Drag force porous particle

When the fluid flows through a porous medium, the -.olid particles exert a force on the fluid equal and opposite to the drag force on the solid particles. This force must be balanced by the pressure gradient in the flow. i.e for flow through a control volume for any chosen direction ... 

In the Darcy model of flow through a porous medium, it is assumed that the flow velocities are low and that momentum changes and viscous forces in the fluid are consequently negligible compared to the drag force on the particles, i.e., if flow through a control volume of the type shown in Fig. 10.5 is considered, then ... 

Problem 9-22. Flow in a Brinkman Medium. Fluid flow in a packed bed or porous medium can be modeled as flow in a Brinkman medium, which we may envision as a bed of spherical particles. Each particle in the bed (there are n particles per unit volume) exerts a drag force on the fluid proportional to fluid velocity relative to the particle given by Stokes law, i.e., ( —Gtt/hiu, where a is the characteristic size of a bed particle). Thus the equations describing the fluid motion on an averaged scale (averaged over many bed particles, for example) are... 

To refine the kinetic rate expression, Civan and Ohen coupled the expansion rate of the indigenous clays with the diffusive flux of water into the porous matrix (see eq 16) as the particles expand, they experience an increase in viscous drag forces exerted by the moving fluid, such that the particles become more easily entrained by the flow. Furthermore, it is assumed that the release rate is proportional to the exposed pore surface area, au, after the deposition of external particles. A simple ex-... 

So far most efforts have been devoted to the determination of the drag force exerted by the surrounding fluid on a translating aggregate. The literature that has been devoted to this topic is already quite impressive and has been recently summarized by Coelho et al. [38]. The purpose of this section is to extend the analysis to electrophoretic mobility, i.e., to isolated particles to which an electric field is applied. As previously stated, the same formalism as for porous media can be applied to suspensions. 

The scope of coverage includes internal flows of Newtonian and non-Newtonian incompressible fluids, adiabatic and isothermal compressible flows (up to sonic or choking conditions), two-phase (gas-liquid, solid-liquid, and gas-solid) flows, external flows (e.g., drag), and flow in porous media. Applications include dimensional analysis and scale-up, piping systems with fittings for Newtonian and non-Newtonian fluids (for unknown driving force, unknown flow rate, unknown diameter, or most economical diameter), compressible pipe flows up to choked flow, flow measurement and control, pumps, compressors, fluid-particle separation methods (e.g.,... 

The hierarchy of equations thereby obtained can be closed by truncating the system at some arbitrary level of approximation. The results eventually obtained by various authors depend on the implicit or explicit hypotheses made in effecting this closure—a clearly unsatisfactory state of affairs. Most contributions in this context aim at calculating the permeability (or, equivalently, the drag) of a porous medium composed of a random array of spheres. The earliest contribution here is due to Brinkman (1947), who empirically added a Darcy term to the Stokes equation in an attempt to represent the hydrodynamic effects of the porous medium. The so-called Brinkman equation thereby obtained was used to calculate the drag exerted on one sphere of the array, as if it were embedded in the porous medium continuum. Tam (1969) considered the same problem, treating the particles as point forces he further assumed, in essence, that the RHS of Eq. (5.2a) was proportional to the average velocity and hence was of the explicit form... 

Due to its simplicity, the Kirkwood-Riseman theory has been widely used in the literature for estimation of the hydrodynamic diameter of colloidal aggregates (Chen et al. 1984 Hess et al. 1986 Wiltzius 1987 Naumann and Bunz 1991 Lattuada et al. 2003 Sandkiihler et al. 2005a). However, this is an approximate approach which considers the hydrodynamic interaction only within a first-order correction of the unperturbed force and which neglects the finite size and the shape of the primary particles. Hence, the Kirkwood-Riseman theory is best applicable for very porous aggregates and is expected to fail for very compact ones (de la Torre and Bloomfield 1977 Binder et al. 2006). Attempts to consider the size and shape of the primary particles within this framework lead to comparably cumbersome expressions of the hydrodynamic drag (de la Torre and Bloomfield 1977) and were obviously not able to compete with other theories or numerical methods. 

Fouling layers, in general, are compressible, that is they become more compact as the extent of their compression increases. Solid compressive pressure is responsible for the compression of a fouling layer according to basic filtration theory [46]. In traditional filtration theory, the derivation of the drag equations of filtration for rigid particle slurries assume that particles are in point contact mode and that compression attends instantaneously. Under this assumption, a force balance can be obtained between liquid pressure over the entire cross-section and the solid compressive pressure on the total mass within the porous layer as ... 

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