Boundary layer, diffusion 384 Subject

Figure 5.18 shows the only reliable Nui c data available near the critical Reynolds number (XI). Since the data were taken with a side support, there is some effect on the separation and transition angles. Thus the values of Nuj are probably subject to error (R2, R3) although the trend with Re should be correct. At Re = 0.87 x 10 the Shi variation is similar to that shown at lower Re in Fig. 5.17. At Re = 1.76 x 10 the critical transition has already occurred, with the separation bubble accounting for the minimum in Nuj c at 0 — 110°. The maximum in Nuj at 0 = 125° reflects the increased transfer rate in the attached turbulent boundary layer. The local minimum at 0 = 160° is due to final separation. These angles do not agree exactly with those in Fig. 5.11 because of the crossflow support and the fact that angular diffusion shifts the...

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... 

To determine the net rale of adsorption of particles suspended in a fluid that is flowing over the collector, one may then solve the usual convective-diffusion equation subject to a reversible first-order reaction as the boundary condition, provided the diffusion boundary layer is much thicker than the interaction boundary layer. 

At any interface there will be boundary layers of liquid not subject to convection. Diffusion of materials to and from the interface will be determined by the thickness of such layers. In previous studies of solvent extraction and partitioning, a wide variety of techniques to set up the liquid-liquid interface have been employed. These are illustrated in Fig. 

Consider convection diffusion toward a spherical particle of radius R, which undergoes translational motion with constant velocity U in a binary infinite diluted solution [3], Assume the particle is small enough so that the Reynolds number is Re = UR/v 1. Then the flow in the vicinity of the particle will be Stoke-sean and there will be no viscous boundary layer at the particle surface. The Peclet diffusion number is equal to Peo = Re Sc. Since for infinite diluted solutions, Sc 10 and the flow can be described as Stokesian for the Re up to Re 0.5, it is perfectly safe to assume Pec 1. Thus, a thin diffusion boundary layer exists at the surface. Assume that a fast heterogeneous reaction happens at the particle surface, i.e. the particle is dissolving in the liquid. The equation of convective diffusion in the boundary diffusion layer, in a spherical system of coordinates r, 6, (p, subject to the condition that concentration does not depend on the azimuthal angle [Pg.128]

Thermoplastics and paint systems that behave Uke thermoplastics are quite often soluble in organic solvents. Many adhesives contain small amounts of such solvents or plasticisers. The diffusion of these products towards the boundary layer can lead to a softening of this layer at the adhesive interface. If the joint is then subjected to stress, the adhesive bond may fail. Since the diffusion process takes place very slowly, months may elapse before the damage manifests itself. Additionally, the user should seek the adhesive manufacturer s advice on an appropriate method of surface preparation. 

A completely general solution of the governing convective diffusion equation (7.2.110), and equation (7.2.111), subject to the boundary conditions (7.2.114), (7.2.115) and (7.2.116) is not available. There are two types of solutions, similarity solutions and integral boundary layer solutions (apart from complete numerical solutions). Common to both of these solutions is the assumption that the particle concentration boundary layer is very thin compared to the membrane channel dimension normal to the axial flow further, the shear stress due to the axial velocity gradient in the particle concentration boundary layer is equal to that at the wall, namely... 

The rate of deposition of Brownian particles is predicted by taking into account the effects of diffusion and convection of single particles and interaction forces between particles and collector [2.1] -[2.6]. It is demonstrated that the interaction forces can be incorporated into a boundary condition that has the form of a first order chemical reaction which takes place on the collector [2.1], and an expression is derived for the rate constant The rate of deposition is obtained by solving the convective diffusion equation subject to that boundary condition. The procedure developed for deposition is extended to the case when both deposition and desorption occur. In the latter case, the interaction potential contains the Bom repulsion, in addition to the London and double-layer interactions [2.2]-[2.7]. Paper [2.7] differs from [2.2] because it considers the deposition at both primary and secondary minima. Papers [2.8], [2.9] and [2.10] treat the deposition of cancer cells or platelets on surfaces. 

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