  We propose in this paper a new multiphase Cahn-Hilliard model with doubly
degenerate mobilities. We prove by a formal asymptotic analysis that it
approximates with second order accuracy the multiphase surface diffusion flow
with mobility coefficients and surface tensions. To illustrate that it lends
itself well to numerical approximation, we propose a simple and effective
numerical scheme together with a very compact Matlab implementation. We provide
the results of various numerical experiments to show the influence of mobility
and surface tension coefficients. Thanks to its second order accuracy and its
good suitability for numerical implementation, our model is very handy for
tackling notably difficult surface diffusion problems. In particular, we show
that it can be used very effectively to simulate numerically the dewetting of
thin liquid tubes on arbitrary solid supports without requiring nonlinear
boundary conditions.
