Further analysis of the analogy between cellular solidification and viscous fingering

Publisher Website
Google Scholar
Abstract
Neglecting capillarity, the analogy between cellular solidification and viscous fingering is revisited in the limit of small Péclet numbers Pλ=λ/ls, where λ is the periodicity and ls the solutal length. Actually, cellular growth also depends on a second Péclet number Pt based on the shift of the tip from the position of the planar front. When Pt is small, the analogy with viscous fingering is legitimate which gives an expression for the tip supersaturation Ω which fits nicely with the available experimental data on succinonitrile-acetone alloys. Neverthless, it turns out that Pt is large for real cells which leads us to develop a step-by-step approach, up to the second order in the small parameter Pλ. At the first order, the Brody-Flemings relation for Ω is recovered but in a rigorous way. The second order results in an integral equation for the profile which is explicitly derived for finite amplitude cells

This publication has 0 references indexed in Scilit: