# Microscopic analysis of the coarsening of an interface in the spinodal decomposition of a binary fluid

Kumaran, V (1998) Microscopic analysis of the coarsening of an interface in the spinodal decomposition of a binary fluid. In: Journal of Chemical Physics, 109 (8). pp. 3240-3244.

 PDF Microscopic_analysis-61.pdf Restricted to Registered users only Download (145kB) | Request a copy

## Abstract

The coarsening of a random interface in a fluid of surface tension $\gamma$ and viscosity $\mu$ is analyzed using a curvature distribution function $A(K_m ,K_g ,t)$ which gives the distribution of the mean curvature $K_m$ and Gaussian curvature $K_g$ on the interface. There is a variation in the area distribution function due to the rate of change of $K_m,K_g$ and the compression of the interface due to tangential motion. The rates of change of mean and Gaussian curvature at a point are related to the rate of change of the normal velocity in the tangential directions along the interface. The fluid velocity is governed by the Stokes equation for a viscous flow, and the velocity field at a point is determined as an integral of the product of the Oseen tensor and the normal force at other points on the interface.Using a general form for this integral, it is shown that there is a characteristic variable $K_*=K_g / K_m^2-4K_g)^{1/2}$ which is independent of time even as $K_m$ and $K_g$ decrease proportional to $t^{-1}$ and $t^{-2}$, respectively. In the late stages, analytical forms for the distribution function are determined in the limit $K_m \ll K_*$ using a similarity variable $\eta = (\gamma K_mt/ \mu)$. Two reasonable approximations are used for the characteristic length for the correlation of the curvature and normal along the interface, and the results for these two approximations are quadratic polynomials in $|\eta|$ which are nonzero for a finite interval about $\eta = 0$. It is expected that the actual distribution function is in between these two limiting cases.

Item Type: Journal Article Journal of Chemical Physics AIP Copyright of this article belongs to The American Institute of Physics. Division of Mechanical Sciences > Chemical Engineering 04 Dec 2006 19 Sep 2010 04:32 http://eprints.iisc.ac.in/id/eprint/9034