Effect of bubble morphology and behavior on power consumption in non-Newtonian fluids’aeration process

Due to a prolonged operation time and low mass transfer efficiency, the primary challenge in the aeration process of non-Newtonian fluids is the high energy consumption, which is closely related to the form and rate of impeller, ventilation, rheological properties and bubble morphology in the reactor. In this perspective, through optimal computational fluid dynamics models and experiments, the relationship between power consumption, volumetric mass transfer rate(kLa) and initial bubble size(d0) was constructed to establish an efficient operation mode for the aeration process of non-Newtonian fluids. It was found that reducing the d0could significantly increase the oxygen mass transfer rate, resulting in an obvious decrease in the ventilation volume and impeller speed. When d0was regulated within 2-5 mm,an optimal kLa could be achieved, and 21% of power consumption could be saved, compared to the case of bubbles with a diameter of 10 mm.

Influence of Anisotropic Permeability and Soret Effect on the Convective Heat and Mass Transfer through a Porous Cavity Saturated by a Non-Newtonian Fluid

In this work, an analytical study is carried out on double-diffusive natural convection through a horizontal anisotropic porous layer saturated with a non-Newtonian fluid by using the Darcy model with the Boussinesq approximations. The horizontal walls of the system are subject to vertical uniform fluxes of heat and mass, whereas the vertical walls are assumed to be adiabatic and impermeable. The Soret effect is taken into consideration. Based on parallel flow approximation theory, the problem is solved in the limit of a thin layer and documented the effects of the physical parameters describing this investigation.

Numerical Analysis of the Mixed Flow of a Non-Newtonian Fluid over a Stretching Sheet with Thermal Radiation

A mathematical model is elaborated for the laminar flow of an Eyring-Powell fluid over a stretching sheet.The considered non-Newtonian fluid has Prandtl number larger than one.The effects of variable fluid properties and heat generation/absorption are also discussed.The balance equations for fluid flow are reduced to a set of ordinary differential equations through a similarity transformation and solved numerically using a Chebyshev spectral scheme.The effect of various parameters on the rate of heat transfer in the thermal boundary regime is investigated,i.e.,thermal conductivity,the heat generation/absorption ratio and the mixed convection parameter.Good agreement appears to exist between theoretical predictions and the existing published results.

UNIFORM ATTRACTOR FOR NONAUTONOMOUS INCOMPRESSIBLE NON-NEWTONIAN FLUID WITH A NEW CLASS OF EXTERNAL FORCES

This paper is joint with [27]. The authors prove in this article the existence and reveal its structure of uniform attractor for a two-dimensional nonautonomous incompressible non-Newtonian fluid with a new class of external forces.

RANDOM ATTRACTOR FOR A TWO-DIMENSIONAL INCOMPRESSIBLE NON-NEWTONIAN FLUID WITH MULTIPLICATIVE NOISE

This article proves that the random dynamical system generated by a twodimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing any bounded nonrandom subset of the phase space.

ON THE EXISTENCE OF LOCAL CLASSICAL SOLUTION FOR A CLASS OF ONE-DIMENSIONAL COMPRESSIBLE NON-NEWTONIAN FLUIDS

In this paper, the aim is to establish the local existence of classical solutions for a class of compressible non-Newtonian fluids with vacuum in one-dimensional bounded intervals, under the assumption that the data satisfies a natural compatibility condition. For the results, the initial density does not need to be bounded below away from zero.

Influence of chemical reaction on heat and mass transfer of non-Newtonian fluid with yield stress by free convection from vertical surface in porous medium considering Soret effect

The effect of chemical reaction on free convection heat and mass transfer for a non-Newtonian power law fluid over a vertical flat plate embedded in a fluid-saturated porous medium has been studied in the presence of the yield stress and the Soret effect. The governing boundary layer equations and boundary conditions are cast into a dimen- sionless form by similarity transformations, and the resulting system of equations is solved by a finite difference method. The results are preSented and discussed for concentration profiles, as well as the Nusselt number and the Sherwood number for various values of the parameters, which govern the problem. The results obtained show that the flow field is influenced appreciably by the presence of the chemical reaction parameter γ the order of.the chemical reaction parameter m, the Soret number St, the buoyancy ratio N, the Lewis number Le, and the dimensionless rheological parameter Ω.

EXISTENCE OF THE UNIFORM TRAJECTORY ATTRACTOR FOR A 3D INCOMPRESSIBLE NON-NEWTONIAN FLUID FLOW

This paper studies the trajectory asymptotic behavior of a non-autonomous in- compressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajectory attractor for the translation semigroup acting on the united trajectory space.

Diffusion of Amino Acids in non-Newtonian Fluids

The amino acids are necessarily nutritious components, their diffusions in body fluid and blood that be- long to typical non-Newtonian fluid are of virtual importance to control the diffusive process and help clinical treatment. In this article, a holographic interferometer has been adopted to measure the diffusivity of amino acids in non-Newtonian fluid with the use of real-time holographic interference technique. In order to prove the reliability of the experimental instrument, the diffusivities of sucrose aqueous solution at 298.15K were determined. The meas- ured result displays a satisfactory accuracy of the apparatus used. Furthermore, the diffusion coefficients of glynine, L-serine, L-threonine and L-valine in polyacrylamide (PAM) aqueous solution at 298.15K were measured, respec- tively. The experimental data were fitted by a newly proposed correlation equation based on Li’s predictive model. The calculating results by the present model are at considerably good agreement with experimental values, and the maximum average deviation is only 0.5%.

Jeffery-Hamel flow of non-Newtonian fluid with nonlinear viscosity and wall friction

A Jeffery-Hamel （J-H） flow model of the non-Newtonian fluid type inside a convergent wedge （inclined walls） with a wall friction is derived by a nonlinear ordinary differential equation with appropriate boundary conditions based on similarity relationships. Unlike the usual power law model, this paper develops nonlinear viscosity based only on a tangential coordinate function due to the radial geometry shape. Two kinds of solutions are developed, i.e., analytical and semi-analytical （numerical） solutions with suitable assumptions. As a result of the parametric examination, it has been found that the Newtonian normalized velocity gradually decreases with the tangential direction progress. Also, an increase in the friction coefficient leads to a decrease in the normalized Newtonian velocity profile values. However, an increase in the Reynolds number causes an increase in the normalized velocity function values. Additionally, for the small values of wedge semi-angle, the present solutions are in good agreement with the previous results in the literature.

Numerical Simulation of Concentration Field on Liquid Side around Bubble during Rising and Coalescing Process in Non-Newtonian Fluid

On the basis of Navier-Stockes equation and convection-diffusion equation, combined with surface tension and penetration models, the equations of moment and mass transfer between bubble and the ambient non-Newtonian liquid were established. The formation of a single bubble from a submersed nozzle of 1.0 mm diameter and the mass transfer from an artificially fixed bubble into the ambient liquid were simulated by the volume-of-fluid （VOF） method. Good agreement between simulation results and experimental data confirmed the validity of the numerical method. Furthermore, the concentration distribution around rising bubbles in shear thinning non-Newtonian fluid was simulated. When the process of a single ellipsoidal bubble with the bubble deformation rate below 2.0 rises, the concentration distribution is a single-tail in the bubble＇s wake, but it is fractal when thebubble deformation rate is greater than 2.0. For the overtaking of two in-line rising bubbles, the concentration distribution area between two bubbles broadens gradually and then coalescence occurs. The bifurcation of concentration distribution appears in the rear of the resultant bubble.

Analytical solutions to the Navier-Stokes equations for non-Newtonian fluid

The pressureless Navier-Stokes equations for non-Newtonian fluid are studied. The analytical solutions with arbitrary time blowup, in radial symmetry, are constructed in this paper. With the previous results for the analytical blowup solutions of the N-dimensional （N ≥ 2） Navier-Stokes equations, we extend the similar structure to construct an analytical family of solutions for the pressureless Navier-Stokes equations with a normal viscosity term （μ（ρ）｜ u｜^α u）.

Hydrothermal analysis of non-Newtonian fluid flow(blood)through the circular tube under prescrib e d non-uniform wall heat flux

The present article aims to investigate the Graetz-Nusselt problem for blood as a non-Newtonian fluid obeying the power-law constitutive equation and flowing inside the axisymmetric tube subjected to nonuniform surface heat flux.After the flow field is determined by solving the continuity and the momentum equations,the energy equation is handled by employing the separation of variables method.The resulting Eigen functions and Eigen values are numerically calculated using MATLAB built-in solver BVP4C.The analysis is first conducted for the situation of constant heat flux and subsequently generalized to apply to the case of sinusoidal variation of wall heat flux along the tube length,using Duhamel’s Theorem.Furthermore,an approximate analytic solution is determined,employing an integral approach to solve the boundary layer equations.With respect to the comparison,the results of approximate solution display acceptable congruence with those of exact solution with an average error of 7.4%.Interestingly,with decreasing the power-law index,the discrepancy between the two presented methods significantly reduces.Eventually,the influences of the controlling parameters such as surface heat flux and power-law index on the non-Newtonian fluid flow’s thermal characteristics and structure are elaborately discussed.It is found that switching from constant wall heat flux to non-uniform wall heat flux that sinusoidally varies along the tube length significantly improves the simulation’s accuracy due to the better characterization of the heat transport phenomenon in non-Newtonian fluid flow through the tube.In the presence of sinusoidally varying wall heat flux with an amplitude of 200 W/m 2 and when the power-law index is 0.25,the maximum arterial wall temperature is found to be about 311.56 K.

Diffusion of Amino Acids in non-Newtonian Fluids

The amino acids are necessarily nutritious components, their diffusions in body fluid and blood that belong to typical non-Newtonian fluid are of virtual importance to control the diffusive process and help clinical treatment. In this article, a holographic interferometer has been adopted to measure the diffusivity of amino acids in non-Newtonian fluid with the use of real-time holographic interference technique. In order to prove the reliability of the experimental instrument, the diffusivities of sucrose aqueous solution at 298.15K were determined. The meas- ured result displays a satisfactory accuracy of the apparatus used. Furthermore, the diffusion coefficients of glynine, L-serine, L-threonine and L-valine in polyacrylamide （PAM） aqueous solution at 298.15K were measured, respec- tively. The experimental data were fitted by a newly proposed correlation equation based on Li＇s predictive model. The calculating results by the present model are at considerably good agreement with experimental values, and the maximum average deviation is only 0.5%.

H^2-regularity random attractors of stochastic non-Newtonian fluids with multiplicative noise

In this paper, the authors study the long time behavior of solutions to stochastic non-Newtonian fluids in a two-dimensional bounded domain, and prove the existence of H2-regularity random attractor.

Effect of thermal conductivity on heat transfer for a power-law non-Newtonian fluid over a continuous stretched surface with various injection parameters

The two-dimensional non-Newtonian steady flow on a power-law stretched surface with suction or injection is studied. Thermal conductivity is assumed to vary as a linear function of temperature. The transformed governing equations in the present study are solved numerically using the Runge-Kutta method. Through a comparison, results for a special case of the problem show excellent agreement with those in a previous work. Two cases are considered, one corresponding to a cooled surface temperature and the other to a uniform surface temperature. Numerical results show that the thermal conductivity variation parameter, the injection parameter, and the power-law index have significant influences on the temperature profiles and the Nusselt number.

THE NUMERICAL SIMULATION OF TURBULENT FLOWS OF NEWTONIAN AND A SORT OF NON-NEWTONIAN FLUID IN 180-DEGREE SQUARE SECTIONED BEND

Using k- model of turbulence and measured wall functions, turbulent flows of Newtonian (pure water) andasort of non-Newtonian fluid (dilute, drag-reduction solution of polymer) in a 180-degree curved bend were simulated numerically. The calculated results agreed well with the measured velocity profiles. On the basis of calculation and measurement, appropriateness of turbulence model to complicated flow in which the large-scale vortex exists was analyzed and discussed.

Diffusion Coefficients of L-Arginine in Non-Newtonian Fluid

L-Arginine is an important component of amino acid injection. Its diffusion in body fluid and blood is of key importance to understand drug diffusion and drug release. As a fundamental demand for study and being a considerably valuable reference for application, in this study, the diffusion coefficients of L-arginine in polyacrylamide（PAM） aqueous solution used as non-Newtonian fluid similar to blood and body fluid were measured using a holographic interferometer. The effects of interaction among molecules and solution concentration on diffusion were analyzed and discussed, respectively. Based on the obstruction-scaling model, a novel modified model was presented for predicting diffusivity of solute in non-Newtonian fluid. Good agreement was achieved between the calculated value and the experimental data.

The size-dependent elastohydrodynamic lubrication contact of a coated half-plane with non-Newtonian fluid

Based on the couple-stress theory,the elastohydrodynamic lubrication(EHL)contact is analyzed with a consideration of the size effect.The lubricant between the contact surface of a homogeneous coated half-plane and a rigid punch is supposed to be the non-Newtonian fluid.The density and viscosity of the lubricant are dependent on fluid pressure.Distributions of film thickness,in-plane stress,and fluid pressure are calculated by solving the nonlinear fluid-solid coupled equations with an iterative method.The effects of the punch radius,size parameter,coating thickness,slide/roll ratio,entraining velocity,resultant normal load,and stiffness ratio on lubricant film thickness,in-plane stress,and fluid pressure are investigated.The results demonstrate that fluid pressure and film thickness are obviously dependent on the size parameter,stiffness ratio,and coating thickness.

PERTURBATION SOLUTION OF NON-NEWTONIAN FLUID AXIAL LAMINAR FLOW THROUGH ECCENTRIC ANNULI

Using the perturbation method, the axial laminar flow of Non-Newtonian fluid through an eccentric annulus is studied in the present paper. The relative eccentricity e is taken as a perturbation parameter, and the first order perturbation solutions of the problem, such as velocity field, limit velocity and pressure gradient, are all obtained.