Computational Fluid Dynamics Modeling of the Filtration of 2D Materials Using Hollow Fiber Membranes

Abstract

The current study presents a computational fluid dynamics (CFDs) model designed to simulate the microfiltration of 2D materials using hollow fiber membranes from their dispersion. Microfiltration has recently been proposed as a cost-effective strategy for 2D material production, involving a dispersion containing a permeating solute (graphene), a fouling material (non-exfoliated graphite), and the solvent. The objective of the model is to investigate the effects of fouling of flat layered structure material (graphite) on the transmembrane pressure (TMP) of the system and the filtration of the permeating solute. COMSOL Multiphysics software was used to numerically solve the coupled Navier–Stokes and mass conservation equations to simulate the flow and mass transfer in the two-dimensional domain. For the TMP calculations, we used the resistance-in-series approach to link the fouling of the foulants to the TMP behavior. The foulant particles were assumed to form a polarization layer and cake on the membrane surface, leading to the increment of the TMP of the system. We also assumed the wettability of the polymeric membrane’s inner wall increases upon fouling due to the flat layered structure of the foulant, which results in the reduction in the TMP. This approach accurately reproduced the experimental TMP behavior with a Mean Absolute Error (MAE) of 0.007 psi. Furthermore, the permeation of the permeating solute was computed by incorporating a fouling-dependent membrane partition coefficient for these particles. The effects of the concentration polarization and cake formation fouling stages on the membrane partition coefficient were encapsulated into our defined model parameters, denoted as (Formula presented.) and (Formula presented.), respectively. This formulation of the partition coefficient yielded permeate concentration profiles, which are in excellent agreement with the experiments. For three feed concentrations of 0.05, 0.1, and 0.3 g/L, our model reproduced the experimental permeate concentration profiles with MAEs of 0.0002, 0.0003, and 0.0022 g/L, respectively. The flexibility of this model enables the users to utilize the size and concentration-dependent (Formula presented.) and (Formula presented.) parameters and optimize their experimental microfiltration setups effectively.