Analytical substrate flux approximation for the Monod boundary value problem

Persistence in a Single Species CSTR Model with Suspended Flocs and Wall Attached Biofilms

“…This is in good agreement with the results of [1], where an analytical approximation of the form j(λ, S) ≈ const · λS K λ +S was derived with a Homotopy Perturbation Method argument, which could be numerically verified for an extended range of biofilm parameters. Stability of the trivial equilibrium E 0 is attained for S in such that ∂j ∂λ (0, S in ) lies beneath k λ ρ γDc , which is represented by the dotted line in Figure 2.…”

A dual-porosity theory for solute transport in biofilm-coated porous media

“…A first-order mass transfer coefficient is used to describe inter-phase diffusive fluxes and it can be computed from pore-scale characteristic features by solving a steady-state closure problem. This work extends and generalizes earlier results obtained for local mass equilibrium conditions [6], specific limit cases of non-equilibrium conditions (reaction-rate limited reaction and transport limited reaction, [24]; analytical works on 1D configurations that deal with such non equilibrium limiting cases have also been the subject of recent work, see for instance [72,73]) and asymptotic non-equilibrium conditions [25]. This model extends also previous non-equilibrium models that were proposed on a more heuristic base.…”

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“…[15] proposed that HPM is not a good choice for solving problems with strong nonlinearity. The same challenge was found in [16], where the same approach was used to find an analytical solution for their diffusive flux study for the biofilm modeling.…”