Hydrodynamic boundary layer region

The velocity of liquid flow around suspended solid particles is reduced by frictional resistance and results in a region characterized by a velocity gradient between the surface of the solid particle and the bulk fluid. This region is termed the hydrodynamic boundary layer and the stagnant layer within it that is diffusion-controlled is often known as the effective diffusion boundary layer. The thickness of this stagnant layer has been suggested to be about 10 times smaller than the thickness of the hydrodynamic boundary layer [13]. 

An important concept in fluid mechanics is the hydrodynamic boundary layer (also known as Prandtl layer) or region where the effective disturbance... 

In many respects, similar to the diffusion layer concept, there is that of the hydrodynamic boundary layer, <5H. The concept was due originally to Prandtl [16] and is defined as the region within which all velocity gradients occur. In practice, there has to be a compromise since all flow functions tend to asymptotic limits at infinite distance this is, to some extent, subjective. Thus for the rotating disc electrode, Levich [3] defines 5H as the distance where the radial and tangential velocity components are within 5% of their bulk values, whereas Riddiford [7] takes a figure of 10% (see below). It has been shown that... 

Typically, the effects of the viscous forces originate at the solid boundary of the body of fluid. The fluid contained in the region of substantial velocity change is called the hydrodynamic boundary layer, Prandtl, 1904 [2]. Similarly, if the fluid and the solid are at different temperatures, the region of substantial temperature change in the fluid is... 

Just as the hydrodynamic boundary layer was defined as that region of the flow where viscous forces are felt, a thermal boundary layer may be defined as that region where temperature gradients are present in the flow. These temperature gradients would result from a heat-exchange process between the fluid and the wall. 

Hydrodynamic boundary layer — is the region of fluid flow at or near a solid surface where the shear stresses are significantly different to those observed in bulk. The interaction between fluid and solid results in a retardation of the fluid flow which gives rise to a boundary layer of slower moving material. As the distance from the surface increases the fluid becomes less affected by these forces and the fluid velocity approaches the freestream velocity. The thickness of the boundary layer is commonly defined as the distance from the surface where the velocity is 99% of the freestream velocity. The hydrodynamic boundary layer is significant in electrochemical measurements whether the convection is forced or natural the effect of the size of the boundary layer has been studied using hydrodynamic measurements such as the rotating disk electrode [i] and - flow-cells [ii]. 

The transport of the growth unit(s) from the bulk solution through the hydrodynamic boundary layer to a region adjacent to the adsorption layer of the crystal. This is often referred to as bulk transport-controlled, volume diffusion-controlled, or simply transport-controlled. 

Relation (3.2.13) is valid in the region of laminar flow past the disk the laminar regime occurs until Re 104 to 105, depending on the roughness of the surface. For low Reynolds numbers (Re < 10), this relation is invalid, because the thickness of the hydrodynamic boundary layer becomes comparable with the disk radius and the boundary effects on the hydrodynamic flow and mass transfer become stronger. 

Numerous experiments and numerical calculations show that the laminar hydrodynamic boundary layer occurs for 5 x 102 < Rex 5 x 105 to 106 [427]. In this region the thermal Peclet number Pe = Pr Rex is large for gases and common liquids. For liquid metals, there is a range of Reynolds numbers, 104 < Rex 106, where the Peclet numbers are also large. 

When a fluid flows past a solid surface there is a thin region near the solid-liquid interface where the velocity becomes reduced owing to the influence of the surface. This region, called the hydrodynamic boundary layer 6, may be... 

For mass transfer processes another boundary layer may be defined, viz. the mass-transfer or diffusion boundary layer , 8. This is a thinner region close to the interface across which, in the case of a laminar hydrodynamic boundary layer around the crystal, mass transfer proceeds by molecular diffusion. Under these conditions the relative magnitudes of the two boundary layers may be roughly estimated from... 

It is worth noticing that f remains nearly constant in a wide range of the Re number (0.6 < Re < 4.3) in the same way as the average current. In this range, it must then be inferred that the diffusion layer upstream and therefore the upstream hydrodynamic boundary layer keep constant thicknesses. This layer could be identified with the region of increased viscosity previously mentioned. An evaluation of both the hydrodynamical and diffusion layer thicknesses -6 and 6 - can be tried in the following way From the mean value 0 -62-1 of 2 Hz found for f and with D 7.10" cm. s", one obtains 6 6 ym. 

It is precisely the loosening of a portion of polymer to which the authors of [47] attribute the observed decrease of viscosity when small quantities of filler are added. In their opinion, the filler particles added to the polymer melt tend to form a double shell (the inner one characterized by high density and a looser outer one) around themselves. The viscosity diminishes until so much filler is added that the entire polymer gets involved in the boundary layer. On further increase of filler content, the boundary layers on the new particles will be formed on account of the already loosened regions of the polymeric matrix. Finally, the layers on all particles become dense and the viscosity rises sharply after that the particle with adsorbed polymer will exhibit the usual hydrodynamic drag. 

---