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The flow induced by a sphere rotating inside an incompressible, non-Newtonian, power law fluid has been investigated numerically. The rotating sphere is enclosed in a concentric cubic box with solid boundaries. The fluid power-law index varied between 0.2 and 2 thereby covering both shear-thinning and shear-thickening fluids and the Reynolds number varied between 0.01 and 10,000. Numerical predictions show significant differences between shear-thinning and shear-thickening fluids. In the first case the flow is confined near the sphere whereas in the second case the flow extends up to the box plates. In creeping flow and shear-thinning fluids the torque is independent of the Reynolds number. [ABSTRACT FROM AUTHOR]

The best-known paper on non-Newtonian fluids in mixing systems is the Metzner and Otto’s work. A central idea of their contribution is based on the assumption that in laminar flow there exists an average shear rate ( γ ̇ av ) around the impeller (whose exact location and geometric shape is not clearly specified), and that it is proportional to the impeller speed ( N ), i.e., γ ̇ av = K s N , where K s is the Metzner-Otto constant. In this work, an in-depth investigation of this assumption is carried out by using computational fluid dynamics (CFD) to calculate the three-dimensional flow induced by a Rushton turbine (RT). It was found that the volume swept by the blades is the region where K s may be computed explicitly as K s = γ ̇ av / N directly from non-Newtonian flow simulations. The obtained K s values in this region were found in good agreement with reported data. Furthermore, power number measurements and data from literature were used to validate the simulations. The CFD method developed in this study can be used to readily and reliably evaluate K s of industrial mixing impellers without resorting to power data of Newtonian fluids. [ABSTRACT FROM AUTHOR]

Many commonly used industrial fluids display non-Newtonian effects. Their rheology exerts a strong influence on flow structure, interface fluctuation, pressure drop, heat transfer and many other flow characteristics. Owing to the complexity of churn flow, knowledge of the flow characteristics with non-Newtonian fluids is not well documented in existing literature. In the present study, we employ the power-law model to describe the non-Newtonian fluid behavior and establish an analytical model to predict pressure gradient, void fraction and wave behavior in churn flow. One churn flow unit is carefully divided into two parts (the falling film region and the wave region) and analyzed separately. The results indicate that liquid viscosity significantly affects the variations of pressure gradient, void fraction, velocity profiles, film thickness and wave behavior. These findings will provide insight into the effect of viscosity on flow structures and benefit a better understanding of the non-Newtonian churn flow. [ABSTRACT FROM AUTHOR]

Bubble pinch-off is a rapid process and until now is not well-understood especially for the final stage near the breakup point. In this work, we aim at investigating the air bubble pinch-off at a submerged nozzle in various fluids, including Newtonian and non-Newtonian fluids. Different fluids exert different effects on the pinch-off dynamics as well as shape evolution immediately after pinch-off. A scaling law was applied to describe the bubble pinch-off in Newtonian fluids and the exponents: b = 0.5 for low viscosity fluids and b = 1 for high viscosity fluids, are in a good agreement with the conventional values predicted by the numerical simulation. For bubbles in non-Newtonian fluids, the pinch-off dynamics is mainly governed by the fluid rheology. The universal scaling exponent exists between 0.5 and 1 for low shear-thinning fluids while a non-universal character occurs for bubble pinch-off in high shear-thinning fluids. Our experimental results were confirmed by the numerical simulation. [ABSTRACT FROM AUTHOR]

• Shear thinning non-Newtonian droplets are constructed by MDPD method. • Diffusion process in non-Newtonian droplets differs from that in Newtonian droplets. • A We-t c relationship is proposed for the control of droplets mixing on solid surface. • Relationship between total mixing time and Weber number follows the power law. The impingement and the following mixing between non-Newtonian droplets on the solid surface are a common phenomenon in industry, where reasonably controlling the mixing is always of vital importance. In this work, Many Body Dissipative Particle Dynamics method is used to reveal the law of this process with two non-Newtonian droplets. Firstly, the variation of droplets morphology with the Weber number of the impinging droplet is studied. Then, by dividing this mixing process into convection-dominated and molecular diffusion-dominated stages, the relationship between duration of the former stage and Weber number is quantitatively determined. In the latter stage, it is found a special phenomenon in the mixing which results from the difference in particle diffusion coefficients. Finally, the mixing time for the two droplets and its variation with the Weber number is proposed, which can be helpful in the design of the related device when mixing is between non-Newtonian droplets. [ABSTRACT FROM AUTHOR]

• Lattice Boltzmann methodology to predict behavior in fluid mechanical systems. • CFD used to model two-fluid blending of non-Newtonian fluids. • CFD used to accurately model mixing of yield stress fluids. • Mixing of radioactive slurry waste and glass frit was modeled using CFD. A numerical approach for predicting the time-accurate fluid flow and mixing properties of non-Newtonian fluids is presented. This approach, which is based on the lattice Boltzmann method, is used to characterize the blending in shear-thinning fluids, as well as cavern formation in yield-stress fluids. Predictions compare favorably to measured data and expectations from first-principles theory. Importantly, across the range of fluids and systems here, the simulations require no reparameterization or retuning between scenarios. This generality is exploited to model a nuclear waste processing unit operation. [ABSTRACT FROM AUTHOR]

Highlights • Solving temperature-dependent viscosity model normally involves much simulation. • Temperature-independent viscosity model gives a simple relation for quick design. • The constant viscosity in this model should be the one at tube-wall temperature. Abstract For a melt flow with viscous heating, a temperature-independent viscosity model is simple to use in estimating its temperature profile. In this model, a constant viscosity is chosen to represent a temperature-dependent one. However, it is still not clear about what value should be selected for the constant viscosity. In this short communication, we derive a relation to find it, followed by validation using existing numerical examples. [ABSTRACT FROM AUTHOR]

This paper presents the experimental study and analysis performed in order to better understand the link between activated sludge properties, rheological behaviour and oxygen transfer. The experimental set-up consists of a bubble column of 0.3 m 3 continuously fed with activated sludge and a capillary rheometer, installed in two different wastewater treatment plants: a conventional activated sludge plant and a membrane bioreactor. In the bubble column, equipped with a fine bubble diffuser, the overall gas hold-up ( ϵ G ) and volumetric oxygen transfer coefficients ( k L a ) were measured. A fraction of the column outflow was sent to the capillary rheometer where the activated sludge rheological behaviour was investigated. Several properties of the studied activated sludge were characterised (MLSS, MLVSS, soluble COD, surfactants, surface tension, soluble cations) and their impact on rheology and oxygen transfer was examined. The experimental data showed that the parameters K and n , from the Ostwald-de Waele rheological model, were strongly related to the suspended solids concentration (in terms of MLSS or MVLSS). An increase in k L a was observed as the superficial gas velocity ( U G ) was increased. Compared to clean water, the k L a coefficient was lower in activated sludge and still reduced with an increase of the MLSS concentration. This reduction could be partially attributed to a lower gas holdup ( ε G ) associated with an increase in the sludge apparent viscosity ( μ app ) leading to a reduction of the specific interfacial area ( a ). Subsequently, an estimation of the mean shear rate exerted by the bubble swarm in the column allowed to evaluate the sludge apparent viscosity ( μ app ) of the mixed liquor at a given superficial gas velocity and MLSS concentration. Finally an empirical correlation linking k L a to the superficial gas velocity ( U G ) and the sludge apparent viscosity was obtained for both types of sludge. The good agreement between the experimental and the fitted data suggests that k L a can be estimated from the superficial gas velocity and the rheological behaviour. [ABSTRACT FROM AUTHOR]

• A mathematical framework is constructed by coupling the hydrodynamics and bubble breakup and coalescence using the complete energy spectrum. • Model results and laboratory data are consistent. • Viscous effects were captured numerically by the entire energy spectrum and improved the k L a and bubble sizes predictions. • For Non Newtonian Fluids The SST turbulence model resulted in a better precision than the κ-ε model. Gas-liquid mass transfer in non-Newtonian fluids is a crucial aspect of the bioprocess industry. Mass transfer is analyzed using the coefficient k L a , which is limited by the rheology since it exerts a barrier to the fluid deformation, significantly affecting the oxygen diffusivity and the bubble breakup and coalescence. However, the traditional mathematical expressions to model the bubble size distribution from bubble breakup and coalescence in turbulent flows of Newtonian fluids are restricted to the inertial sub-range of turbulence where the kinetic energy is dominated only by the microscales. Application of the Newtonian models to non-Newtonian fluids could result in inaccurate predictions by not considering the continuous phase rheology. The main goal of this research is the numerical determination and experimental comparison of bubble sizes in different axial positions of a bioreactor stirred by a Rushton turbine. Emphasis was placed on the viscosity effects on simulating bubble dispersion in a Newtonian fluid (water) and its comparison with a non-Newtonian fluid (0.4 % CMC). The mathematical framework is constructed by coupling the hydrodynamics (through computational fluid dynamics CFD) and bubble breakup and coalescence from a turbulence perspective using the complete energy spectrum that considers the contributions from the energy containing, inertial, and dissipation sub-ranges. This is achieved by including the second-order structure–function. The results of bubble sizes and k L a were compared with experimental data, and acceptable agreement was achieved. Therefore, it is shown that the viscous effects were captured numerically by the entire energy spectrum and improved the predictions of the k L a and bubble sizes compared to the traditional structure function turbulence models. [ABSTRACT FROM AUTHOR]

• The mechanism of electrospray granulation was investigated. • The microdripping mode was characterized by monodisperse fine droplets formation. • The crucial parameters governing the electrospray granulation process were obtained. • The physical basis on operating desirable conditions precisely was provided. The application of electric fields is of great interest in the terrestrial and space domains owing to its ability to enhance the discrete phases' fragmentation and control particle size. Therefore, adopting electrostatic spray to prepare microspheres has become a feasible method. In this study, the mechanism for this process was discussed, taking into account a determined non-Newtonian fluid. The result shows that tiny and uniform microspheres can be obtained by carefully consideration of the parameters, which are highly problematic to achieve in engineering and laboratory environments. Also, the electrostatic breakup modes of non-Newtonian fluid include dripping, microdripping, and oscillating microdripping, and their characteristics are different from those of Newtonian fluid. In particular, the transition from dripping mode to microdripping mode presents a mutation state that has not appeared in previous literature. In addition, the effects of applied voltage, flow rate, and suspension liquid concentration on the breakup mode, droplet size, and falling frequency were discussed. Accordingly, the critical operating parameters affecting the electrostatic breakup characteristics and the desirable breakup modes for the preparation of microspheres were identified. The present work is expected to provide theoretical guidance for the preparation of microspheres. [ABSTRACT FROM AUTHOR]

Numerical simulations were carried out to investigate the flow dynamics and mixing behavior in T-shaped and serpentine microchannels with non-Newtonian working fluids using shear-dependent viscosity models. As an illustrative case study, the microfluidic transport of blood was considered. The Carreau-Yasuda and Casson non-Newtonian blood viscosity models were used to capture the non-Newtonian characteristics. Steady Navier-Stokes equations with a diffusion-convection model for species concentration were solved in flow and mixing analyses. Under similar operating conditions, flow dynamics and mixing were compared between the working fluids: water (a Newtonian fluid), and blood using the Carreau-Yasuda non-Newtonian model. For a mass flow rate of m ̇ 10 − 2 k g, the mixing performances of both the fluids were found to be nearly equivalent, and decreased with flow rate. With increased flow rate, the mixing with water was significantly improved. However, a negligible change in mixing performance was observed using the Carreau-Yasuda model for blood. Also, the pumping power needed was considerably higher for the blood sample (~1bar) than for water (~0.40bar) at the same flow rate. The mixing behavior with the Carreau-Yasuda blood model was compared for T-shaped and serpentine channels over a fixed mixing length. The serpentine channel showed better mixing performance over the flow rate range considered. [ABSTRACT FROM AUTHOR]

Abstract: Mass transfer and mixing performances are very critical for xanthan gum fermentation process. Power consumption, local and average volumetric mass transfer coefficient (k L a) were compared for six impeller combinations in a 50L perspex tank with xanthan gum solutions. Impellers used in various combinations can be distinguished as two categories: “small-diameter” impeller, which include Rushton turbine, hollow blade turbine and wide-blade hydrofoil impeller and “large-diameter” including ellipse gate impeller, Intermig and double helical ribbon. The results show that in order to gain the same power input, the rotating speed of “small-diameter” impeller combinations increases as the concentration of xanthan gum increases, while it decreases for “large-diameter” impeller combinations. The two categories also show distinguished mass transfer rates. For the “small-diameter” impeller combinations, the k L a values near the wall region drop faster than that in other areas as the concentration of xanthan gum increases. While for the “large-diameter” impeller combinations, the distribution of k L a is homogenous except in the bottom area but with poor gas dispersion capabilities as concentration of xanthan gum increases. The averaged k L a for each impller combination was correlated well with the specific gassed power input, superficial gas velocity and effective viscosity. The obtained correlation shows that the k L a strongly depends on specific power input and viscosity, but is less influenced by the gas flow rate. [Copyright &y& Elsevier]

[Display omitted] • Mathematical model of two-phase Taylor flow for non-Newtonian fluids is extended. • Center and border of vortices, mean velocity and frequency of circulation are found. • Conditions of transition from circulation to by-pass mode of Taylor flow. • The film around the liquid plug is the only area not involved in Taylor circulations. • The coincidence with the Newtonian fluids as a limiting case was checked. Based on the recently published mathematical model for non-Newtonian two-phase flow in microchannels (Abiev, 2022) an extension that allows to calculate the majority of important parameters of two-phase Taylor flow for non-Newtonian fluids was developed and is presented in this paper. The following parameters could now be calculated theoretically for two-phase Taylor flow of non-Newtonian fluids (both for liquid slug and liquid plug): (i) the center of Taylor vortices, (ii) their boundaries, (iii) mean velocities and frequency of circulation, (iv) mean velocities in by-pass and transit films, and (v) transition from circulation to by-pass flow conditions. The coincidence with the Newtonian fluids as a limiting case was evaluated. The obtained results represent crucial input data for the three-layer mass transfer model, the frequency of circulation-based mass transfer model, and are useful for the understanding of the influence of various parameters on heat and mass transfer intensity in Taylor flows. [ABSTRACT FROM AUTHOR]

Abstract: Slot die coating onto porous media is a distinct field in the coating industry and has broad applications. One important technical issue related to coating porous media is how to predict and control the fluid penetration depth, which directly affects the appearance, properties, and performance of the resulting material. Up to now, the analytical relationship between processing parameters and the final penetration depth are still not well understood. Existing modeling work either uses oversimplified assumption of pressure distribution in the coating bead, or does not provide a simple expression to predict the penetration depth and often requires a complex calculation procedure. Furthermore, previous models are limited to Newtonian fluids. In this study, new computational fluid dynamics (CFD) and analytical models to study the penetration of fluid into porous media during slot die coating were developed for Newtonian and non-Newtonian fluids. Penetration driven by the pressure in coating bead was considered in these models. To this end, basic analytical models that can easily and rapidly calculate the penetration depth were developed and the results were compared to CFD models. It was found that there exists good agreement between the analytical and CFD models when coating Newtonian and non-Newtonian fluids, having an overall relative error of less than 6% and ranging between 12–26%, respectively. Results from a parametric study, when coating Newtonian fluids, showed that viscosity has a negligible effect on the penetration depth; whereas coating speed, flow rate, permeability and porosity are more important. Based on the experimental analysis, similar trends exist for the measured and predicted values of the penetration depth when coating non-Newtonian fluids. [Copyright &y& Elsevier]

Abstract: A porous media model is developed for non-Newtonian blood flow through reticulated foam at Reynolds numbers ranging from 10−8 to 10. This empirical model effectively divides the pressure gradient versus flow speed curve into three regimes, in which either the non-Newtonian viscous forces, the Newtonian viscous forces, or the inertial fluid forces are most prevalent. When compared to simulation data of blood flow through two reticulated foam geometries, the model adequately captures the pressure gradient within all three regimes, especially that within the Newtonian regime where blood transitions from a power-law to a constant viscosity fluid. [Copyright &y& Elsevier]

Abstract: The motion and interactions of three equal-interval parallel bubbles in non-Newtonian fluids were numerically simulated by volume of fluid method (VOF), in which the continuous surface tension model and the power-law model were adopted to represent surface tension and rheological properties of non-Newtonian fluids, respectively. The computational method was validated by the comparison of the processes of coalescence of two in-line bubbles and rising of two parallel bubbles between experiment and simulation. This method was then applied to study the effect of initial bubble diameter, initial horizontal bubble interval and rheological properties of non-Newtonian fluids on lateral coalescence and rising of three parallel bubbles. The dimensionless critical horizontal interval of bubble coalescence was obtained under different physical property conditions. The critical horizontal interval of bubble coalescence decreases with the increase of initial bubble diameter and flow index of non-Newtonian fluids. When the initial horizontal bubble interval is less than the critical horizontal interval of bubble coalescence, three bubbles will coalesce into a bigger bubble. The coalescing bubble could breakup into two identical daughter bubbles when the initial bubble diameter was increased or the flow index of non-Newtonian fluids was decreased. Three parallel bubbles rising in non-Newtonian fluids will experience repulsive interactions once the initial horizontal bubble interval is greater than the critical horizontal interval of bubble coalescence, the horizontal bubble interval increased gradually owing to the repulsive effect, while the vertical distance between bubbles varied dramatically for spherical bubble and ellipsoidal bubble due to the differences of their flow field structures. [Copyright &y& Elsevier]

Abstract: Coal water slurry (CWS) gasification technology, which is one of clean and efficient coal gasification approaches, catches wide attention presently. To investigate breakup and atomization of coal water slurry, eight kinds of CWS are observed using high speed digital camera. Based on morphology, the breakup regimes of CWS can be termed different modes: Rayleigh-type breakup, fiber-type breakup and atomization. The Rayleigh-type breakup is the main atomization regime of high viscosity CWS. When the viscosity of CWS is low, the CWS jet is Rayleigh-type breakup at low air velocity; and fiber-type breakup at high air velocity. When the air velocity is very high, all CWS jets are in atomization regime. The dimensionless CWS jet breakup length is studied and correlated, which decreases with Weber number and momentum flux ratio, increases with Ohnesorge number. Finally, a simplified formula is studied to estimate the oscillation frequency of CWS jet. The model estimates are consistent with the experimental results. [Copyright &y& Elsevier]

Abstract: The mixing in non-intermeshing counter rotating internal batch mixers using cam, banbury and roller rotor were evaluated experimentally using thermo scientific Haake and numerical FEM simulation using the commercial CFD package Polyflow. The Carreau–Yasuda flow model was used with mesh superposition technique to generate velocity profiles and particle trajectories for HDPE. Differences in velocity profile with respect to rotor angles were examined. Distributive mixing was evaluated experimentally, as well as numerically by particle tracking analysis. Flow stretching was evaluated using the length of stretch and mixing efficiency. Since material points stayed on their streamlines near to rotor wall in the cam and banbury mixer, roller mixer was found to be generally more effective and efficient, although there were still areas of poor mixing found in all. [Copyright &y& Elsevier]

Abstract: The effect of channel shape on the friction factor-Reynolds number relationship for laminar, open channel flow of three non-Newtonian fluids was investigated. For each channel shape, the data can be described by a general relationship, f=K/Re where f is the Fanning friction factor and Re is the appropriate Reynolds number corresponding to the flow curve model used to describe the non-Newtonian behaviour exhibited by the test fluid. The K values were found to be 14.6 for triangular channels with a vertex angle of 90°, 16.2 for semi-circular channels, 16.4 for rectangular channels and 17.6 for trapezoidal channels with 60° sides. These K values were found to be in line with those reported by and for open channel flow of Newtonian fluids as opposed to the assumption made by of using a constant value of 16 based on the pipe flow paradigm for all channel shapes. [Copyright &y& Elsevier]

Abstract: Transient squeeze flow and recovery experiments are simulated for a rubber compound. The rheological behaviour of the selected compound is described with a multi-mode Leonov model developed for filled uncured elastomers. The calculation is performed with the finite element software POLYFLOW. In particular, we focus on the deformation undergone under the application of a load, and on the subsequent recovery that develop upon cessation of the squeezing force. We also try to establish a possible empirical relationship between the applied squeeze force and time interval (input data) and the resulting deformation and recovery (output quantities). [Copyright &y& Elsevier]

Abstract: A numerical parametric study of the laminar pipe transport of coarse particles in non-Newtonian carrier fluids of the power law type has been conducted using an Eulerian–Eulerian computational fluid dynamics (CFD) model. The predicted flow fields have been successfully validated by experimental measurements of particle velocity profiles obtained using a positron emission particle tracking technique, whilst solid–liquid pressure drop has been validated using relevant correlations gleaned from the literature. The study is concerned with nearly-neutrally buoyant particles flowing in a horizontal or vertical pipe. The effects of various parameters on the flow properties of such mixtures have been investigated over a wide range of conditions. The variables studied are: particle diameter (2–9mm), mean solids concentration (5–40% v/v), mean mixture velocity (25–125mms−1), and rheological properties of the carrier fluid (k=0.15–20Pas n ; n=0.6–0.9). A few additional runs have been conducted for shear thickening fluids, i.e. n>1. Whilst the effects of varying the power law parameters and the mixture flowrate for shear thinning fluids are relatively small over the range of values considered, particle size and solids concentration have a significant bearing on the flow regime, the uniformity of the normalised particle radial distribution and of the normalised velocity profiles of both phases, and the magnitude of the solid–liquid pressure drop. The maximum particle velocity is always significantly less than twice the mean flow velocity for shear thinning fluids, but it can exceed this value in shear thickening fluids. In vertical down-flow, particles are uniformly distributed over the pipe cross-section, and particle diameter and concentration have little effect on the normalised velocity and concentration profiles. Pressure drop, however, is greatly influenced by particle concentration. [Copyright &y& Elsevier]

Abstract: A functional form of equation for predicting pressure drop in a modified non-Newtonian downflow bubble column has been formulated. The equation has been developed based on the bubble formation, drag at interface and the wettability effect of the liquid. Also the bubble–liquid interfacial shear stress in two-phase flow is analyzed and correlated with the dynamic, geometric and physical variables. The functional form of equation appears to predict the pressure drop satisfactorily for two-phase dispersed flow in the co-current modified downflow bubble column with carboxy methyl cellulose (CMC) solution in water with different concentrations. [Copyright &y& Elsevier]

Abstract: A finite element numerical study has been carried out on the isothermal flow of power law fluids in lid-driven cavities with axial throughflow. The effects of the tangential flow Reynolds number , axial flow Reynolds number , cavity aspect ratio and shear thinning property of the fluids on tangential and axial velocity distributions and the frictional pressure drop are studied. Where comparison is possible, very good agreement is found between current numerical results and published asymptotic and numerical results. For shear thinning materials in long thin cavities in the tangential flow dominated flow regime, the numerical results show that the frictional pressure drop lies between two extreme conditions, namely the results for duct flow and analytical results from lubrication theory. For shear thinning materials in a lid-driven cavity, the interaction between the tangential flow and axial flow is very complex because the flow is dependent on the flow Reynolds numbers and the ratio of the average axial velocity and the lid velocity. For both Newtonian and shear thinning fluids, the axial velocity peak is shifted and the frictional pressure drop is increased with increasing tangential flow Reynolds number. The results are highly relevant to industrial devices such as screw extruders and scraped surface heat exchangers. [Copyright &y& Elsevier]

Abstract: The present work aims at understanding the behavior of individual bubbles in non-Newtonian fluids. By means of a Particle Image Velocimetry (PIV) device, the complete flow field around either a single non-spherical bubble rising in polyacrylamide (PAAm) solutions or a solid sphere settling down in the same fluids shows for the first time the similar coexistence of three distinct zones: a central downward flow behind the bubble or the sphere (negative wake), a conical upward flow surrounding the negative wake zone, and an upward flow zone in front of the bubble or the sphere. This excludes then the possible influence of the interface deformation on the negative wake. A theoretical lattice Boltzmann scheme coupled to a sixth-order Maxwell model was developed for computing the complex flow field around a solid sphere. The good agreement with the experimental measurements provides evidence that the physical mechanism responsible for the negative wake in such fluids could be related to the fluid''s viscoelastic properties. [Copyright &y& Elsevier]

Abstract: This paper presents an analysis using computational and scaling methods of pulsatile capillary Poiseuille flow of a model anisotropic viscoelastic discotic liquid crystalline material. The analysis shows that pulsatile pressure drops applied to anisotropic materials can result in flow-rate enhancement or reduction, defined as the relative flow-rate change with respect to the steady-state flow rate, for a given average pressure drop, amplitude, and frequency. It is found that flow-rate modification in pulsatile flow is a direct result of orientation-dependent viscosity. The role of average pressure drop, oscillation amplitude, and frequency on flow enhancement is characterized and explained. The new mechanism of flow-enhancement in liquid crystals subjected to pulsatile pressure is expected to be useful to the fundamental understanding of pulsatile flows of anisotropic suspensions and anisotropic biological fluids. [Copyright &y& Elsevier]

Abstract: The three-layer model concept developed previously for solid–liquid flow has been adapted to model solids transport in inclined channels. The present model predicts the pressure loss and transport rate of solids in Newtonian and power-law fluid suspensions by assuming stratified flow conditions. Sets of stationary sand bed transport rate tests were performed to verify the predictions of the model. A 70-mm flow loop was constructed to measure the average transport rates and critical flow rates, which are required to initiate the motion of solids bed particles. The tests were carried out by eroding stationary sand beds with water and an aqueous solution of poly anionic cellulose (PAC) in a transparent pipe. Four sand beds with different particle size ranges were used. The average transport rates of the beds were predicted using the model. The model predictions show a satisfactory agreement with experimentally measured results when the grain Reynolds number is between 15 and 400 and the flow rate is sufficiently higher than the critical flow rate. Therefore, with some degree of limitation, the three-layer model can be applicable for predicting the transport rates of stationary solids beds in inclined channels for both Newtonian and power-law fluids. [Copyright &y& Elsevier]

This study presents a mechanistic model that predicts the critical velocity, which is required to initiate the movement of solid bed particles. The model is developed by considering fluid flow over a stationary bed of solid particles of uniform thickness, which is resting on an inclined pipe wall. Sets of sand bed critical velocity tests were performed to verify the predictions of the model. An 80 mm flow loop with recirculation facilities was constructed to measure the critical velocities of the sand beds. The tests were carried out by observing the movement of the bed particles in a transparent pipe while regulating the flowrate of the fluid. Water and aqueous solutions of PolyAnoinic Cellulose were used as a test fluid. The critical velocities of four sand beds with different particle size ranges were measured. The model was used to predict the critical velocities of the beds. The model predictions and experimentally measured data show satisfactory agreement. The results also indicated that the critical velocity is influenced by the properties of the fluid, flow parameters, and particle size. [Copyright &y& Elsevier]

• Breakup of non-Newtonian droplet in microfluidic Y-junction was investigated. • Three breakup stages were observed. • Variation of the width of the neck during droplet breakup was studied. • Effect of rheological property on droplet breakup dynamics was studied. Dynamics of non-Newtonian droplet (CMC aqueous solution) breakup with partial obstruction in microfluidic Y-junction was visually investigated. Three breakup stages were found: squeezing, transition and pinch-off. The effects of the concentration c of CMC, continuous capillary number Ca c and dispersed phase local capillary number Ca d on droplet breakup were studied. In squeezing stage and transition stage, the breakup process could be promoted by increasing Ca d or decreasing c. The pinch-off stage relied primarily on the surface tension and was almost independent of inertial force and viscous force. For the shear thinning non-Newtonian droplet, the length of the daughter droplet was always linearly stretched with time until breakup and the maximum gap width increased with Ca c , but decreased with the increases of c and Ca d. [ABSTRACT FROM AUTHOR]

• Viscosity correction factor derived from first principles for constant wall temperature. • Viscosity correction to Nusselt number for convective heat transfer in laminar flow. • Detailed thermal boundary layer analysis for Prandtl number >1. The role of variable viscosity on the heat transfer in non-Newtonian fluid flow has not been adequately explored in the past. Typically, non-Newtonian fluids are described by the power-law type behaviour as τ = K γ ̇ n (τ : shear stress; K : consistency index; γ ̇ : shear rate; n : power-law exponent). The viscosity correction factor in the form of K w K ∞ m (w : wall; ∞ : bulk) is a function of n. Traditionally, the Sieder-Tate correction for Newtonian fluid, μ w μ ∞ - 0.14 was the popular choice (μ w : fluid viscosity at the wall, μ ∞ : bulk) (Metzner et al. 1957). This is the first work on postulating the viscosity correction from the fundamental boundary layer analysis in non-Newtonian fluid. The mathematical predictions are validated with the literature experimental data. Inaccurate estimation of the viscosity correction leads to under- or over-predictions of the heat transfer coefficient, consequently, affects the effective heat transfer area. The correlations developed in this work would help in improved area calculations, thus, better performance and economic benefits. [ABSTRACT FROM AUTHOR]