Wall-enhanced dendritic growth: An exact Wiener-Hopf-Hankel solution for oblique reflection

A solidifying dendrite advancing toward an oblique impermeable wall senses the wall through reflection of its own diffusive depletion field. The strength of this reflection depends on both wall obliquity and the unsteady kinematics of the closing gap, and cannot be captured by any quasistatic frozen offset construction. We solve the moving boundary diffusion problem exactly in the laboratory frame (wall fixed, dendrite advancing at constant speed) by recasting it as a Wiener-Hopf-Hankel system on a pair of spectral branches. The resulting upper triangular operator is inverted sequentially: first as a Fredholm integral equation on the lower branch, then as a scalar Wiener-Hopf problem on the upper branch, reaching a closed form solution via Cagniard-de Hoop. A Padé-Abrahams rational reduction of the spectral radical reduces the entire scheme to a low cost algebraic system at each Laplace node. The exact unsteady solution inverts the classical starvation picture. Measured against an isolated dendrite at the same elapsed time, the wall correction is weakly suppressive while the tip is more than about two diffusion lengths from the wall, where the reflected depletion returns with little retardation and acts as ordinary blockage, but the suppression never exceeds one percent. As the gap closes the correction changes sign and the feeding rises to 31 percent above the isolated reference at grazing incidence, because the reflected field carries a memory of wider past gaps and delivers more solute than the instantaneous geometry would allow. The enhancement is governed by the oblique Péclet number Pe θ = v d 0 sin θ / D and is strongest at grazing incidence, where it exceeds the preceding suppression by a factor of 30.