Revealing The Effects Of Membrane Morphology On The Rejection Of Oil Droplets Via Network Modeling

Oily wastewater without adequate treatment could cause negative impacts on the environment.In comparison with conventional methods(like centrifugation,gravity separation,and chemicals-based demulsification),membrane-based treatment is emerging as an effective and flexible way to removing the oil and reclaiming the water from an oil-in-water emulsion.Despite the advantages,it is still challenging to reveal the underlying mechanisms accounting for the complex interactions between the oil droplets and the porous membrane substructures,which are of great value in designing novel membranes for better performance of the oily wastewater treatment via membrane separations.Therefore,the objective of the current study is to establish a correlation between the rejection of oil droplets and the membrane morphology,which could be exploited to derive a set of design heuristics for developing improved membranes(as a rejector or a coalescer).The current study employed a network-based approach to theoretically investigate the effects of membrane morphology on the rejection of oil droplets.The porous membrane was numerically discretized into a system of cubic unit cells,whose coordinate directions were exploited to derive a bond-node structure.This discretization provided a locally linear spatial domain with various topological structures for the numerical analysis.Methods based on the finite element analysis and ‘maze' solver were developed to determine,in a complementary sense,the active groups that are composed of connected unit cells with a nonzero flow rate.The size(i.e.,number of the unit cells)of the network in the lateral direction was optimized to minimize the negative effects resulting from the uncertainty of the network substructures.In order to enhance the modeling efficiency,the numerical solver for the finite element analysis was also optimized in terms of the setting of iterative tolerance and the use of preconditioning.Moreover,a criterion based the normalized flux was successfully established to accurately determine the active groups in the network.The network was varied from a highly connected structure to a straight-through one by continuously changing the lateral blockage probability while fixing the transverse blockage probability at different values.The deposition of a single oil droplet was then simulated in a statistical fashion to evaluate the trans-droplet pressure(TDP)as a function of the lateral blockage probability.The distribution of the TDPs was also studied for the deposition of multiple oil droplets(i.e.,varied surface coverage).The corresponding variations in the topological characteristics on the active groups were exploited to interpret the dependence of the TDP on the blockage probability.A critical pressure model developed in prior work was discussed and adapted to the network model for predicting the initial rejection of oil droplets as a function of thetrans-membrane pressure(TMP)during a process of oily wastewater treatment.The modeling results for networks with a different connectivity were compared to correlate the initial rejection of oil droplets with the topological structures of the network.The effects of the emulsion concentration on the initial rejection were also discussed in the context of varied initial surface coverage.All the modeling results confirm the hypothesis that the TDP could be considerably less than the TMP when the membrane has a highly connected structure and thereby give rise to a relatively high rejection of oil droplets.Moreover,a high surface coverage by the oil droplets could substantially change the distribution of pressure within the membrane structure,which might decrease the rejection.It is desirable that the network model would offer a powerful tool for enhancing the performance of membrane-based oil wastewater treatment.