We investigate how a filter media microstructure influences filtration performance. We derive a theory that generalizes classical multiscale models for regular structures to account for filter media with more realistic microstructures, comprising random microstructures with polydisperse unidirectional fibres. Our multiscale model accounts for the fluid flow and contaminant transport at the microscale (over which the media structure is fully resolved) and allows us to obtain macroscopic properties such as the effective permeability, diffusivity, and fibre surface area. As the fibres grow due to contaminant adsorption this leads to contact of neighbouring fibres. We propose an agglomeration algorithm that describes the resulting behaviour of the fibres upon contact, allowing us to explore the subsequent time evolution of the filter media in a simple and robust way. We perform a comprehensive investigation of the influence of the filter-media microstructure on filter performance in a spectrum of possible filtration scenarios.

Filtration in general, and the dead end depth filtration of solid particles out of fluid in particular, is intrinsic multiscale problem. The deposition (capturing of particles) essentially depends on local velocity, on microgeometry (pore scale geometry) of the filtering medium and on the diameter distribution of the particles. The deposited (captured) particles change the microstructure of the porous media what leads to change of permeability. The changed permeability directly influences the velocity field and pressure distribution inside the filter element. To close the loop, we mention that the velocity influences the transport and deposition of particles. In certain cases one can evaluate the filtration efficiency considering only microscale or only macroscale models, but in general an accurate prediction of the filtration efficiency requires multiscale models and algorithms. This paper discusses the single scale and the multiscale models, and presents a fractional time step discretization algorithm for the multiscale problem. The velocity within the filter element is computed at macroscale, and is used as input for the solution of microscale problems at selected locations of the porous medium. The microscale problem is solved with respect to transport and capturing of individual particles, and its solution is postprocessed to provide permeability values for macroscale computations. Results from computational experiments with an oil filter are presented and discussed

This study presents the dynamic capillary pressure model (Hassanizadeh and Gray, Adv Water Resour 13:169-186, 1990; Water Resour Res 29:3389-3405, 1993) adapted for the needs of paper manufacturing process simulations. The dynamic capillary pressuresaturation relation is included in a one-dimensional simulation model for the pressing section of a paper machine. The one-dimensional model is derived from a two-dimensional model by averaging with respect to the vertical direction. Then, the model is discretized by the finite volume method and solved by Newton's method. The numerical experiments are carried out for parameters typical for the paper layer. The dynamic capillary pressure-saturation relation shows significant influence on the distribution of water pressure. The behavior of the solution agrees with laboratory experiments (Beck, Fluid pressure in a press nip: measurements and conclusions, 1983).

The membrane morphology significantly influences membrane performance. For osmotically driven membrane processes, the morphology strongly affects the internal concentration polarization. Different membrane morphologies were generated by simulation and their influence on membrane performance was studied, using a 3Dmodel. The simulation results were experimentally validated for two classical phase-inversion membrane morphologies: sponge-and finger-like structures.Membrane porosity and scanning electron microscopy image information were used as model input. The permeance results from the simulation fit well the experimentally measured permeances. Water permeances were predicted for different kinds of finger-like cavity membranes with different finger-like cavity lengths and various finger-like cavity sets, as well as for membranes with cylindrical cavities. The results provide realistic information on how to increase water permeance, and also illustrate that membrane's complete morphology is important for the accurate water permeance evaluation. Evaluations only based on porosity might be misleading, and the new 3D simulation approach gives a more realistic representation.

KAUST RepositoryPore-scale modeling and simulation of flow, transport, and adsorptive or osmotic effects in membranes: the influence of membrane microstructureReceived: date / Accepted: date Abstract The selection of an appropriate membrane for a particular application is a complex and expensive process. Computational modeling can significantly aid membrane researchers and manufacturers in this process. The membrane morphology is highly influential on its efficiency within several applications, but is often overlooked in simulation. Two such applications which are very important in the provision of clean water are forward osmosis and filtration using functionalized micro/ultra/nano-filtration membranes. Herein, we investigate the effect of the membrane morphology in these two applications. First we present results of the separation process using resolved finger-and sponge-like support layers. Second, we represent the functionalization of a typical microfiltration membrane using absorptive pore walls, and illustrate the effect of different microstructures on the reactive process. Such numerical modeling will aid manufacturers in optimizing operating conditions and designing efficient membranes.