The research results presented here are part of a more extensive effort regarding sustained bioconvection in porous media. Bioconvection is the phenomenon of gravity driven fluid motion due to buoyancy forces resulting from density differences between the fluid and motile micro-organisms suspended in the fluid. While the field of bio-convection in pure fluids emerged substantially over the past decade the corresponding effects of bio-convection in porous media received much less attention, despite the fact that micro-organisms grow naturally in porous environments; soil, food and human tissues serve as basic examples. The research focuses in two major new directions. The first deals with the theoretical and experimental investigation of bio-convection in porous media. The second major new direction is linked to the sustainability of the bioconvection motion. The existing work on bio-convection in both pure fluids and porous media exclude micro-organism growth during the bio-convection because the time scales concerned were very short. However, when the question of the sustainability of this convection over long times arises, microorganism growth has to be accounted for. If sustained bio-convection in porous media is possible it opens the avenue to investigate its impact on microbial proliferation in soil, food and human tissue, an important avenue for application of the theoretical results. Then, if bio-convection enhances microbial proliferation it may be undesirable in some cases, e.g. in food, or it might be desirable if specific micro-organisms that can be used for contaminated soil remediation will be "helped" by the bio-convection process to access contaminated regions in the soil. The theoretical and experimental results presented in this paper reflect the process of monotonic growth of motile microorganisms (e.g. the PAOI strain of Pseudomonas Aeruginosa) to be included in the bioconvection process. A new proposed model is shown to be the appropriate one to better reflect both conceptually as well as practically the microbial growth process.