The effect of fluid flow due to the crystal-melt density change on the growth of a parabolic isothermal dendrite

Abstract The Ivantsov analysis of an isolated isothermal dendrite (with zero surface tension) growing into a supercooled liquid is extended to include the effects of the fluid flow due to volume contraction or expansion upon solidification. For an axisymmetric paraboloidal dendrite an analytic solution to the Navier-Stokes equations is obtained. The magnitude of the flow is proportional to the relative density change ϵ and the flow becomes negligible far from the surface of the dendrite. The temperature field consistent with this flow can also be found explicitly. The well-known expression that relates the dimensionless supercooling to the Peclet number in the absence of fluid flow is modified for nonzero ϵ, but the effect is of order ϵ and hence is seen to be minor for most values of ϵ and dimensionless supercooling that occur in practice.