  In this paper, we study a mean curvature type flow with capillary boundary in
the unit ball. Our flow preserves the volume of the bounded domain enclosed by
the hypersurface, and monotonically decreases an energy functional $E$. We show
that it has the longtime existence and subconverges to spherical caps. As an
application, we solve an isoperimetric problem for hypersurfaces with capillary
boundary.
