Impact of convective transport and inert membrane on action of the bio-catalytic filter

We describe two types of enzyme-containing filters. The first type consists of a semi-permeable membrane with immobilized enzyme covered with inert membrane, permeable for the substrate and badly permeable for the product. The second filter type is a semi-permeable enzyme containing a membrane where substrate is pumping through the membrane. The first type is described by a system of two reaction–diffusion equations. The diffusion is described by Fick’s law, and the reaction is described by the Michaelis–Menten term. We obtain mathematical expression of the effectiveness of the bio-catalytic active filters to generate flux of the product and parameter describing permeability of the bio-catalytic filter for substrate. An inert membrane leads to the increase of the product flow through the bio-catalytic membrane about three times and possesses the optimal thickness of the later. Decreasing permeability of inert membrane for product decreases the product flow back, and increases product flow forward about six times. The second-type filter is described by a system of two reaction–diffusion–convection equations. The included convection term is a principal innovation of the research. The convection term increases the transport of the substrate and restricts the flux of the product in the back direction. The convection term increases both rate of the product generation and the capacity to consume the substrate more than 12 times.