Thinning viscous flow

The comparison of flow conductivity coefficients obtained from Equation (5.76) with their counterparts, found assuming flat boundary surfaces in a thin-layer flow, provides a quantitative estimate for the error involved in ignoring the cui"vature of the layer. For highly viscous flows, the derived pressure potential equation should be solved in conjunction with an energy equation, obtained using an asymptotic expansion similar to the outlined procedure. This derivation is routine and to avoid repetition is not given here. 

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... 

Consider a fully developed turbulent flow through a pipe of circular cross section. A turbulent boundary layer will exist with a thin viscous sublayer immediately adjacent to the wall, beyond which is the buffer or generation layer and finally the fully turbulent outer part of the boundary layer. 

Thinning of the anodic oxide coverage is found at sharp 90° edges of the substrate. This effect has been ascribed to oxide stress, because similar results are found for low-temperature thermal oxidation under conditions where viscous flow is not present. For oxide thicknesses in excess of about 100 nm, cracks develop in... 

Hiemenz (in 1911) first recognized that the relatively simple analysis for the inviscid flow approaching a stagnation plane could be extended to include a viscous boundary layer [429]. An essential feature of the Hiemenz analysis is that the inviscid flow is relatively unaffected by the viscous interactions near the surface. As far as the inviscid flow is concerned, the thin viscous boundary layer changes the apparent position of the surface. Other than that, the inviscid flow is essentially unperturbed. Thus knowledge of the inviscid-flow solution, which is quite simple, provides boundary conditions for the viscous boundary layer. The inviscid and viscous behavior can be knitted together in a way that reduces the Navier-Stokes equations to a system of ordinary differential equations. 

The traditional view of stagnation flow was presented in the previous sections, that is, a semi-infinite inviscid potential flow interacting with a thin viscous boundary layer near the stagnation surface. In that case there is no physically based characteristic length scale. 

In polymer processing, we frequently encounter creeping viscous flow in slowly tapering, relatively narrow, gaps as did the ancient Egyptians so depicted in Fig. 2.5. These flows are usually solved by the well-known lubrication approximation, which originates with the famous work by Osborne Reynolds, in which he laid the foundations of hydrodynamic lubrication.14 The theoretical analysis of lubrication deals with the hydrodynamic behavior of thin films from a fraction of a mil (10 in) to a few mils thick. High pressures of the... 

In extrusion blow moulding a parison may sag under its own weight after leaving the die, with unwanted and perhaps random thinning as a result. In part this behaviour may be attributable to an elastic effect (to uncoiling of the chains) but also to viscous flow as the molecules move in relation to each other. It is reasonable to believe that the elastic element will become more important with ... 

When a crack propagates in polystyrene at low crack velocities, the craze ruptures close to its median plane by a mechanism having the approximate characteristics of viscous flow. Each fracture surface is then covered by a thin layer of craze. At higher crack velocities, however, failure occurs along the boundaries between the craze and the adjacent bulk polymer by practically brittle fracture (I). The change in fracture... 

The development of viscous and inviscid regious of flow as a result of iu-serting h flat plate parallel into a fluid stream of uniform velocity is shown in Fig. 6 7. The fluid slicks to the plate on both sides because of the no slip con dition, and the thin boundary layer in which the viscous effects are significant near the plate surface is the viscous flow region. The regiou of flow on both sides away from the plate and unaffected by the presence of the plate is the inviscid flow region. 

Hard sphere systems are characterized by viscous flow and for low solids loading (less than 5%) they can be described as Newtonian fluid. At higher loadings, cluster formation takes place and the fluid cau acquire shear thinning or thickening behavior. The viscosity and solids loading are correlated with the... 

The fundamental theorems needed to make use of a molecular dynamics simulation have now been listed. Applications to other problems such as lubrication by a thin film or the related one of viscous flow between two closely spaced plates or down a narrow cylindrical tube will be discussed below. 

Otherwise, the separation factor will be smaller. The narrow pore-size distributions and the small pores of ceramic and glass membranes allow separation due to Knudsen diffusion (for the appropriate pressure range) by preferential diffusion of the lighter component through the membrane. In composite membranes, the thin permselective layer can be in the Knudsen diffusion regime and thus be responsible for all the separation. The support layers, with their larger-diameter pores, are usually in the viscous-flow regime. 

This part of the chapter deals with the effects of viscosity on an electrolyte flowing in the electrochemical reactor in two dimensions. The boundary layers appear on the surface of bodies in viscous flow because the fluid seems to stick to the electrocatalyst s surface. As we have described above, right at the surface, the flow has zero speed, and this fluid transfers a linear momentum to the adjacent layers through the action of dynamic viscosity. Therefore, a thin fluid... 

The foam-dilatational viscosity, K, arises because of two primary mechanisms (37) (1) viscous flow within the thin films, and (2) interfacial tension gradients acting along the foam bubble surfaces. The effect of interfacial tension gradients is to increase the foam viscosity as they impede flow near the surfaces of the thin foam films by contributing to a larger film stress. As in the wet foam (eq 6), the foam dilatational viscosity for a dry foam, K, is inversely proportional to film thickness as well (eq 9). 

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). 

Osborn Re molds in 1883 in a classical experiment, observed two kinds of fluid flow within a pipe namely laminar or streamline flow (sometimes called viscous flow) and turbulent flow. In the former a thin filament of dye in the centre of the pipe remained coherent, whereas for turbulent flow the filament of dye was broken up by the action of the turbulence or turbulent eddies. 

A fundamental key in coating is to spread the liquid over a relatively large substrate by means of viscous forces while maintaining a thin layer of uniform thickness at the substrate by the action of surface tension. Although surface tension stresses are quite small compared with the pressure differences associated with the spreading of the viscous flow, they are important because they fix the amount of fluid laid down. 

There has been some discussion on the permeation process being controlled by surface reaction for thin membranes in the literature. In this case, the reduction of the membrane thickness will not increase the hydrogen permeation fluxes. The same phenomena will occur when the permeation process is controlled by one or more of the mass transfer resistances, including the formation of a boundary layer between the bulk gas phase and the membrane surface and flow through the support pores by Knudsen diffusion and viscous flow. There are only a few studies in the literature addressing the existence of these resistances. The reduction of these resistances is critical for the membrane to achieve its maximum permeation flux. 

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