. In the latter case, we show that interfaces which are initially close to a circle converge to a circle in finite time and keep that shape for later times.

Flow of a Self-Similar Non-Newtonian Fluid Using Fractal Dimensions

Abstract: In this paper, the study of the fully developed flow of a self-similar (fractal) power-law fluid is presented. The rheological way of behaving of the fluid is modeled utilizing the Ostwald–de Waele relationship (covering shear-thinning, Newtonian and shear-thickening fluids). A self-similar (fractal) fluid is depicted as a continuum in a noninteger dimensional space. Involving vector calculus for the instance of a noninteger dimensional space, we determine an analytical solution of the Cauchy equation for the instance of a non-Newtonian self-similar fluid flow in a cylindrical pipe. The plot of the velocity profile obtained shows that the rheological behavior of a non-Newtonian power-law fluid is essentially impacted by its self-similar structure. A self-similar shear thinning fluid and a self-similar Newtonian fluid take on a shear-thickening way of behaving, and a self-similar shear-thickening fluid becomes more shear thickening. This approach has many useful applications in industry, for the investigation of blood flow and fractal fluid hydrology.