  In this paper, we introduce a new constrained mean curvature type flow for
capillary boundary hypersurfaces in space forms. We show the flow exists for
all time and converges globally to a spherical cap. Moreover, the flow
preserves the volume of the bounded domain enclosed by the hypersurface and
decreases the total energy. As a by-product, we give a flow proof of the
capillary isoperimetric inequality for the starshaped capillary boundary
hypersurfaces in space forms.
