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.

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.

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.

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.

Bubble Formation in Non-Newtonian Fluids Using Laser Image Measurement System

A self-developed laser image measurement system was established to study the behavior of bubble for- mation at a single orifice in non-Newtonian polyacrylamide(PAAm)solutions.Images of bubbles were captured by a CCD camera and volumes of bubbles were digitally analyzed online.The effects of rheological property of PAAm solution,orifice,reservoir,and gas flowrate on bubble formation were studied experimentally.It is found that the volume of bubble increases with the concentration of PAAm solution,the diameter of the orifice,and the gas flowrate,respectively,whereas little effect of reservoir is observed in experiments.

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.

Dynamics of stochastic non-Newtonian fluids driven by fractional Brownian motion with Hurst parameter H∈(1/4,1/2)

A two-dimensional （2D） stochastic incompressible non-Newtonian fluid driven by the genuine cylindrical fractional Brownian motion （FBM） is studied with the Hurst parameter ∈ （1/4,1/2） under the Dirichlet boundary condition. The existence and regularity of the stochastic convolution corresponding to the stochastic non-Newtonian fluids are obtained by the estimate on the and the identity of the infinite double series spectrum of the spatial differential operator in the analytic number theory. The existence of the mild solution and the random attractor of a random dynamical system are then obtained for the stochastic non-Newtonian systems with ∈ （1/2,1） without any additional restriction on the parameter H.

Free-surface Simulations of Newtonian and Non-Newtonian Fluids with the Lattice Boltzmann Method

This paper describes the application of a three-dimensional lattice Boltzmann method （LBM） to Newtonian and non-Newtonian （Bingham fluid in this work） flows with free surfaces. A mass tracking algorithm was incorporated to capture the free surface, whereas Papanastasiou＇s modified model was used for Bingham fluids. The lattice Boltzmann method was first validated using two benchmarks： Newtonian flow through a square cross-section tube and Bingham flow through a circular cross-section tube. Afterward, the dam-break problem for the Newtonian fluid and the slump test for Bingham fluid were simulated to validate the free-surface-capturing algorithm. The numerical results were in good agreement with analytical results, as well as other simulations, thereby proving the validity and correctness of the current method. The proposed method is a promising substitute for time-consuming and costly physical experiments to solve problems encountered in geotechnical and geological engineering, such as the surge and debris flow induced by a landslide or earthquake.

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.

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.

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.

On energy boundary layer equations in power law non-Newtonian fluids

The hear transfer mechanism and the constitutive models for energy boundary layer in power law fluids were investigated.Two energy transfer constitutive equations models were proposed based on the assumption of similarity of velocity field momentum diffusion and temperature field heat transfer.The governing systems of partial different equations were transformed into ordinary differential equations respectively by using the similarity transformation group.One model was assumed that Prandtl number is a constant,and the other model was assumed that viscosity diffusion is analogous to thermal diffusion.The solutions were presented analytically and numerically by using the Runge-Kutta formulas and shooting technique and the associated transfer characteristics were discussed.

A REMARK ON THE ATTRACTORS OF NON-NEWTONIAN FLUIDS

This paper corrects some mistakes in the proof of absorbing sets theorem of at-tractors of non-Newtonian fluids, and establishes again the existence of bounded absorbing sets.

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.

Boundary layer flow on a moving surface in otherwise quiescent pseudo-plastic non-Newtonian fluids

A theoretical analysis for the boundary layer flow over a continuous moving surface in an otherwise quiescent pseudo-plastic non-Newtonian fluid medium was presented. The types of potential flows necessary for similar solutions to the boundary layer equations were determined and the solutions were numerically presented for different values of power law exponent.

Enhanced mixing efficiency for a novel 3D Tesla micromixer for Newtonian and non-Newtonian fluids

The fabrication of constructs with gradients for chemical,mechanical,or electrical composition is becoming critical to achieving more complex structures,particularly in 3D printing and biofabrication.This need is underscored by the complexity of in vivo tissues,which exhibit heterogeneous structures comprised of diverse cells and matrices.Drawing inspiration from the classical Tesla valve,our study introduces a new concept of micromixers to address this complexity.The innovative micromixer design is tailored to enhance the re-creation of in vivo tissue structures and demonstrates an advanced capability to efficiently mix both Newtonian and non-Newtonian fluids.Notably,our 3D Tesla valve micromixer achieves higher mixing efficiency with fewer cycles,which represents a significant improvement over the traditional mixing method.This advance is pivotal for the field of 3D printing and bioprinting,and offers a robust tool that could facilitate the development of gradient hydrogel-based constructs that could also accurately mimic the intricate heterogeneity of natural tissues.