The internal circulations on internal mass transfer rate of a single drop in nonlinear uniaxial extensional flow

The internal flow of a droplet in the nonlinear extensional flow field will exhibit more than two internal circulations with the variation of nonlinear intensity(E).In this paper,the effect of positions and sizes of internal circulations on internal mass transfer rate of a single spherical droplet in a nonlinear extensional flow field is studied and compared with that in a linear extensional flow field.The simulation results show that when E≥0,there are two symmetrical internal circulations in the droplet,which is the same with that in a linear extensional flow.The limit value of mass transfer rate Sh is 15,which is equal to that in a linear extensional flow,no matter how large E is.When E≤-3/7,the number of internal flow circulation of a droplet increase to four and the transfer rate Sh increases.When E=-1,the maximum internal transfer rate Sh equals 30 which is twice of that in a linear extensional flow.The generation of new flow circulations in droplets and the circulation positions will enhance mass transfer when E≤-3/7,which provides a new idea for enhancing the internal mass transfer rate of droplets.

Temperature Effect on the Conformation Transition of Ultra-high Molecular Weight Polyethylene/Polypropylene Blends Undergoing Continuous Volume Extensional Flow:A Mesoscopic Simulation

Due to the multiformity and complexity of chain conformation under external flow and the challenge of systematically investigating the transient conformation and dynamic evolution process of polymer chains at the molecular level by means of present experimental techniques,a universal description of both chain conformation and dynamics with respect to continuous volume extensional flow(CVEF)is still absent.Taking into account the temperature effect,we performed dissipative particle dynamics(DPD)simulations with the particles corresponding to the repeat units of polymers over a wide temperature range and analyzed the correlation with the conformational properties of ultra-high molecular weight polyethylene/polypropylene(UHMWPE/PP)blend in response to the CVEF.With time evolution,the polymer chains become highly oriented parallel to the flow direction instead of the initial random coiling and self-aggregation.It is found that a high temperature is necessary for more substantial compactness to take place than low temperature.The low-k plateau and low-k peak in structure factor S(k)curves suggest a low degree of conformational diversity and a high degree of chain stretching.It is also concluded that the intra-molecular C-C bond interaction is the main driving force for the dynamics process of the chain conformations undergoing CVEF,where the motion of the alkyl chains is seriously restricted owing to the increase in bond interaction potential,resulting in a reduction of the difference in diffusion rates among alkyl chains.

External mass transfer from/to a single sphere in a nonlinear uniaxial extensional creeping flow

This work systematically simulates the external mass transfer from/to a spherical drop and solid particle suspended in a nonlinear uniaxial extensional creeping flow.The mass transfer problem is governed by three dimensionless parameters:the viscosity ratio(λ),the Peclet number(Pe),and the nonlinear intensity of the flow(E).The existing mass transfer theory,valid for very large Peclet numbers only,is expanded,by numerical simulations,to include a much larger range of Peclet numbers(1≤Pe≤105).The simulation results show that the dimensionless mass transfer rate,expressed as the Sherwood number(5 h),agrees well with the theoretical results at the convection-dominated regime(Pe>103).Only when E>5/4,the simulated Sh for a solid sphere in the nonlinear uniaxial extensional flow is larger than theoretical results because the theory neglects the effect of the vortex formed outside the particle on the rate of mass transfer.Empirical correlations are proposed to predict the influence of the dimensionless governing parameters(λ,Pe,E)on the Sherwood number(Sh).The maximum deviations of all empirical correlations are less than 15%when compared to the numerical simulated results.

EXTENSIONAL FLOW OF BULK POLYMERS STUDIED BY DYNAMIC MONTE CARLO SIMULATIONS

Dynamic Monte Carlo simulations of bulk lattice polymers driven through planar geometries with sequentially converging, parallel and diverging spaces between two neutrally repulsive solid plates are reported. The spatial profiles of polymer velocity and deformation along the course of such a laminar extensional flow have been carefully analyzed. The results appear consistent with experimental observations in literature. In the entrance and exit regions, a linear dependence of chain extension upon the excess velocity has been observed. Moreover, an annexed shear flow and a molecular-dispersion effect are found. The results demonstrate a useful strategy of this approach to study polymer flows and bring new insights into the non-Newtonian-fluid behaviors of bulk polymers in capillary rheometers and micro-fluidic devices.

CONSTITUTIVE EQUATION OF CO-ROTATIONAL DERIVATIVE TYPE FOR ANISOTROPIC-VISCOELASTIC FLUID

A constitutive equation theory of Oldroyd fluid B type,i.e.the co-rotational derivative type,is developed for the anisotropic-viscoelastic fluid of liquid crystalline(LC)polymer.Analyzing the influence of the orientational motion on the material behavior and neglecting the influence,the constitutive equation is applied to a simple case for the hydrodynamic motion when the orientational contribution is neglected in it and the anisotropic relaxation,retardation times and anisotropic viscosi- ties are introduced to describe the macroscopic behavior of the anisotropic LC polymer fluid.Using the equation for the shear flow of LC polymer fluid,the analytical expressions of the apparent viscosity and the normal stress differences are given which are in a good agreement with the experimental results of Baek et al.For the fiber spinning flow of the fluid,the analytical expression of the extensional viscosity is given.

An unsymmetric constitutive equation for anisotropic viscoelastic fluid

A continuum constitutive theory of corotational derivative type is developed for the anisotropic viscoelastic fluid-liquid crystalline （LC） polymers. A concept of anisotropic viscoelastic simple fluid is introduced. The stress tensor instead of the velocity gradient tensor D in the classic Leslie-Ericksen theory is described by the first Rivlin-Ericksen tensor A and a spin tensor W measured with respect to a co-rotational coordinate system. A model LCP-H on this theory is proposed and the characteristic unsymmetric behaviour of the shear stress is predicted for LC polymer liquids. Two shear stresses thereby in shear flow of LC polymer liquids lead to internal vortex flow and rotational flow. The conclusion could be of theoretical meaning for the modern liquid crystalline display technology. By using the equation, extrusion-extensional flows of the fluid are studied for fiber spinning of LC polymer melts, the elongational viscosity vs. extension rate with variation of shear rate is given in figures. A considerable increase of elongational viscosity and bifurcation behaviour are observed when the orientational motion of the director vector is considered. The contraction of extru- date of LC polymer melts is caused by the high elongational viscosity. For anisotropic viscoelastic fluids, an important advance has been made in the investigation on the constitutive equation on the basis of which a seriesof new anisotropic non-Newtonian fluid problems can be addressed.