Abstract
Membrane rejection models generally neglect the effect of the pore entrance on intrapore particle transport. However, entrance effects are expected to be particularly important with ultrathin membranes, where membrane thickness is typically comparable to pore size. In this work, a 2D model was developed to simulate particle motion for spherical particles moving at small Re and infinite Pe from the reservoir outside the pore into a slit pore. Using a finite element method, particles were tracked as they accelerated across the pore entrance until they reached a steady velocity in the pore. The axial position in the pore where particle motion becomes steady is defined as the particle entrance length (PEL). PELs were found to be comparable to the fluid entrance length, larger than the pore size and larger than the thickness typical of many ultrathin membranes. Results also show that, in the absence of particle diffusion, hydrodynamic particle–membrane interactions at the pore mouth result in particle “funneling” in the pore, yielding cross-pore particle concentration profiles focused at the pore centerline. The implications of these phenomena on rejection from ultrathin membranes are examined.
Highlights
With the development of many new fabrication techniques, there has been an increasing interest in using ultrathin membranes in water purification, for biological, pharmaceutical and other separations as well as for sensing devices [1,2,3,4,5,6,7,8,9,10,11,12,13]
We report results from a model describing spherical particle motion from the reservoir outside the membrane into a slit pore
Our model neglects the impact of neighboring pores on particle motion into a pore, an assumption
Summary
With the development of many new fabrication techniques, there has been an increasing interest in using ultrathin membranes in water purification, for biological, pharmaceutical and other separations as well as for sensing devices [1,2,3,4,5,6,7,8,9,10,11,12,13]. Equation (2) is focused on particle transport within a pore and is based on the assumption that thermodynamic equilibrium is established at the pore mouth This means that a Boltzmann expression can be used to give the time-averaged probability of finding a particle at a given position and orientation in the pore. When the pore length (i.e., membrane thickness) and pore size are of comparable magnitude (as is the case with ultrathin membranes [4,6,8,10,17]), Equation (3) predicts that the fluid profile may not be fully developed within the membrane, making Equation (2) of questionable validity for estimating particle rejection. The relationship between the PEL and the FEL, relative particle size, pore entrance geometry and Reh are examined and discussed in the context of ultrathin membranes where pore entrance effects are expected to be important
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