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.

Molecular dynamics simulation of the flow mechanism of shear-thinning fluids in a microchannel

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

Natural Convection of a Power-Law Nanofluid in a Square Cavity with a Vertical Fin

The behavior of non-Newtonian power-law nanofluids under free convection heat transfer conditions in a cooled square enclosure equipped with a heated fin is investigated numerically.In particular,the impact of nanofluids,composed of water and Al_(2)O_(3),TiO_(2),and Cu nanoparticles,on heat transfer enhancement is examined.The aim of this research is also to analyze the influence of different parameters,including the Rayleigh number(Ra=10^(4)-10^(6)),nanoparticle volume fraction(φ=0%-20%),non-Newtonian power-law indexes(n=0.6-1.4),and fin dimensions(Ar=0.3,0.5,and 0.7).Streamlines and isotherms are used to depict flow and related heat transfer characteristics.Results indicate that thermal performance improves with increasing Rayleigh number,regardless of the nanoparticle type or nanofluid rheological behavior.This suggests that the buoyancy force has a significant impact on heat transfer,particularly near the heat source.The Nusselt number is more sensitive to variations in Cu nanoparticle volume fractions compared to Al₂O₃and TiO₂.Moreover,the average Nusselt numbers for power-law nanofluids with n<1(n>1)are greater(smaller)than for Newtonian fluids due to the decrease(increase)in viscosity with increasing(decreasing)shear rate,at the same values of Rayleigh number Ra owing to the amplification(attenuation)of the convective transfer.Notably,the most substantial enhancement is observed with Cu-water shear-thinning nanofluid,where the Nusselt number increases by 136%when changing from Newtonian to shear thinning behavior and by 154.9%when adding 16%nanoparticle volume fraction.Moreover,an even larger increase of 57%in the average Nusselt number is obtained on increasing the fin length from 0.3 to 0.7.

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.

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.

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.

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.

ON INTEGRABILITY UP TO THE BOUNDARY OF THE WEAK SOLUTIONS TO A NON-NEWTONIAN FLUID

This work consider boundary integrability of the weak solutions of a non-Newtonian compressible fluids in a bounded domain in dimension three, which has the constitutive equartions as ■The existence result of weak solutions can be get based on Galerkin approximation. With the linear operator B constructed by BOGOVSKII, we show that the density ■is square integrable up to the boundary.

GLOBAL EXISTENCE OF STRONG SOLUTIONS OF NAVIER-STOKES EQUATIONS WITH NON-NEWTONIAN POTENTIAL FOR ONE-DIMENSIONAL ISENTROPIC COMPRESSIBLE FLUIDS

The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals. We prove two global existence results on strong solutions of isentropic compressible Navier-Stokes equations. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition.

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.

STABILITY OF BOUNDARY LAYER TO AN OUTFLOW PROBLEM FOR A COMPRESSIBLE NON-NEWTONIAN FLUID IN THE HALF SPACE

This paper investigates the large-time behavior of solutions to an outflow problem for a compressible non-Newtonian fluid in a half space. The main concern is to analyze the phenomena that happens when the compressible non-Newtonian fluid blows out through the boundary. Based on the existence of the stationary solution, it is proved that there exists a boundary layer(i.e., the stationary solution) to the outflow problem and the boundary layer is nonlinearly stable under small initial perturbation.

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.

A novel predictive model of drag coefficient and settling velocity of drill cuttings in non-Newtonian drilling fluids

In oil and gas well drilling operations,it is of great significance to accurately predict the drag coefficient and settling velocity of drill cuttings in non-Newtonian drilling fluids.In this paper,the free-falling of 172 groups of spheres and 522 groups of irregular-shaped sand particles in Newtonian/non-Newtonian fluids were investigated experimentally.It was found that the drag coefficient calculated based on Newtonian correlations can result in a significant error when the particle settles in the non-Newtonian fluid.Therefore,predictive models of drag coefficient were established respectively for different types of fluids.The validity of the proposed drag coefficient model of spheres was verified by comparing it with the previous works.On this basis,the drag coefficient model of irregular-shaped sand particles was established by introducing a shape factor.The models do not use the shape factor that requires detailed threedimensional shape and size information.Instead,two-dimensional geometric information(circularity)is obtained via image analysis techniques.The present new models predict the settling velocity of sand particles in the power-law fluid and Herschel-Bulkley fluid accurately with a mean relative error of5.03%and 6.74%,respectively,which verifies the accuracy of the model.

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%.

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.

ANALYTICAL SOLUTION OF FLOW OF SECOND-ORDER NON-NEWTONIAN FLUIDS THROUGH ANNULAR PIPES

This paper presents an analytical solution to the unsteady flow of the second-order non-Newtonian fluids by the use of intergral transformation method. Based on the numerical results, the effect of non-Newtonian coefficient Hc and other parameters on the flow are analysed. It is shown that the annular flow has a shorter characteristic time than the general pipe flow while the correspondent velocity, average velocity have a ... nailer value for a given Hc. Else, when radii ratio keeps unchanged, the shear stress of inner wall of annular flow will change with the inner radius -compared with the general pipe flow and is always smaller than that of the outer wall.

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.

A Novel Blood Coagulation Measuring Method Based on the Viscoelasticity of Non-Newtonian Fluid

There are complex and perfect coagulation, anticoagulation and fibrinolysis systems in the human body and their fine regulatory mechanisms. Once the coagulation system and its regulatory mechanisms are destroyed, bleeding or thrombosis will occur very soon. In the blood coagulation, the blood viscoelasticity changes. Therefore, the thrombus elasticity measurement technology can be used to continuously monitor the changing blood viscoelasticity in order to study the process of coagulation. The results of the interaction among the various components of the blood can be obtained from coagulation to fibrinolysis by bedside detection. The traditional electromagnetic induction sensors, based on conventional coil inductance, are manufactured complexly, high cost and non-linear. Therefore, this paper proposes a non-Newtonian fluid viscoelasticity measurement method based on the piezoelectric effect. We use the piezoelectric bimorphs with the diameter of 21 mm and the total thickness of 0.38 mm and DSM coupling probes with the length of 3 mm, 5 mm and 7 mm to design the piezoelectric bimorphs driver. The viscoelasticity of different non-Newtonian fluids is tested. The vibration amplitudes of the piezoelectric bimorphs and liquid surfaces range from 0.43 μm to 3.52 μm. Consequently, the feasibility of in vitro detection of thrombus is confirmed in principle and the above scheme is validated theoretically and experimentally, which provides the basis for the measurement of blood viscoelasticity, the in vitro detection of thrombus and the manufacture of blood coagulation instrument.