Computer simulation study of the permeability of driven polymers through porous media

A computer simulation model is used to study the permeability of polymer chains driven by a biased flow field through a porous medium in two dimensions. The chains are modeled by constrained self-avoiding walks, which reptate through the heterogeneous medium with a biased probability imposed by the driven field. A linear response description is used to evaluate an effective permeability. The permeability {σ} shows an unusual decay behavior on reducing the porosity pₛ. We find that the permeability decreases on increasing the bias above a characteristic value Bc. This characteristic bias shows a logarithmic decay on reducing the porosity, Bc{~}-{γ} ln(1-pₛ), with {γ}{}0.35. The permeability decays with the length (Lc) of the chains; at low polymer concentration it shows a power-law decay, {σ}{~}Lc^-α, the exponent {α} is nonuniversal and depends on both the porosity as well as the biased field ({α}{}1.64--3.73). We find that the biased field B and porosity pₛ affect the conformation of the chains. The radius of gyration Rg of the chains increases with increasing biased field in high porosity, while it decreases on decreasing the porosity at high field bias. In high porosity and low polymer concentrations, the radius of gyration shows a power-law dependence on the chain length, Rg{~}Lc^ν, with {ν} depending on the biased field ({ν}{}0.84--0.94). In order to explain the deviations from the Darcy Law for the polymer flow, a plausible nonlinear response theory via a power-law response formula is suggested; we point out the associated complexities involved in addressing the flow problems in driven polymers.