A phase-field model of Hele-Shaw flows in the high viscosity contrast regime

A one-sided phase-field model is proposed to study the dynamics of unstable interfaces of Hele-Shaw flows in the high viscosity contrast regime. The corresponding macroscopic equations are obtained by means of an asymptotic expansion from the phase-field model. Numerical integrations of the phase-field model in a rectangular Hele-Shaw cell reproduce finger competition with the final evolution to a steady state finger the width of which goes to one half of the channel width as the velocity increases

Canonical phase space approach to the noisy Burgers equation: Probability distributions

We present a canonical phase space approach to stochastic systems described by Langevin equations driven by white noise. Mapping the associated Fokker-Planck equation to a Hamilton-Jacobi equation in the nonperturbative weak noise limit we invoke a {\em principle of least action} for the determination of the probability distributions. We apply the scheme to the noisy Burgers and KPZ equations and discuss the time-dependent and stationary probability distributions. In one dimension we derive the long-time skew distribution approaching the symmetric stationary Gaussian distribution. In the short-time region we discuss heuristically the nonlinear soliton contributions and derive an expression for the distribution in accordance with the directed polymer-replica and asymmetric exclusion model results. We also comment on the distribution in higher dimensions.Comment: 18 pages Revtex file, including 8 eps-figures, submitted to Phys. Rev.

EFFECT OF MIXING CONDITIONS ON FLOCCULATION KINETICS OF WASTEWATERS CONTAINING PROTEINS AND OTHER BIOLOGICAL COMPOUNDS USING FIBROUS MATERIALS AND POLYELECTROLYTES

The application of a combined system of a polyelectrolyte, carboxymethyl cellulose (CMC), and highly fibrillated fibrous materials, cellulose triacetate fibrets (CTF), for the recovery of proteins and other biological compounds from model and actual biological systems has been demonstrated . In the present work, reaction batches were scaled-up to a one-liter agitated vessel, with a standard configuration. The effect of mixing conditions on the adsorption and flocculation process was studied. It was observed that flocculation time was very fast, occurring within the period of polymer addition. Long term shearing did not result in floc breakage and the values of percentage light transmission and protein concentration of the final filtrate remained the same during the incubation period. Increasing the shear rate resulted in improved process efficiency, up to an optimum value, above which performance was poorer. Perikinetic and orthokinetic rate parameters were calculated and results analyzed in view of these parameters