Interaction between growth and transport phenomena in living mixtures
Alfio Grillo, G. Zingali, Davide Borrello, Salvatore Federico, Walter Herzog, Gaetano Giaquinta · Journal of Physics Conference Series · 2007
Biological growth is regulated by the presence of several chemical substances, and is modulated by thermo-mechanical stimuli. The evolution of chemical substances is described by the advection-diffusion-reaction process of solutes dissolved in the fluid-phase of a biphasic mixture with mass exchange between phases. We present a picture in which growth, by changing material symmetries, modifies the environment in which transport processes take place, and we outline a possible interaction between growth and chemical agents. In order to study this interaction, we use averaging methods to determine the macroscopic counterparts of the transport properties defined at the microscale, and, by writing the macroscopic transport equation in material form, we illustrate how these properties are modulated by growth. In the case of anisotropic growth, such a modulation has a geometric meaning, and is related to both the change of material symmetries, and the development of material inhomogeneities. By regarding growth as a process characterized by a time-scale much slower than that of the transport process of interest, we provide an asymptotic analysis of transport in a growing porous medium based on the adiabatic approximation. We prove that the macroscopic concentration of chemical substances is "renormalized" by the anisotropy of growth.