Nonequilibrium steady state of critical fluids under shear flow: A renormalization group approach

Abstract

Renormalization group method is applied to a new situation, that is, to critical fluids in the presence of uniform shear flow. As the critical point is approached, the equilibrium correlation length ξ exceeds a new length k c −1 associated with the rate of shear. Then the rate of shear can no longer be treated in the usual linear response scheme and the system crosses over into a new unexplored regime of strong shear. The RG recursion equations are found to be not separable into dynamic and static parts in contrast to the usual cases in critical dynamics. Here distortion and suppression of long wavelength fluctuations ( k < k c ) by the flow become essential, and the following unexpected features are encountered in the steady state: (i) Order parameter fluctuations with k < k c are highly anisotropic but are suppressed on the average below their equilibrium levels. As a consequence, the phase transition aquires the mean field character. (ii) The spatial correlation function is also highly anisotropic and is long-ranged along the direction of flow. This means that critical fluctuations with size greater than k c −1 are elongated along the direction of flow. (iii) Kinetic coefficients are independent of the reduced temperature, but depend on the rate of shear, and display a weak anisotropy. (iv) The critical temperature is lowered and the equation of state and the interfacial profile assume the mean field forms. (v) The critical exponents are given by the mean field values.