Moisture transport in swelling media modelled with a Lattice Boltzmann scheme having a deforming lattice

• Novel Lattice Boltzmann scheme describes swelling and shrinkage of gels.
• Self-similar profiles of moisture content are observed.
• Reduced-order model is derived for regular regime of swelling.

In this paper we present a novel numerical scheme for simulating the one-dimensional deformation of hydrogel material due to drying or rehydration. The scheme is based on the versatile Lattice Boltzmann method, which has been extended such that the computational grid (lattice) deforms due to shrinkage or swelling. This property of a deforming grid is new to the Lattice Boltzmann method, and a detailed description of this new method is given. Via simulations we show that self-similar moisture concentration profiles occur in two periods in both drying and swelling processes: the penetration period and the regular regime. Given the property of self-similarity, we have been able to formulate a reduced-order model for the regular regime of swelling.