Viscous flow, resist

Membrane Structure and Compaction. Membrane compaction has been considered as results of an increase in the effective thickness of the active surface layer and/or an added viscous flow resistance in the porous region underneath. (1, 2 ) It will be more reasonable to consider that water flux is inversely proportional to the effective thickness of the membrane which can be assumed to increase with time. 

Additionally, Biot (1956a, b) introduced a complex correction function (F) which accounts for a frequency-dependent viscous flow resistance (r /K). In fact, while the assumption of an ideal Poiseuille flow is valid for lower frequencies, deviations of this law occnr at higher frequencies. For short wavelengths the inflnence of pore flnid viscosity confines to a thin skin depth close to the sediment frame, so that the pore fluid seems to be less viscous. To take these effects into account the complex fnnction (F) modifies the viscous flow resistance (p/K) as a fnnction of pore size, pore flnid density, viscosity and freqnency. A complete definition of (F) can be fonnd in Stoll (1989). 

As a consequence of this, i enever bulk dlffusional resistance domin ates Knudsen diffusional resistance, so that 1, it follows that fi 1 also, and hence viscous flow dominates Knudsen streaming. Thus when we physically approach the limit of bulk diffusion control, by increasing the pore sizes or the pressure, we must simultaneously approach the limit of viscous flow. This justifies a statement made in Chapter 5. 

Deflocculation and Slurry Thinning. Sihcates are used as deflocculants, ie, agents that maintain high sohds slurry viscosities at increased sohds concentrations. Soluble sihcates suppress the formation of ordered stmctures within clay slurries that creates resistance to viscous flow within the various sytems. Laboratory trials are necessary, because the complexity of the systems precludes the use of a universal deflocculant. Sihcates are employed in thinning of limestone or clay slurries used in the wet-process manufacture of cements and bricks, clay refining, and petroleum drilling muds (see also... 

From the standpoint of collector design and performance, the most important size-related property of a dust particfe is its dynamic behavior. Particles larger than 100 [Lm are readily collectible by simple inertial or gravitational methods. For particles under 100 Im, the range of principal difficulty in dust collection, the resistance to motion in a gas is viscous (see Sec. 6, Thud and Particle Mechanics ), and for such particles, the most useful size specification is commonly the Stokes settling diameter, which is the diameter of the spherical particle of the same density that has the same terminal velocity in viscous flow as the particle in question. It is yet more convenient in many circumstances to use the aerodynamic diameter, which is the diameter of the particle of unit density (1 g/cm ) that has the same terminal settling velocity. Use of the aerodynamic diameter permits direct comparisons of the dynamic behavior of particles that are actually of different sizes, shapes, and densities [Raabe, J. Air Pollut. Control As.soc., 26, 856 (1976)]. 

The addition of a flux results not only in a mixture of silica and flux having a lower melting temperature than that of the silica, but also in the melt being less viscous, flowing more easily than silica (viscosity is a measure of the resistance of fluids, liquids, and also gases, to flow fluids with high viscosity flow more slowly than do those with low viscosity). As a consequence of its relatively low viscosity, the hot molten mixture of silica and flux, a type of early glass, can be shaped with relative ease. 

We note that our previous descriptions of flow processes have tacitly assumed laminar flow. For example, flow in capillaries was described by balancing pressure-derived forces against viscous forces, ignoring acceleration (inertial) effects. Darcy s law, Eq. 4.18, is also based on laminar flow. With turbulence, flow resistance increases the pressure gradient is no longer linearly related to flow (see Eqs. 4.18 through 4.20) but increases more rapidly as expressed by... 

Viscosity — A measure of the frictional resistance a fluid offers to an applied shear force under the conditions of - laminar flow. According to Newton s law of viscous flow... 

Stokes considered the resistance experienced by a sphere moving uniformly through an incompressible viscous fluid. Viscous flow implies a low Reynolds number Re. He assumed an infinite medium, rigid particle, no slipping at the surface of the particle. Stokes pointed out that his solution was erroneous in the case of a cylinder. 

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