non-Newtonian Power-law Fluid Research Articles

Modelling Flow and Mixing in the Proximal Small Intestine.

The small intestine is the primary site of enzymatic digestion and nutrient absorption in humans. Intestinal contractions facilitate digesta mixing, transport and contact with the absorptive surfaces. These motility patterns are regulated by an underlying electrical activity, termed slow waves. In this study, we use computational fluid dynamics simulation of flow and mixing of intestinal contents in the human duodenum with anatomically realistic geometry and contraction patterns. Parameters including the amplitude of contraction (10-50% reduction of radius) and the rheology of the digesta (Newtonian vs Non-Newtonian power law fluid) were altered in-order to study their effects on mixing. Interesting flow features such as stagnation points and reversed flow were observed with digesta. Increases in the amplitude of contraction lead to increased propulsion of digesta along the intestine and increased mixing.

Analysis of power consumption for gas dispersion in non-Newtonian fluids with a coaxial mixer: New correlations for Reynolds and power numbers

Coaxial mixers are efficient in mixing of highly viscous fluids. The main objective of this study was to assess the power consumption for the gas dispersion in carboxymethyl cellulose solution, a power-law non-Newtonian fluid, with a coaxial mixer consisting of an anchor impeller and two central impellers as a function of the speed ratio (central impeller speed/anchor speed), fluid rheology, pumping direction of the central impeller, and the rotation mode (co-rotating vs. counter-rotating). This goal was achieved using both experimental and numerical approaches. A computational fluid dynamic model (CFD) was developed and validated using the experimental data. Electrical resistance tomography (ERT) was employed to measure the gas holdup. New equivalent impeller speed and diameter were defined and two novel correlations for the Power number and Reynolds number were proposed and successfully validated at different operating conditions. Additionally, new dimensionless correlations for the ratio of the gassed to un-gassed power consumption and the aerated power number as a function of the flow number, Froude number, and Reynolds number were developed and successfully tested for different coaxial mixing configurations.

Modeling of Newtonian droplet formation in power-law non-Newtonian fluids in a flow-focusing device

Droplet formation in a flow-focusing device was modeled using the open source CFD package, OpenFOAM, with the VOF model for two-phase flow. Predictions using the interFoam solver and a power-law non-Newtonian model were first validated against experimental data in the literature. Then, the formation of Newtonian fluid droplets in power-law fluids was modeled during tubing, squeezing, dripping and jetting. The effects of the continuous phase rheological parameters on the droplet formation were investigated by changing the power law index (n) and the consistency coefficient (K). The results show that the droplet length and the spacing between two droplets decrease as n or K increase. However, the formation frequency and droplet velocity in the main channel increase as n or K increase. The results also show that n has a greater effect than K on the droplet formation. A method was developed to calculate the capillary number of the power-law continuous phase in the squeezing and dripping regimes including the influences of n and K. For a given dispersed phase flow rate, the formation frequency is inversely proportional to the droplet volume. A scaling law was also developed to predict the formation frequency since the droplet volume is found to vary linearly with the non-dimensional droplet length. The present work is useful for controlling droplet formation and designing microfluidic devices in areas where non-Newtonian fluids are used as the continuous phase.

Enhanced Electro-Osmotic Flow of Power-Law Fluids in Hydrophilic Patterned Nanochannel

Abstract In this paper, electro-osmotic flow (EOF) enhancement of non-Newtonian power-law fluids in a modulated nanochannel with polarized wall is proposed. The channel walls are embedded with periodically arranged rectangular grooves, placed vertically with the direction of electric field. The key aspect of the present study is to achieve enhanced EOF of power-law fluids due to periodic groove patterns. The flow characteristics are studied through Poisson–Nernst–Plank-based Navier–Stokes model associated with electrochemical boundary conditions. Some random-phase differences between the grooves in both the walls are allowed to find the best configuration for the EOF enhancement in case of both Pseudo-plastic fluid, Dilatant fluid, and compared to Newtonian fluid. A notable enhancement factor is observed when groove width is much larger than its depth along with overlapped EDL. It is also found that EOF enhancement for shear-thinning fluid is quite better than the other fluids, for the same set of physical parameters. A comparison of enhancement factor for power-law fluid is also presented when the grooves are replaced with hydrophobic strips. It is worth to mention here that the present study assumes no-slip condition which is true for wetting (hydrophilic) surface over nonwetting (hydrophobic) strips which is common occurrence in regards to nanoconfinements.

Hydrodynamic flow of non-Newtonian power-law fluid past a moving wedge or a stretching sheet: a unified computational approach

A unified mathematical equation that combines two different boundary-layer flows of viscous and incompressible Ostwald-de Waele fluid is derived and studied. The motion of the mainstream and the wedge is approximated in the power-law manner, i.e, in terms of the power of the distance from the leading boundary-layer edge. It is also considered that the wedge can move in the same and opposite direction to that of the mainstream. The governing partial differential equations are transformed into the nonlinear ordinary differential equation using a new set of similarity variables. This transformed equation subjected to the boundary conditions describing the flow is then solved using the Chebyshev collocation method. Further, these numerical results are then validated by determining the flow behaviour at far-field by performing asymptotics. The velocity ratio parameter effectively captures and distinguishes two boundary-layer flows. The boundary layer thickness for shear-thinning fluid is thinner compared to corresponding parameters for shear-thickening fluids and is markedly separated by the Newtonian fluid. Further, the boundary-layer flow of the non-Newtonian fluid predicts an infinite viscosity for shear-thinning fluid quite away from the surface. The hydrodynamics of the obtained results is explained thoroughly.

Computational study on MHD power-law fluid in tilted enclosure having sinusoidal heated sidewall

PurposeIn the present computational study, the heat transfer and two-dimensional natural convection flow of non-Newtonian power-law fluid in a tilted rectangular enclosure is examined. The left wall of enclosure is subjected to spatially varying sinusoidal temperature distribution and right wall is cooled isothermally while the upper and lower walls are retained to be adiabatic. The flow is considered to be laminar, steady and incompressible under the influence of magnetic field. The governing mass, momentum and energy equations are transformed into dimensionless form in terms of stream function, vorticity and temperature.Design/methodology/approachThen resulted highly non-linear partial differential equations are solved computationally using Galerkin finite element method.FindingsThe exhaustive flow pattern and temperature fields are displayed through streamlines and isotherm contours for various parameters, namely, Prandtl number, Rayleigh number, Hartmann number by considering different power-law index and inclination angle. The effect of inclination angle on average Nusselt number is also shown graphically. This problem observes the potential vortex flow with elliptical core. The results show that the circular strength of the vortex formed reduces as the magnetic field strength grows. As the inclination angle increases the intensity of flow field decreases while the value of average Nusselt number increases.Originality/valueThis study has important applications in thermal management such as cooling techniques used in buildings, nuclear reactors, heat exchangers and power generators.

Natural convection and radiation heat transfer of power-law fluid food in symmetrical open containers

In order to avoid insufficient sterilization caused by uneven heating and nutrition loss generated by excessive heating, researchers and scientists have focused on the topics of controllable heat transfer and predictable temperature fields in food processing. In this paper, the temperature distribution of power-law liquid food under the combination impacts of the thermal radiation and natural convection is studied by the numerical technique. Three kinds of open symmetrical heating containers commonly used are paid attention to, and the height and cross-sectional area of containers are set to equal for the convenience of comparing the effect of the container geometry on the temperature fields. The governing equations are treated in a dimensionless way as well as the boundary conditions. The finite element method is used to obtain the solutions, which has been proved robust and accurate. It has been displayed that the temperatures in the cylindrical container (i.e., the noodle bowl) are the highest, which proves its best heating effect. The liquids of egg yolk and egg white are adopted as special cases of non-Newtonian power-law fluids. The temperature fields of egg yolk and egg white are less affected by the generalized Grashof number than the thermal radiation number NR. The technique of adjusting the generalized Grashof number and the thermal radiation to control the heat transfer behavior applied in the present research could be extended to related food engineering applications.

Buoyant rise of anorthosite from a layered basic complex triggered by Rayleigh-Taylor instability: Insights from a numerical modeling study

AbstractA major unsolved problem of the Proterozoic is the genesis and tectonic evolution of the massif type anorthosites. The idea of large-scale floating of plagioclase crystals in a basaltic magma chamber eventually generating massif type anorthosite diapirs from the floatation cumulates is not supported by observations of the major layered basic complexes of Proterozoic to Eocene age. In this paper, we test and propose a new genetic process of anorthosite diapirism through Rayleigh-Taylor instability. We have carried out a numerical modeling study of parallel, horizontal, multiple layers of norite and anorthosite, in a model layered basic complex, behaving like Newtonian or non-Newtonian power law fluids in a jelly sandwich model of the continental lithosphere. We have shown that in this pressure-temperature-rheology configuration the model lithosphere generates Rayleigh-Taylor instability, which triggers diapirism of the anorthosite. In our model, the anorthosite diapirs buoyantly rise through stages of simple, symmetrical upwelling and pronounced bulbous growth to a full-blown mushroom-like form. This is the growth path of diapirs in nearly all analog and numerical previous studies on diapirism. Our anorthosite diapirs fully conform to this path. Furthermore, we demonstrate that the progressive diapirism brings in striking internal changes within the diapir itself. In the process, the lowermost anorthosite layer rises displacing the upper norite and anorthosite layers as progressively stretched and isolated segments driven to the margin of the rising diapir—a feature commonly seen in natural anorthosite massifs. We propose that a large plume-generated basaltic magma chamber may be ponded at the viscous lower crust or ductile-plastic upper mantle or further down in the weaker mantle of the jelly sandwich type continental lithosphere. The magma may cool and crystallize very slowly and resolve into a thick-layered basic complex with anorthosite layers. Rheologically behaving like Newtonian or non-Newtonian power law fluids, the layers of the basic complex with built-in density inversions would generate RT (Rayleigh-Taylor) instability. The RT instability would trigger a buoyant rise of the unstable anorthosite from the layered complex. The upward driven anorthosite, accumulated as anorthosite plutons, would gradually ascend across the lower and middle crust as anorthosite diapirs.

Effect of Horizontal Spacing on Natural Convection to Power-Law Fluids from Two Horizontally Aligned Cylinders

This paper expounds the effect of horizontal spacing between two horizontally aligned circular cylinders on laminar natural convection to non-Newtonian power-law fluids. Numerical computations have been carried out for the following range of conditions: Grashof number (10 to 105), Prandtl number (0.71 to 100), horizontal spacing (0 to 20 times the cylinder diameter), and power-law index (0.4 to 1.6). The flow, pressure, and thermal fields are pictorially visualized in terms of streamlines, pressure contours, and temperature contours, respectively. The average Nusselt number shows a positive reliance on both Grashof and Prandtl numbers, whereas an adverse dependence is observed on power-law index. Irrespective of all other parameters, shear-thinning fluid behavior is seen to promote the convection, whereas shear-thickening behavior impedes it with reference to the Newtonian fluid. With decrease in the horizontal spacing, the average Nusselt number increases and attains a maximum value corresponding to the optimal spacing, however, it diminishes greatly with further reduction in spacing. Furthermore, the average Nusselt number is in excess of 21-89% at the optimal spacing compared to no-spacing. Finally, this paper is concluded with producing a new correlation for the average Nusselt number.

Mixed convection in the semi-circular lid-driven cavity with heated curved wall subjugated to constant heat flux for non-Newtonian power-law fluids

Abstract The present numerical work delineates the flow and heat transfer characteristics due to the combined convection (free and forced) inside semi-circular, top lid-driven cavity. The flow conditions are assumed to be laminar, steady-state, incompressible, and for non-Newtonian power-law fluids. The curved surface of the cavity is subjugated to constant heat flux (CHF) thermal condition, while the top wall is sliding with uniform velocity (Ulid) along –x-direction. The governing parameters utilized for numerical experimentation are Richardson number (Ri = 0.1–10), non-Newtonian power-law index (n = 0.5–1.5), modified Prandtl number (Pr = 1–100) and Grashof number (Gr = 104). The study is also intended to provide a comparative explanation for the use of adiabatic blockage of varying cross-sections on the flow and thermal patterns in the cavity. In particular, the influence of the shape of blockage in the cavity, viz., circular, square, and triangular investigated. Normalized Nusselt numbers have also plotted to give the idea of heat transfer enhancement/deterioration by the presence of block with that of the absence of block. Empirical correlations are also developed for summarizing the results of the study. The triangular block shows better heat transfer results as compared with the circular and square blocks in the semi-circular cavity.

Mixed convection in the heated semi-circular lid-driven cavity for non-Newtonian power-law fluids: Effect of presence and shape of the block

The present work delineates the hydrodynamics and thermal characteristics due to mixed convection in the lid-driven semi-circular cavity affected by the presence of the adiabatic block at its geometric center for two-dimensional, steady-state, laminar and for non-Newtonian power-law fluids. The semi-circular cavity has a diameter of D . The horizontal wall/lid is sliding with a uniform horizontal velocity ( u = U ) and is subjugated to the ambient thermal condition; while the curved surface is subjugated to a higher isothermal temperature. The convective characteristics inside the system is explored for the broad range of Richardson number (0.1 ≤ Ri ≤ 10), Prandtl number (1 ≤ Pr ≤ 100) and non-Newtonian power-law index (0.5 ≤ n ≤ 1.5) at a constant Grashof number of 10 4 . Apart from this, the effect of shape (cross-section) of the inserted block, i.e. , circular, square and triangular on heat transfer characteristics has also been explored. It is observed that the shear thickening fluids display better cooling characteristics. Besides, the cavity with immersed triangular block shows better heat transfer results than the circular and square blocks. The deviations observed in the flow and heat transfer characteristics in the cavity by inserting an adiabatic block as compared with cavity without block have been ascertained by calculating normalized Nusselt number ( Nu N ). The presence of the block was found to have a diminishing effect on the heat transfer due to convection in the cavity. In the end, the results of the study are summarized in the form of a predictive correlation exhibiting the functional dependence of average Nusselt number with Prandtl number, power-law index, and Richardson number.

Entropy analysis of EMHD non-Newtonian fluid flow induced by Riga plate with slip and convective boundary phenomena

Our paper is consecrated to show the influence of variable fluid properties in EMHD non-Newtonian power-law fluid along a moving Riga plate. Slip velocity phenomenon is considered at the surface which is convectively heated. Entropy analysis is elaborated employing thermodynamic second relation. The governing nonlinear PDEs are altered into ODEs through adequate propinquity transformations which have been solved numerically via the shooting method with the fourth-order Runge–Kutta algorithm through Mathematica software (bvp4c). Characteristics of different basic parameters on velocity, temperature, entropy generation and Bejan number are highlighted through graphs. The outcomes exhibit that the minimum entropy rate in the flow system can be obtained either with rising viscosity parameter and slip parameter or declining dimensionless parameter and thermal conductivity parameter. The entropy rate is minimal for dilatant fluid when compared to pseudo plastic fluid with the most governing parameters. Contrast behavior on the thermal field is noticed for larger values of viscosity parameter and thermal conductivity parameter.

On the terminal velocity of single bubbles rising in non-Newtonian power-law liquids

To describe bubbly flows, an accurate prediction of the bubble rise velocity is crucial. For non-Newtonian fluids, closures for the bubble rise velocity provided in the literature are usually empirical and rather restricted in their applicability. In this work, a Front-Tracking Computational Fluid Dynamics model has been used to investigate the behaviour of a single bubble rising in a power-law fluid, for a very wide range of viscosities covering both shear-thinning and shear-thickening behaviour, where the power-law exponent n was varied between 0.5 and 1.5 and for three different bubble diameters (viz. 0.5 mm, 2 mm and 4 mm). The non-Newtonian behaviour of the continuous phase strongly influences the shape of the single rising bubbles caused by the viscosity profiles that develop in the flow field. As a consequence, large non-spherical bubbles become more spherical in shear-thickening fluids (in comparison to the same bubble in a Newtonian liquid), whereas small spherical bubbles lose their sphericity in shear-thinning fluids. To determine the bubble rise velocity for bubbles in non-Newtonian fluids with a power law behaviour, the drag closure derived for bubbles rising in Newtonian liquids proposed by Dijkhuizen et al. (2010), which combines viscous drag and shape-induced drag in a single correlation, is adapted using a modified Reynolds number. In this work it is shown that this adapted correlation is able to predict the terminal rise velocity of single bubbles rising in non-Newtonian power-law fluids within 20% accuracy for the majority of the investigated cases, provided that the drag regime does not change.

New Integral Solutions for Magnetohydrodynamic Free Convection of Power-Law Fluids Over a Horizontal Plate

An integral analysis has been performed to theoretically investigate the magnetohydrodynamic natural convection flow of non-Newtonian power-law fluids over a semi-infinite horizontal plate with constant surface heat flux. The governing boundary layer equations are transformed into a set of coupled ordinary differential equations using stretching transformation. The resultant equations are solved analytically using the integral method. A set of new infinite polynomial series are introduced for presenting the velocity and pressure profiles, providing more accurate results compared with traditional solutions. Implicit expressions for the Nusselt number and friction coefficient are presented for wide ranges of the generalized Prandtl number (Pr*), the non-Newtonian power-law viscosity index (n), and the generalized Hartmann number (Ha*).

A theoretical study on the capillary rise of non-Newtonian power-law fluids

The phenomena of capillary rise with the effect of displaced fluids are ubiquitous in both science and engineering, and the mathematical models and their analytical solutions of this problem have also received increasing attention. In this paper, a theoretical study on the rising dynamics of non-Newtonian power-law fluids in a capillary is performed, and the classical Lucas–Washburn equation is generalized to a nonlinear second-order differential equation in which the effects of the power-law index and displaced fluids are included. We analyze the imbibition behaviors of power-law fluids under the influence of displaced fluids in details, and also present some analytical solutions of different special cases and different time stages. The results show that for different special cases, it takes shorter time for shear thickening fluid to reach the equilibrium height. For different time stages, however, the rising phenomena of power-law fluids are more complex, and the average time for the shear-thinning fluid to reach the equilibrium height is longer compared to shear-thickening fluid, but an opposite phenomenon is observed for the case of μ1,0/μ2,0=100 (here μ1,0/μ2,0 is the viscosity ratio of two power-law fluids) in viscous time stage. In inertial time stages, the density ratio of the absorbed fluid to the displaced fluid also has a significant effect on the rising dynamics of imbibing fluid. Furthermore, the effect of dynamic contact angle is also included in the governing equation and analytical solutions. Through a comparison between the theoretical results and experimental data, a good agreement is observed. These results can be used as a priori for liquid absorption in industrial applications, including oil recovery, fuel cells and water collection of artificial silk.

Augmentation and diminution of non-Boussinesq effects due to non-Newtonian power-law behavior in natural convection

This study investigates the extent and significance of augmentation and diminution of non-Oberbeck–Boussinesq (NOB) effects due to power-law rheology in natural convection. The relative significance of each temperature dependent thermophysical property of a non-Newtonian power-law fluid was first evaluated using an order of magnitude analysis. The limiting criteria were derived for a class of fluids having an Arrhenius-type thermodependent consistency index, and a constant power-law index. Significant fluid property dependencies were identified, incorporated into the conservation equations, and solved numerically. The benchmark problem of natural convection around an isothermal vertical flat plate, immersed in a quiescent power-law fluid, was re-investigated from the viewpoint of NOB effects. It was found that power-law rheology significantly augmented or diminished the acceleration of flow caused by NOB effects. Compared to the Newtonian case, strong shear thinning behavior more than doubled the NOB acceleration of the flow field, and shear thickening inhibited the acceleration by nearly half. Numerical solutions facilitated the visualization of velocity and temperature distributions, and thus provided insights to the underlying physics. It is demonstrated that the cumulative effect of the power-law behavior and temperature dependence of properties is more than a mere superposition of the individual effects. Important contributions from the present work include modifications to the OB approximation’s limiting criteria applicable to power-law fluids, insights into the effect of temperature dependent properties on the flow field and consequent heat transfer, and their correspondence to the results of the order of magnitude analysis. The present investigation of the underlying physics of augmentation and diminution facilitate a better understanding for future studies of NOB effects combined with non-Newtonian behavior.

Boundary-layer flow of the power-law fluid over a moving wedge: a linear stability analysis

We study the stability of the two-dimensional boundary-layer flow of a power-law (Ostwald de Waele) non-Newtonian fluid over a moving wedge. The mainstream velocity is assumed to have a power of distance from the leading boundary layer, such that the system admits to the self-similar solutions. We discuss the problem in question for both shear-thickening and shear-thinning fluids which lead to a non-uniqueness (double solutions) in the base flow solutions. We then address an issue of the stability of the non-unique solutions. A linear eigenvalue analysis of the double solution reveals that the basic flow represented by the first solution is always stable, and this flow is practically encountered. The system becomes unstable to the second solutions which have the mode-two perturbations with larger boundary-layer thickness. The first and second solutions form a tongue-like structure in the solution space. Furthermore, the modification of the viscosity for the power-law fluids reveals that the system predicts an infinite viscosity in the confinement of the boundary-layer region. Extensive comparisons of the solutions with the existing models with Newtonian fluid are made, and a physical explanation behind these solutions is proposed.

Experimental study on rheological properties of nanoparticle-stabilized carbon dioxide foam

In relationship with the potential application of nanoparticle (NP) foam technology in CO2 enhanced oil recovery (EOR) and greenhouse geological storage in tight reservoirs, the rheological properties of the NP-stabilized CO2 foam with surfactant (α-olefin sulfonate-AOS) solution were experimentally investigated. The foam was treated as a power-law non-Newtonian fluid, and the relationships between the shear stress and shear rate as well as the apparent viscosity of foam and foam quality were determined under influential parameters including the NP additive, internal gas type, salinity, and oil presence. Critical foam quality values in the range 91–96% were observed for the NP-stabilized foam, whereas no such values were obtained for the corresponding AOS-CO2 foam. The results show the NP-AOS-CO2 foam has lower viscosity compared to the NP-AOS-N2 foam, and the solution salinity decreases the viscosity of the NP-AOS-CO2 foam, whereas oil presence has no obvious effect on the foam viscosity.

SLIP FLOW AND HEAT TRANSFER OF MHD POWER LAW FLUID OVER A POROUS SHEET IN THE PRESENCE OF JOULE HEATING AND HEAT SOURCE/SINK

An analysis has been carried out to study the MHD flow and heat transfer of a non-Newtonian power-law fluid over a porous sheet in the presence of partial slip and Joule heating. Here, thermal conductivity is assumed as a function of temperature. An external heat source is also applied. The governing equations are reduced into the system of non-linear ordinary differential equations by using similarity transformations. This system along with appropriate boundary conditions are solved numerically using the shooting technique with Runge-Kutta fourth order iteration scheme. The effects of suction/injection parameter, Eckert number and heat source parameter on the velocity and temperature profiles are studied. It is observed that the temperature profile increases with decreasing value of heat source parameter, Eckert number and suction/injection parameter. The influence of different parameters on the velocity and temperature profile is presented through graphs. The effect of all physical parameters on skin friction and local Nusselt number is displayed through tables.

Effect on flow characteristics of blood in overlapping stenosed artery considering the axial variation of viscosity using power-law non-Newtonian fluid model

In the present investigation, a mathematical model is developed to study the effect of non-Newtonian behaviour of blood on overlapping stenosed artery considering power-law fluid model. The constitutive equations of the model are solved analytically with the help of given boundary conditions to get different expressions for flow characteristics such as flow rate, flow resistance and wall shear stress considering no-slip condition at the wall and viscosity variation as axial. The flow of blood is taken to be steady, incompressible, laminar and one-dimensional. In this paper, we have concluded that the flow rate decreases while flow resistance and wall shear stress increases with the increase in stenosis size and also the comparison of these flow characteristics has been done for linear and quadratic variation of viscosity.