The pressure drop across combined polydisperse spherical particle - Cylindrical fiber networks

In the fibrous filtration of particles in gas and liquid flows, loading is the act of particles depositing onto fibers. Loaded particles alter the filter microstructure and can have a profound influence on the pressure drop across a filter medium. Of interest is therefore a simple approach to predict the pressure drop across a loaded filter, accounting for both fibers and loaded, spherical particles. In the present study, we use computational fluid dynamics simulations to develop a simple predictive model for the pressure drop across fibrous media composed of a combination of cylindrical fibers and spherical particles. Specifically, the pressure drop is calculated via an in-house written code to solve the incompressible viscous flow equations in a periodic domain, with the particles and fibers accounted for via the immersed boundary method. For calculations, we generate randomly oriented three-dimensional virtual fibrous networks with prescribed microstructures, including network total solidity, fiber orientation angle distribution, fiber radius distribution, and particle radius distribution (both polydisperse). We find that irrespective of network geometry, by defining a single effective network diameter, the product of the dimensionless pressure drop per unit length and the Reynolds number can be expressed solely a function of the total solidity of the network (particle solidity plus fiber solidity) for fiber solidities in 0.03-0.20 range and particle solidities in the 0.0-0.08 range. The effective diameter, employed in both non-dimensionalization of the pressure drop and the Reynolds number definition, is found to depend upon the first and second moments of the fiber diameter distribution functions, and the second and third moments of the particle diameter distribution functions. We develop a regression equation to fit calculation results; the functional form of the equation is based upon a linear combination of the low and high solidity limits for the permeability term in Darcy's Law. We additionally apply this pressure drop relationship in loading simulations to examine the evolution of filter pressure drop and figure of merit as loading proceeds. Test results on model filters show that the pressure drop increases significantly as loading proceeds, with loading of the front regions of filters contributing most significantly to the pressure drop. Interestingly, model results suggest that the figure of merit first increases upon loading and then decreases, justifying preloading of filters to increase performance.