Time periodic electroosmotic flow of micropolar fluids through microparallel channel

The time periodic electroosmotic flow of an incompressible micropolar fluid between two infinitely extended microparallel plates is studied.The analytical solutions of the velocity and microrotation are derived under the Debye-H(u|¨)ckel approximation.The effects of the related dimensionless parameters,e.g.,the micropolar parameter,the frequency,the electrokinetic width,and the wall zeta potential ratio of the upper plate to the lower plate,on the electroosmotic velocity and microrotation are investigated.The results show that the amplitudes of the velocity and the volume flow rate will drop to zero when the micropolar parameter increases from 0 to 1.The effects of the electrokinetic width and the frequency on the velocity of the micropolar fluid are similar to those of the Newtonian fluid.However,the dependence of the microrotation on the related parameters mentioned above is complex.In order to describe these effects clearly,the dimensionless microrotation strength and the penetration depth of the microrotation are defined,which are used to explain the variation of the microrotation.In addition,the effects of various parameters on the dimensionless stress tensor at the walls are studied.     

The flow of incompressible immiscible fluids between two plates

Summary The flow of layers of different heights of n incompressible immiscible fluids between two plates has been considered and it has been shown that whatever be the number of fluids and whatever be their heights, a unique velocity maximum always exists and a formula for finding the layer in which this maximum occurs has been given. For the particular case of two layers it has been shown that the curve of total flux against the ratio of the heights of the fluids has always a point of inflexion. Further this ratio has been determined so that the fluxes of the two fluids are equal.     

Stagnation-point flow of upper-convected Maxwell fluids

Two-dimensional stagnation-point flow of viscoelastic fluids is studied theoretically assuming that the fluid obeys the upper-convected Maxwell (UCM) model. Boundary-layer theory is used to simplify the equations of motion which are further reduced to a single non-linear third-order ODE using the concept of stream function coupled with the technique of the similarity solution. The equation so obtained was solved using Chebyshev pseudo-spectral collocation-point method. Based on the results obtained in the present work, it is concluded that the well-established but controversial prediction that in stagnation-point flows of viscoelastic fluids the velocity inside the boundary layer may exceed that outside the layer may just be an artifact of the rheological model used in previous studies (namely, the second-grade model). No such peculiarity is predicted to exist for the Maxwell model. For a UCM fluid, a thickening of the boundary layer and a drop in wall skin friction coefficient is predicted to occur the higher the elasticity number. These predictions are in direct contradiction with those reported in the literature for a second-grade fluid.     

Analytical and numerical solutions of electro-osmotically driven flow of a third grade fluid between micro-parallel plates

Electro-osmotic flow of a third grade fluid between micro-parallel plates is considered. The equations of motion are derived and made dimensionless. Approximate analytical solutions are obtained by perturbation techniques. Constant viscosity and temperature dependent viscosity (Reynolds model) cases are treated separately. Numerical solutions of the equations are also obtained. Influences of non-Newtonian parameter, Joule heating effect, viscosity index and electro-kinetic effect on the velocity and temperature profiles are shown. Approximate and numerical solutions are contrasted.     

Exact solution of electroosmotic flow in generalized Burgers fluid

An exact solution is developed for the time periodic electroosmotic flow of a non-Newtonian fluid between the micro-parallel plates. The constitutive equations of a generalized Burgers fluid are used in the mathematical formulation. The resulting problem is solved by a Fourier transform technique. Graphs are plotted and discussed for various emerging parameters of interest.     

Control of homogeneous shear flow of multimode Maxwell fluids

We consider a homogeneous parallel shear flow of a multimode Maxwell fluid. This problem results in a set of ordinary differential equations for the stresses. In this system, we view the shear rate as a control and consider the problem of steering the system to a given state of stress. The objective is to steer the system from given initial stresses to a final state of stress, allowing the shear rate to vary in an arbitrary fashion. We show that this problem is related to a calculus of variations problem. For the case of two modes, we obtain a characterization of the set of achievable streses.     

Pressure effects on electroosmotic flow of power-law fluids in rectangular microchannels

In this paper, the fully developed electroosmotic flow of power-law fluids in rectangular microchannels in the presence of pressure gradient is analyzed. The electrical potential and momentum equations are numerically solved through a finite difference procedure for a non-uniform grid. A complete parametric study reveals that the pressure effects are more pronounced at higher values of the channel aspect ratio and smaller values of the flow behavior index. The Poiseuille number is found to be an increasing function of the channel aspect ratio for pressure assisted flow and a decreasing function of this parameter for pressure opposed flow. It is also observed that the Poiseuille number is increased by increasing the zeta potential. Furthermore, the results show that an increase in the flow behavior index results in a lower flow rate ratio, defined to be the ratio of the flow rate to that of a Newtonian fluid at the same conditions. Moreover, whereas the flow rate ratio in the presence of an opposed pressure gradient is smaller than that of a favorable pressure force for shear thinnings, the opposite is true for shear-thickening fluids.     

Unsteady flow of viscoelastic fluid between two cylinders using fractional Maxwell model

The unsteady flow of an incompressible fractional Maxwell fluid between two infinite coaxial cylinders is studied by means of integral transforms.The motion of the fluid is due to the inner cylinder that applies a time dependent torsional shear to the fluid.The exact solutions for velocity and shear stress are presented in series form in terms of some generalized functions.They can easily be particularized to give similar solutions for Maxwell and Newtonian fluids.Finally,the influence of pertinent parameters on the fluid motion,as well as a comparison between models,is highlighted by graphical illustrations.     

Transient free convection flow between two vertical parallel plates

Transient free convection flow between two infinite vertical parallel plates has been investigated and good agreement was found between the results for large values of time and the well known ones for the steady-state problem.     

Viscoplastic flow between two approaching or parallel circular plates

The problem of the flow of a viscoplastic medium between two parallel circular plates in translatory coaxial relative motion is solved. The Bingham model [1] of a viscoplastic medium is assumed. The problem is solved in the inertialess thin layer approximation [2] for arbitrary values of the viscosity coefficient and yield stress.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 9–17, January–February, 1996.     

Numerical solution to the shearing flow of granular materials between two plates

We study the shearing flow of granular materials between two horizontal flat plates where the top plate is moving with a constant speed. The constitutive relation used for the stress is based on the continuum model proposed by Rajagopal and Massoudi (DOE Report, DOE/PETC/TR-90/3, 1990). The material coefficients such as viscosity and normal stress coefficients are based on the model of Boyle and Massoudi (Int. J. Eng. Sci 28 (1990) 1261). The governing equations are non-dimensionalized and the resulting system of non-linear differential equations is solved numerically using finite difference technique.     

Simultaneous convection and radiation in flow between two parallel plates

A numerical solution is described for simultaneous forced convection and radiation in flow between two parallel plates forming ahannel. The front plate is transparent to thermal radiation while the back one is thermally insulated. Analyses for both flow and heat are presented for the case of a non-emitting ‘blackened’ fluid. The governing equations of the stream function and the temperature together with their boundary conditions are presented in non-dimensional expressions. The solution is found to depend on eight dimensionless parameters, namely the ratio of the height of the channel to the distance between the plates, the initial dimensionless temperature, the optical thickness, the absorptivities of both plates, the Reynolds number, the Prandtl number and the heat transfer coefficient from the front plate to the surroundings. The numerical solution is obtained using a finite-difference technique. A study has been made of the effect of the initial temperature of the flow at the channel inlet, the dimensionless loss coefficient from the front plate, the absorptivity of the back plate and the optical thickness, on the temperature distribution in the channel, the heat collection efficiency and the average temperature rise in the channel. Results showed that increasing the optical thickness increases the temperature of the front plate and decreases the temperature of the back plate. Also, increasing the optical thickness increases the efficiency of heat collection, which reaches its maximum asymptotic value at an optical thickness of about 1.5. Moreover, the location of the maximum temperature is found to depend on both the optical thickness and the dimensionless heat loss coefficient from the front plate.     

A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates

The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. A generalized Maxwell model with the fractional calculus was considered. Exact solutions of some unsteady flows of a viscoelastic fluid between two parallel plates are obtained by using the theory of Laplace transform and Fourier transform for fractional calculus. The flows generated by impulsively started motions of one of the plates are examined. The flows generated by periodic oscillations of one of the plates are also studied.     

Rarefied gas shear flow between two movable segments of parallel plates

A study is made of the two-dimensional steady-state rarefied gas flow observed between two parallel plane surfaces of finite and different length when one of the surfaces is fixed and the other moves parallel to itself at a constant velocity, while remaining within the bounds of a given segment with fixed ends (the motion is similar to that of a conveyer belt). This flow can be regarded as a twodimensional counterpart of the classical one-dimensional Couette flow. The corresponding problem is formulated in a rectangular domain for the nonlinear kinetic equation with a model collision operator and is solved by a finite-difference method for various boundary conditions. For simplicity's sake, the flow was studied under conditions such that it can be considered near-isothermal. The gas pressures on each side of the gap formed by the plates may be the same or different. If the pressures on both sides of the gap are equal, then a near-zero-gradient flow develops between the plates. In this case, the greater the plate length, the nearer the flow in the middle of the gap to one-dimensional Couette flow. The end effects are examined, together with the conditions in which the flow in the middle of the domain can be assumed to be practically one-dimensional. In the zero-gradient regime, the system operates, in general, as a pump transferring gas from one side of the gap the other. The ability to pump gas also remains if a small counterpressure exists.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 150–155, May–June, 1995.The work was financially supported by the Russian Foundation for Fundamental Research (project No. 93-013-17928).     

The motion of rodlike particles in the pressure-driven flow between two flat plates

The motion of freely suspended rodlike particles has been observed in the pressure-driven flow between the two flat plates of a Hele Shaw flow cell at low Reynolds numbers. Data are reported for rodlike particles with aspect ratios of 12.0 suspended in a Newtonian fluid for gap thickness to particle length ratios of 3, 6, and 20; and for rodlike particles with aspect ratios between 5 and 8 in a non-Newtonian fluid (79.25 wt.% water, 20.2 wt.% glycerine, and 0.55 wt.% polyacrylamide). For the Newtonian fluid, the time-dependent orientation of the particles near and far from walls was shown to be in quantitative agreement with Jeffery's theory for ellipsoids suspended in a simple shear flow if an effective aspect ratio is calculated from the experimental period of rotation. Particles aligned with the flow direction and less than a particle half-length from a wall interacted irreversibly with the wall. For the non-Newtonian fluid, the timedependent orientation far from a wall was shown to be in qualitative agreement with Leal's theory for a second-order fluid; however, particles that were aligned with the flow direction and were near walls did not rotate.     

Pulsatile electroosmotic flow of a Maxwell fluid in a parallel flat plate microchannel with asymmetric zeta potentials

The pulsatile electroosmotic flow (PEOF) of a Maxwell fluid in a parallel flat plate microchannel with asymmetric wall zeta potentials is theoretically analyzed. By combining the linear Maxwell viscoelastic model, the Cauchy equation, and the electric field solution obtained from the linearized Poisson-Boltzmann equation, a hyperbolic partial differential equation is obtained to derive the flow field. The PEOF is controlled by the angular Reynolds number, the ratio of the zeta potentials of the microchannel walls, the electrokinetic parameter, and the elasticity number. The main results obtained from this analysis show strong oscillations in the velocity profiles when the values of the elasticity number and the angular Reynolds number increase due to the competition among the elastic, viscous, inertial, and electric forces in the flow.     

平行平板间Couette流起动过程的运算微积解

求解平行平板间Couette流的起动过程通常使用分离变量法,得到的速度分布在平板间距趋于无穷时难以逼近Stokes第一问题的解,而两者在物理上却是完全一致的. 本文利用运算微积法和Heaviside算子进行求解,不但解决了这一问题,而且具有运算简单的特点.