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.

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.

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.

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.

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 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.

Spray Atomization and Structure of Supersonic Liquid Jet with Various Viscosities of Non-Newtonian Fluids

These experimental investigations are designed to study shock wave characteristics and spray structure. Supersonic liq- uid jets injected into ambient fields are empirically studied using projectile impacts in a two-stage light gas gun. This study looks primarily at the design of the nozzle assembly, the tip velocity of the high speed jet, the structure of the spray jet and the shock wave generation process. The supersonic liquid jets were visualized using an ultra high-speed camera and the schlieren system for visualization to quantitatively analyze the shock wave angle. The experimental re- sults with straight cone nozzle types and various non-Newtonian fluid viscosities are presented in this paper. The effects of nozzle geometry on the jet behavior are described. The characteristics of the shock wave generation and spray jet structure were found to be significantly related to the nozzle geometry. The expansion gases accelerated the projectile, which had a mass of 6 grams, from 250 m/s. As a result, it was found that the maximum jet velocity appeared in the liquid jet with high viscosity properties. Supersonic liquid jets, which occurred at the leading edge the shock waves and the compression waves in front of the jets, were observed. Also, the shock waves significantly affected the atomization process for each spray droplet.

HEAT TRANSFER STUDIES OF HIGHLY VISCOUS NON-NEWTONIAN FLUIDS IN VERTICAL TUBES BY FINITE ELEMENT METHOD

A numerical method capable is developed for handling steady laminar flow and heat trans-fer of a highly viscous power-law fluid whose density,viscosity,specific heat and thermalconductivity,vary with temperature.The governing equations are found to be continuity,monmentumand energy expressions.Important effects such as varying viscosity,natural convection and viscousdissipation are incorporated in the theoretical model.These equations are being attracted by employing a decoupled finite element method.Galerkin’sprinciple is used to handle the momentum and continuity equations.Consistent(SU/PG)andnon-consistent(SU)streamline upwind methods are employed for the energy equation.Comparisonof calculated results and experimental data shows good agreement.Similar results are obtained withSU and SU/PG methods.Velocity and temperature profiles which provide insights into the processare also given.

Study on Non-Newtonian Behaviors of Lennard-Jones Fluids via Molecular Dynamics Simulations

Using nonequilibrium molecular dynamics simulations, we study the non-Newtonian rhe-ological behaviors of a monoatomic fluid governed by the Lennard-Jones potential. Both steady Couette and oscillatory shear flows are investigated. Shear thinning and normal stress effects are observed in the steady Couette flow simulations. The radial distribution function is calculated at different shear rates to exhibit the change of the microscopic struc- ture of molecules due to shear. We observe that for a larger shear rate the repulsion between molecules is more powerful while the attraction is weaker, and the above phenomena can also be confirmed by the analyses of the potential energy. By applying an oscillatory shear to the system, several findings are worth mentioning here： First, the phase difference between the shear stress and shear rate increases with the frequency. Second, the real part of complex viscosity first increases and then decreases while the imaginary part tends to increase mono- tonically, which results in the increase of the proportion of the imaginary part to the real part with the increasing frequency. Third, the ratio of the elastic modulus to the viscous modulus also increases with the frequency. These phenomena all indicate the appearance of viscoelasticity and the domination of elasticity over viscosity at high oscillation frequency for Lennard-Jones fluids.

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.

Effects of impingement and friction of swirling air stream on prefilming airblast atomization of non-Newtonian fluids

Liquids to be broken up using a prefilming airblast atomizer are usually Newton liquids with relatively low viscosities.While in some industrial processes,such as spray drying,liquids to be atomized are high concentration suspensions or non-Newtonian fluids with high viscosities.In this paper,non-Newtonian fluids with viscosity up to 4.4 Pa·s were effectively atomized using a specially designed prefilming airblast atomizer.The atomizer enabled liquid to extend to a thickness-adjustable film and forced the atomizing air stream to swirl with 30° or 45° through gas distributors with spiral slots.The liquid film was impinged by the swirling air stream resulting in the disintegration of the film into drops.Drop sizes were measured using a laser diffraction technique.An improved four-parameter mathematical model was established to relate the Sauter mean diameter of drops to the atomization conditions in terms of power dependencies on three dimensionless groups:Weber number,Ohnesorge number and air liquid mass ratio.The friction on the surface of the liquid film made by swirling air stream played an important role in the prefilming atomization at the conditions of low air velocity and low liquid viscosity.In this case,the liquid film was disintegrated into drops according to the classical wavy-sheet mechanism,thus thinner liquid films and high swirl levels of the atomizing air produced smaller drops.With the increase of the air velocity and the liquid viscosity,the effect of the friction on the prefilming atomization relatively weakened,whereas the impingement on the liquid film made by atomizing air stream in a direction normal to the liquid film and corresponding momentum transfer gradually strengthened and eventually dominated the disruption of liquid into drops,which induced that the initial thickness of the liquid film and the swirl of atomizing air stream exercised a minor influence on the drop sizes.

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 liddriven semi-circular cavity affected by the presence of the adiabatic block at its geometric center for twodimensional,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.

Modified Model of Bubble Formation in Non-Newtonian Fluids

Based on the comprehensive forces balance model, a modified model of the formation of a single bub-ble in non-Newtonian fluid under constant flowrate was developed by taking account of the effect of the ingoing gas through orifice as well as its variation on the radial expansion of bubble. The modified model involves the radial expansion equation of bubble surface and the forces balance equation in vertical direction of the bubble respec-tively. The shape variation of bubbles formed in polyacrylamide (PAM) aqueous solutions under various conditions was predicted numerically. The practical formation of bubbles was real-time visualized and recorded by a CCD camera and a computer by means of a special laser image measurement system. Results show that the predicted shapes of the bubbles by the present model agree well with experimental observation.

A three-dimensional immersed boundary method for non-Newtonian fluids

Fluid-structure-interaction （FSI） phenomenon is common in science and engineering. The fluidinvolved in an FSI problem may be non-Newtonian such as blood. A popular framework for FSIproblems is Peskin’s immersed boundary （IB） method. However, most of the IB formulations arebased on Newtonian fluids. In this letter, we report an extension of the IB framework to FSIinvolving Oldroyd-B and FENE-P fluids in three dimensions using the lattice Boltzmann approach.The new method is tested on two FSI model problems. Numerical experiments show that themethod is conditionally stable and convergent with the first order of accuracy.

ANALYTICAL SOLUTIONS FOR EQUATIONS OF UNSTEADY FLOW OF NON-NEWTONIAN FLUIDS IN TUBE

This paper presents analytieal solutions to the partial differential equations for unsteady flow of the second-order fluid and Maxwell fluid in tube by using the integral transform method. It can be used to analyse the behaviour of axial velocity and shear stress for unsteady flow of nun-Newtonian visco-elastie fluids in tube, and to provide a theoretical base for the projection of pipe-line engineering.

A Transient Multidimensional CFD Approach to the Analysis of a Control Valve Using Non-Newtonian Fluids

In this paper the flow through a control directional valve is studied by means of a CFD （computational fluid-dynamics） analysis under transient operating conditions. The mesh motion is resolved on a time basis as a function of the external actuation system In the analysis, an open source fluid-dynamics code is used and both cavitation and turbulence are accounted for in the modeling. Moreover, the numerical model of the working fluid is modified in order to account also for the non-Newtonian fluids. The effects of the shear rate on the shear stress are accounted for both by using experimental measurements and correlations available in literature, such as the Herschel-Bulkley model. The analysis determines the performance of the control directional valve under different operating conditions when using either Newtonian or non-Newtonian fluids. In particular, the discharge coefficient, the recirculating regions, the flow acceleration angle and the pressure and velocity fields are investigated.

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.