NEWTONIAN FLUID SPHERE WITH RIGID OR MOBILE INTERFACE IN A SHEAR-THINNING LIQUID: DRAG AND MASS TRANSFER

The drag force and the mass transfer rate of a Newtonian fluid sphere, having mobile or rigid interface, moving in a power law fluid, are obtained by an approximate solution of equations of motion in the creeping flow regime. It is shown that both the drag and mass transfer increase as the flow index of the external fluid decreases.

The increase of drag due to the pseudoplastic anomaly is more significant at large viscosity ratio parameter. The results obtained are in good agreement with available experimental data and with those analyses based on variational principle when the non-Newtonian flow behavior is not very pronounced.

Also, the predicted mass transfer rates are in good agreement with the trends presented in the literature. Unlike in the case of drag force, the effect of the pseudoplastic anomaly on mass transfer rate is more pronounced for low values of the viscosity ratio parameter. The analysis was extended to include the case when the surface of the sphere was immobilized by surface-active contaminants.     

DRAG AND MASS TRANSFER IN SLOW NON-NEWTONIAN FLOWS OVER AN ENSEMBLE OF NEWTONIAN SPHERICAL DROPS OR BUBBLES

An approximate solution for the slow motion of an ensemble of spherical drops through a power law fluid is obtained using Happel's free-surface cell model. It is shown that the drag coefficient decreases with decrease of the flow index and that this reduction is more significant at low voidage and large viscosity ratio parameter. The effect of the pseudoplastic anomaly on the mass transfer rate is more pronounced at low voidage for large values of viscosity ratio parameter, unlike the case of a single spherical drop

The present analysis covers the whole range of values of viscosity ratio parameter from infinity (an assemblage of solid spheres) to zero (a swarm of bubbles) and reduces to the solutions for those cases already known

The results for the motion of an ensemble of spherical drops also provide the basis for proposing a tentative expression for the expansion of liquid-liquid fluidized bed at low Reynolds number.     

The effect of surfactant on terminal velocity of and mass transfer from a fluid sphere in a non-newtonian fluid

The effect of interfacial tension gradients on creeping flow past a fluid sphere (bubble or drop) in a non-Newtonian fluid is investigated. The drag force and the Sherwood number for contaminated fluid spheres moving in a non-Newtonian fluid are obtained by an approximate solution of equations of motion in the creeping flow regime. It has been found that surface-active agents decrease both the terminal velocity and the mass transfer rate. The influence of the flow index of the power-law on both the drag coefficient and the Sherwood number is superimposed over the influence of the interfacial tension gradient. Comparisons between the present analysis and the available experimental data in the literature show reasonable agreement for the terminal velocity and the Sherwood number.     

减阻型纳米流体在圆管内的流动和换热特性

实验测定了在Reynolds数4000～16000范围内,质量分数0～0.5%的石墨、多壁碳纳米管、Al₂O₃、Cu、Al、Fe₂O₃、Zn纳米粒子加入到100～400 mg·kg^-1浓度的十六烷基三甲基氯化铵(CTAC)减阻剂中所制备的减阻型纳米流体的摩擦阻力系数和对流传热系数。结果表明:在CTAC中加入水杨酸钠(NaSal)与去离子水所配制的减阻剂具有一定的稳定性和很强的减阻特性,当减阻剂浓度为200 mg·kg^-1时其减阻特性最优。石墨纳米粒子在增强对流换热和减少流动阻力方面具有较佳的综合性能,当石墨纳米颗粒质量分数为0.4%时,其综合性能因子K是去离子水的5倍。最后给出了减阻型石墨纳米流体在圆管内的流动阻力和换热关联式,其计算值和实验值吻合良好。     

Mass transfer from a contaminated fluid sphere

The unsteady mass transfer from a contaminated fluid sphere moving in an unbounded fluid is examined numerically for unsteady‐state transfer. The effect of the interface contamination and the flow regime on the concentration profiles, inside and outside a fluid sphere, is investigated for different ranges of Reynolds number (0 < Re < 200) and Peclet number (0 < Pe < 10⁵), viscosity ratio between the dispersed phase and the continuous phase (0 < κ < 10), and the stagnant‐cap angle (0° < θ_cap < 180°). It was found that the stagnant‐cap angle significantly influences the mass transfer from the sphere to a surrounding medium. For all Peclet and Reynolds numbers and κ, the contamination reduces the mass transfer flux. The average Sherwood number increases with an increase of stagnant‐cap angle and reaches a maximum equal to the average one for a clean fluid sphere at low viscosity ratio and large Peclet numbers. A predictive equation for the Sherwood number is derived from these numerical results. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

MOTION OF A CIRCULATING POWER-LAW DROP TRANSLATING THROUGH NEWTONIAN FLUIDS AT INTERMEDIATE REYNOLDS NUMBERS

The equations of motion for the flow of a power-law fluid sphere in a Newtonian continuous phase have been approximately satisfied by Galerkin's method: External and internal stream functions have been obtained for the following ranges of variables: 10-50 for Re₀, 0.1-1000 for the viscosity ratio parameters, X, and 0.6-1.0 for the dispersed phase power-law index, n_i,. It is predicted that pseudoplasticity in the dispersed phase causes a reduction in the circulation within the drop and that it has a minor effect on the drag coefficients and the rates of mass transfer in the continuous phase     

MOTION OF AND MASS TRANSFER FROM AN ASSEMBLAGE OF SOLID SPHERES MOVING IN A NON-NEWTONIAN FLUID AT HIGH REYNOLDS NUMBERS

An approximate solution for the motion of an assemblage of solid spheres moving in a power-law fluid in the high Reynolds number region is obtained using a combination of Happel's free-surface cell model and the boundary layer theory. It is theoretically predicted that the drag coefficient will decrease with the increase of the shear-thinning anomaly. The results of the present analysis are in reasonably good agreement with the available experimental data for fixed and fluidized beds. The influence of the non-Newtonian behavior on the mass transfer rate from an assemblage of solid spheres is also discussed.     

MOTION OF AND MASS TRANSFER FROM AN ASSEMBLAGE OF SOLID SPHERES MOVING IN A NON-NEWTONIAN FLUID AT HIGH REYNOLDS NUMBERS

An approximate solution for the motion of an assemblage of solid spheres moving in a power-law fluid in the high Reynolds number region is obtained using a combination of Happel's free-surface cell model and the boundary layer theory. It is theoretically predicted that the drag coefficient will decrease with the increase of the shear-thinning anomaly. The results of the present analysis are in reasonably good agreement with the available experimental data for fixed and fluidized beds. The influence of the non-Newtonian behavior on the mass transfer rate from an assemblage of solid spheres is also discussed.     

Mass transfer from spheres submerged in Newtonian and non-Newtonian fluids

Mass transfer from spheres immersed in Newtonian and power-law fluid flows in the high Reynolds number region is discussed using a modified penetration model. By defining appropriate characteristic velocity and length, the proposed model in which a velocity gradient at the transfer surface is taken account of can be used to evaluate the rate of mass transfer from a sphere in complicated practical flow situations. The proposed model compares reasonably well with previously reported experimental data and correlations for mass transfer from a sphere in a fluid flowing at uniform approach velocity, in a fixed or fluidised bed, and in a stirred tank. Futhermore, good agreement is found between the model and the available experimental data and correlation for mass transfer from a rotating sphere.     

A multiscale mass transfer model for gas-solid riser flows: Part II—Sub-grid simulation of ozone decomposition

This article is to test the EMMS-based multiscale mass transfer model through computational fluid dynamics (CFD) simulation of ozone decomposition in a circulating fluidized bed (CFB) reactor. Three modeling approaches, namely types A, B and C, are classified according to their drag coefficient closure and mass transfer equations. Simulation results show that the routine approach (type C) with assumption of homogeneous flow and concentration overestimates the ozone conversion rate, introduction of structure-dependent drag force will improve the model prediction (type B), while the best fit to experimental data is obtained by the multiscale mass transfer approach (type A), which takes into account the sub-grid heterogeneity of both flow and concentration. In general, multiscale behavior of mass transfer is more distinct especially for the dense riser flow. The fair agreement between our new model with literature data suggests a fresh paradigm for the CFB related reaction simulation.     

Effect of the viscosity ratio on mass transfer from a fluid sphere at low to very high Peclet numbers

The effect of the viscosity ratio on mass transfer from a fluid sphere is examined in this paper. Numerical solutions of the Navier-Stokes equations off motion and the equations of mass transfer have been obtained for the unsteady state transfer from a fluid sphere moving in an unbounded fluid medium of different viscosity. The effects of the viscosity ratio and the flow on the concentration profiles were investigated for Reynolds number, viscosity ratio and Péclet number ranges of 0?Re?400, 0?κ?1000 and , respectively. The local and average Sherwood numbers are also presented graphically. The steady state results show that the average Sherwood number is increasing as Peclet number increases for a fixed viscosity ratio. However, for a fixed Peclet number, the average Sherwood number is decreasing as the viscosity ratio increases and reaches a limit value corresponding to the average Sherwood number for a solid spherical particle. From the numerical results, a predictive equation for the Sherwood number in terms of the Peclet number, the Reynolds number and the viscosity ratio is derived.     

Drag and mass transfer in a creeping flow of a carreau fluid over drops or bubbles

Estimates for the upper bound on the drag coefficient for a single drop or bubble or a swarm of drops or bubbles translating in a Carreau fluid are obtained using variational principles. The effects of a wide range of shear thinning properties, holdup and viscosity ratios on drag and mass transfer rate are discussed. Recently published predictions of approximate analytical solutions are verified and found to be reasonable if shear thinning behaviour is not pronounced.     

Hydrodynamic Model for Horizontal Two‐phase Flow Through Porous Media

A unidirectional, two‐fluid model based on the volume‐average mass and momentum balance equations was developed for the prediction of two‐phase pressure drop and external liquid hold‐up in horizontally positioned packed beds experiencing stratified, annular and dispersed bubble flow regimes. The so‐called slit model drag force closures were used for the stratified and annular flow regimes. In the case of dispersed bubble flow regime, the liquid‐solid interaction force was formulated on the basis of the Kozeny‐Carman equation by taking into account the presence of bubbles in reducing the available volume for the flowing liquid. The gas‐liquid interaction force was evaluated by using the respective solutions of drag coefficient for an isolated bubble in viscous and turbulent flows. The proposed drag force expressions for the different flow patterns occurring in the bed associated with the two‐fluid model resulted in a predictive method requiring no adjustable parameter to describe the hydrodynamics for horizontal two‐phase flow in packed beds.     

CaCl_2配位PA6/甲酸溶液的流变性能研究

将相对黏度(ηr)为17.3～22.7的聚酰胺6(PA6)溶于甲酸中制备干法纺丝溶液,加入CaCl2作为配位剂,研究了溶液浓度、CaCl2/PA6配位比、PA6的ηr及溶液温度等对纺丝溶液流变性能的影响。结果表明:经CaCl2配位后的PA6/甲酸溶液属于假塑性流体,具有明显的非牛顿流体行为;溶液的表观黏度随PA6的ηr及溶液浓度的升高而升高,随温度升高而降低,CaCl2/PA6配位比为0.12～0.20对其影响不大;随着PA6的ηr及溶液浓度的增加,溶液的非牛顿指数减小,结构黏度指数增大;PA6的ηr约18.0,溶液中PA6质量分数控制在13%～18%,溶液可纺性较好;溶液的黏流活化能随着PA6的ηr的增加而增加。     

Drag on individual cubic assemblies of spheres in non-newtonian tube flow

An obstacle in modeling aseptic processing of particulate foods is the lack of a reliable estimator for the drag force of the non-Newtonian liquid phase on the suspended particles as they flow through the holding tubes of such systems. The objective was to develop an expression for the drag force on cubic assemblies of spherical particles suspended in a pseudoplastic fluid flowing in a tube. An apparatus was assembled for direct measurement of the drag force exerted by solutions of sodium carboxymethyl cellulose (CMC) on the assemblies inside a tube. An empirical drag correction factor, as a function of particle volume fraction (applicable to Stokes' law), was developed.     

THE SLOW MOTION OF A SPHERICAL PARTICLE IN A CARREAU FLUID

The drag on a spherical particle is studied for two limiting cases, namely for the rigid sphere and for the bubble. An approximate solution is found for creeping flow around a particle suspended in a shear-thinning fluid. The three parameter Carreau model is used to represent the suspending liquid. The drag force on the particle for both cases is calculated by a perturbation method around the Newtonian solution in the limit of small Carreau number. The resulting expressions are found to be dependent on the Carreau number and on the power-law index.     

Hydrodynamic drag forces on two porous spheres moving along their centerline

This paper numerically evaluates the hydrodynamic drag force exerted on two highly porous spheres moving steadily along their centerline (sphere #1 and sphere #2) through a quiescent Newtonian fluid over a Reynolds number ranging from 0.1 to 40. At creeping flow limit, the drag forces exerted on both spheres were identical. At higher Reynolds numbers the drag force on sphere #1 was higher than sphere #2, revealing the shading effects produced by sphere #1 on sphere #2. At dimensionless diameter (β, =d_f/2k^0.5, d_f and k are floc diameter and interior permeability, respectively) >20, the spheres can be regarded nonporous. At β<20, the drag forces dropped. At β<2, the drag forces approached “no-spheres” limit. An increased size ratio of two spheres (d_f1/d_f2) would increase the drag force on sphere #1 and reduce that on sphere #2. At increasing β for both spheres, the drag force on sphere #2 was increased because of the more difficult advective flow through its interior, and at the same time the drag was reduced owing to the stronger wake flow produced by the denser sphere #1. The competition between these two effects leads to complicated dependence of drag force on sphere #2 on β value. These effects were minimal when β became low. Two identical spheres could move steadily along their centerline. At higher Reynolds number, the two spheres would move closer because of the incorporation of inertia force. For spheres of different diameters, the sphere # 2 would move faster than sphere #1 regardless of their size ratio and β value. This occurrence yielded efficient coagulation when two porous spheres were moving in-line.     

复合阻燃剂/PET共混物的流变性研究

将复合阻燃剂/PET共混改性,其质量比为2%～7%。研究表明,复合体系为非牛顿假塑性流体,其表观黏度随剪切速率的增大而减小;随着复合阻燃剂含量增大,共混物非牛顿流动指数下降,剪切速率上升,流变性能改善;共混物的黏流活化能为78.3 kJ/mo1,黏温依赖性与普通PET相似。     

Motion of entrained particles in gas streams

Recent work on the drag experienced by an entrained particle in relative motion through a fluid is reviewed. It is shown that fluid turbulence, acceleration, particle shape and orientation, and particle-fluid mass transfer can all have a significant effect on the value of the drag force, particularly when the non-idealities cause a change in the flow pattern around the particle. Conditions under which the drag force can be predicted with certainty are still very limited, and some potentially valuable directions for future research are suggested.     

Modeling of gas–liquid flow in a rotating packed bed using an Eulerian multi-fluid approach

Rotating packed beds (RPBs) are ideal candidates for CO₂ removal from offshore natural gas due to their good mass transfer performance and significant volume savings. This article proposes an Eulerian multi-fluid approach to simulate the gas–liquid flow in RPBs. Three new multiphase drag force models are constructed based on single-phase drag force models for wire mesh packings. Based on the Eulerian multi-fluid approach, a new RPB simulation framework is developed. The predicted results using the new simulation framework with the new drag force models are compared with the experimental data. When using the Kołodziej model and the modified Kołodziej model, the predicted overall liquid holdup shows good agreement with the experimental data with errors less than 20%. In addition, the pressure drop predicted by these three models are reasonable compared with the experimental data. This work lays a foundation for RPB simulation of gas–liquid flow using Eulerian multi-fluid approach.