  We investigate the swelling and shrinking of L_beta lamellar gel phases
composed of surfactant and fatty alcohol after contact with aqueous
poly(ethylene-glycol) solutions. The height change $\Delta h(t)$ is
diffusion-like with a swelling coefficient, S: $\Delta h = S \sqrt{t}$. On
increasing polymer concentration we observe sequentially slower swelling,
absence of swelling, and finally shrinking of the lamellar phase. This behavior
is summarized in a non-equilibrium diagram and the composition dependence of S
quantitatively described by a generic model. We find a diffusion coefficient,
the only free parameter, consistent with previous measurements.
