Rotating Couette Flow of a Binary Liquid Mixture

Abstract

Impulsively started, rotating Couette flow of a binary, perfect solution is discussed for the purpose of exhibiting possible multifluid phenomena. It is shown that inhomogeneity due to baro-diffusion can give rise to phenomena which are commonly thought of as rheological effects.

Stability of circular Couette flow of binary mixtures

“…I n terms of mass fractions, we have PbRg* log p = [a log pa + f;b log 7are the viscosities of the two pure components and 5, and gb For specific mixtures, a polynomial correction in powers of G* can be added to (8) to give a better fit. Kulinski (1966) gave an example of this for a waterglycerol mixture.…”

“…However, since viscosity is dependent on concentration, the flow field will be concentration-dependent. Equations (15) and (16) were integrated numerically, and the results compare favourably with Kulinski (1966) when the notation is adjusted. We have chosen the average concentration of the mixture, 6' , rather than the concentration at the inner cylinder, as the controlling parameter.…”

“…Yih 1965) neglected mass diffusivity. Kulinski (1966), in his analysis of the transient Couette flow problem of a heterogeneous fluid, compares the short time scale required for establishing the velocity profile to the long mass diffusion scale required for the final concentration profile.…”

“…(27 1 cannot be satisfied because of the nature of the singular perturbation implied by e + 0. However, the conditions that c = 0 at r = RJR, and 1 are satisfied by (23a),and Kulinski (1966) shows that ( 2 8 ) is satisfied to order [Co( 1 ) -Co(R,/R,)] in this case. The calculations shown in figure 1 illustrate that this is adequate.…”

“…Essentially, the heavier component tends to migrate towards the outer cylinder and a concentration gradient is developed across the annulus. The steady-state and transient solutions of this problem have been reported by Kulinski (1966) but, to date, no quantitative analysis of the stability of such a flow has been attempted. One may say that the presence of the heavier fluid on the outside is The interest in heterogeneous fluid flow problems with either W .…”