Viscous flow relative to arrays of cylinders

Abstract

The free‐surface model, successfully employed to predict sedimentation, resistance to flow, and viscosity in assemblages of spherical particles, has been extended to the case of flow relative to cylinders. It is shown to be in good agreement with existing data on beds of fibers of various types and flow through bundles of heat‐exchanger tubes for cases where it can reasonably be expected to apply. Close agreement in the dilute range with the only theoretical treatment for flow parallel to a square array of cylinders provides interesting validation of the model.

Permeability of electrospun fiber mats under hydraulic flow

“…The permeability constant for a highly porous fibrous medium has been derived analytically for flow around a cylinder by Happel [12].…”

“…The mechanical stress arises from the drag of fluid on the surface of the medium as the fluid flows. The drag also results in the drop of the hydraulic pressure in the direction of the flow [12]. The mechanical stress on the fiber mat increases in the flow direction because the force propagates via the fiber-fiber contacts [23].…”

“…Electrospun mats can be approximated as planar fibrous networks. From the review by Jackson and James [21], analytical permeability models for flow perpendicular to a 2-D array of cylinders developed by Happel [12] and by Spielman and Goren [15] fit the experimental data well in the solidity range ~0.05 to 0.3 (where solidity is defined as 1-porosity). Since Happel's equation is considerably simpler and does not involve implicit functions of permeability, Happel's model is chosen for this work.…”

“…Equations for permeability constants that account for the drag forces exerted on the liquid by the solid medium have been developed for flow through a 2-D array of cylinders that are aligned parallel [12,13] or perpendicular [12,13,14] to the direction of the flow, as well as through 3-D random arrays of cylinders [15]. Mao and Russell [16,17] included the effect of fiber orientation in both 2-D and 3-D arrays.…”

Separation of oil-in-water emulsions using electrospun fiber membranes and modeling of the fouling mechanism

“…In this section, we present a model wherein the foulants are assumed to form a uniform coating that envelops the fibers that make up the membrane, both reducing the available volume of the membrane for transport and increasing the effective diameter of the fibers, as shown in Figure 2. We have previously shown that the permeability of electrospun fiber membranes is reasonably welldescribed by Happel's equation for solidities up to 50-60% [18,29]. The normalized flux can be approximated by the following equation:…”