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A multiphasic model for the volume change of polyelectrolyte hydrogels that takes into account conservation of mass and momentum is derived. The gradient of chemical/electrochemical potentials of water and mobile ions is taken as the driving force for the volume change of the polyelectrolyte hydrogel, which is damped by the frictional forces between different phases and balanced by the elastic restoring force of the polymer network. Employing the model constructed here, the free swelling of a spherical polyelectrolyte hydrogel immersed in salt solution is simulated by the finite element method. The simulation shows that the polyelectrolyte hydrogel swells from the surface to the interior when the concentration of the external salt solution decreases. The swelling kinetics for ordinary hydrogels with high frictional coefficient between the polymer network and water is controlled by the collective diffusion of the polymer network, while for fast-response hydrogels it is controlled by the ionic diffusion in the hydrogel.

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