Monotectic Composite Growth with Fluid Flow

Abstract

In this paper, we present two different models for the description of composite monotectic growth. We focus our interest on the evolution of a fibrous mircostructure with liquid L 2 fibers. We assume that the thermocapillary forces on the L 1 - L 2 interface induce convection in the liquid phases. This Marangoni convection has a strong influence on the transport of solute depending on the local temperature gradient and the Peclet number. In addition, the density differences of the phases also affect the flow field. The resulting flow field changes the transport of solute and therefore the mean undercooling. First we describe an analytical approach for the calculation of the concentration field and the mean constitutional undercooling. We use a series of approximations in order to get some analytically tractable equations. With this extended.lackson and Hunt theory we get some insight into the effect of the flow field on monotectic composite growth. The second model is more acurate. We solve numerically the diffusion equation coupled with the Navier-Stokes equation in the L 1 phase to find the minimal undercooling for a given velocity and temperature gradient. We neglect diffusion and convection in the L 2 fiber in both models. The minimal undercooling defines the mean rod spacing, that could be plotted in a monotectic Jackson and Hunt diagram.