  We study the interface between a solid trapped within a bath of liquid by a
suitably shaped non-uniform external potential. Such a potential may be
constructed using lasers, external electric or magnetic fields or a surface
template. We study a two dimensional case where a thin strip of solid, created
in this way, is surrounded on either side by a bath of liquid with which it can
easily exchange particles. Since height fluctuations of the interface cost
energy, this interface is constrained to remain flat at all length scales.
However, when such a solid is stressed by altering the depth of the potential;
beyond a certain limit, it responds by relieving stress by novel interfacial
fluctuations which involve addition or deletion of entire lattice layers of the
crystal. This ``layering'' transition is a generic feature of the system
regardless of the details of the interaction potential. We show how such
interfacial fluctuations influence mass, momentum and energy transport across
the interface. Tiny momentum impulses produce weak shock waves which travel
through the interface and cause the spallation of crystal layers into the
liquid. Kinetic and energetic constraints prevent spallation of partial layers
from the crystal, a fact which may be of some practical use. We also study heat
transport through the liquid-solid interface and obtain the resistances in
liquid, solid and interfacial regions (Kapitza resistance) as the solid
undergoes such layering transitions. Heat conduction, which shows strong
signatures of the structural transformations, can be understood using a free
volume calculation.
