Modeling swelling effects during coffee extraction with smoothed particle hydrodynamics
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It is commonly assumed that coffee particles swell during filtration, but it has not been clarified how different degrees of swelling affect the extraction. In this article, we propose a grain swelling model to investigate the influences of swelling on both intra-grain and inter-grain transport. The swelling is modeled through a diffusion process of excess water into the grains. The geometric expansion of the grains is connected to the local concentration of excess water through a specified deformation gradient tensor. Diffusion of soluble compounds inside the grains is coupled with the swelling dynamics through a modified diffusion equation. Inter-grain transport is modeled by solving the Navier-Stokes equation and diffusion equations. This model is solved numerically in the framework of smoothed particle hydrodynamics, and it is used to simulate the extraction of a minimal coffee bed setup and to investigate the effect of a small degree of particle swelling (< 8 % in size) on the extraction kinetics. It is found that under the normal operating parameter regime of espresso filtration, swelling affects the extraction mainly through the change of inter-grain transport. Swelling also alters the diffusion inside the grains, but this process has a secondary effect on the extraction. In general, swelling slightly impedes the extraction rate, but enhances the strength considerably at both fixed brewing time and fixed brewing volume. Our results justify the endeavor in the literatures to clarify the effect of possible swelling on brewing and preparation variables during coffee extraction.