Akira Onuki

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.

Light scattering by critical fluids under shear flow

Abstract Our theory of critical fluids under shear flow is used to analyze the light scattering experiments of Beysens et al. on a critical fluid mixture flowing through a capillary pipe. The scattered light intensity integrated over frequency, the turbidity, and the transmittency are calculated numerically and found to be in good agreement with the experiments. Various critical amplitudes are also calculated to order ϵ where ϵ = 4 − d, d being the spatial dimensionality of the system. They are found to be considerably different from those near equilibrium in the case of strong shear.

Theory of helium under heat flow near the λ point. I. Interface of He I and He II

A He I-He II interface is shown to exist under heat flow and is studied near the λ point. The temperature in the superfluid region is found to be of the form Tλ −T ∝ Q3/4 if dynamic scaling is assumed, where Tλ is the critical temperature andQ is the heat flow. In the normal region the temperature has a finite gradient. Here we are neglecting a small thermal resistance due to vortices in the superfluid region. In a finite system with size much greater than the correlation length a first-order phase transition occurs as an inverted bifurcation as the temperature at the cooler boundary is lowered slightly below Tλ. Namely, the system will jump from the disordered state to a state in which the two phases are separated by an interface. The theory can be constructed analogously to the theory of superconductors in a magnetic field.

Light scattering by critical fluids in the presence of a uniform shear flow

Abstract Some predictions are made on dynamic light scattering by critical fluids in the presence of a shear flow. A Doppler shift broadening is predicted to occur whenever the scattering vector has a component along the direction of flow.

Non-Newtonian effect and normal stress effect in critical fluids

Abstract The non-newtonian effect and the normal stress effect in classical fluids near critical points under shear flow are considered with the renormalization group method.

Non-newtonian effect and long-range correlation in shear flow in two dimensions

Abstract A steady state of a two-dimensional incompressible fluid with shear flow is considered. The nonlinear (non-newtonian) shear viscosity is obtained and the correlation of velocity field fluctuations is found to become long-ranged.

Flow birefringence in critical fluids

Abstract Large flow birefringence is predicted to occur in critical fluids under flow. This effect seems to be readily measurable with high accuracy.

Langevin equation with multi-Poissonian noise

A general master equation is shown to be equivalent to a Langevin equation whose noise is expressed as a linear superposition of Poissonian random variables (multi-Poissonian noise). As typical examples, a birth and death process and a Boltzmann-Langevin equation are given.

Critical Phenomena under Non-Uniform External Force Fields

Effects of non-uniform external force fields which vary in one direction, say, along the z-axis, on critical phenomena are studied in a general way. Nature of critical phenomena depends crucially on a type of the spectrum of a one-dimensional eigenvalue problem besides the symmetry breaking nature of the force. In particular, if the external potential maintains the symmetry of the order parameter and the lowest eig<cnvalue is isolated, there is a crossover from the d-dimensional bulk critical phenomena to the d -1-dimensional surface critical phenomena. On the other hand, if the external potential breaks the symmetry, a sharp phase transition disappears as for the liquid-gas transition under the gravitational field. The cases with periodic external potentials are also discussed.

Non-newtonian effect near the critical point

Abstract In the presence of a shear flow the order parameter fluctuations are distorted and suppressed by the shear and there appears a new correlation length independent of temperature sufficiently near the critical point.