Hydrodynamic layer

A very similar effect of the surface concentration on the conformation of adsorbed macromolecules was observed by Cohen Stuart et al. [25] who studied the diffusion of the polystyrene latex particles in aqueous solutions of PEO by photon-correlation spectroscopy. The thickness of the hydrodynamic layer 8 (nm) calculated from the loss of the particle diffusivity was low at low coverage but showed a steep increase as the adsorbed amount exceeded a certain threshold. Concretely, 8 increased from 40 to 170 nm when the surface concentration of PEO rose from 1.0 to 1.5 mg/m2. This character of the dependence is consistent with the calculations made by the authors [25] according to the theory developed by Scheutjens and Fleer [10,12] which predicts a similar variation of the hydrodynamic layer thickness of adsorbed polymer with coverage. The dominant contribution to this thickness comes from long tails which extend far into the solution. 

HPLC, reverse phase 150, 167 Hydrodynamic layer, thickness 141 Hydrogels, applications 99, 105, 127 —, collapse 113, 127-129... 

Initially it was assumed that no solution movement occurs within the diffusion layer. Actually, a velocity gradient exists in a layer, termed the hydrodynamic boundary layer (or the Prandtl layer), where the fluid velocity increases from zero at the interface to the constant bulk value (U). The thickness of the hydrodynamic layer, dH, is related to that of the diffusion layer ... 

If diffusion occurs towards the surface of the plate, the motion of the liquid at a distance from the surface inside the hydrodynamic layer is sufficient to maintain the original concentration in the bulk of the solution, c°. A decrease of the concentration to a value c at the phase boundary... 

The force-distance profiles Al, A2 appear to show the relaxed, or quasi-equilibrium limit for the interaction between the mica plates bearing the PEO in the good solvent conditions of the present study. The adsorbed layer thicknesses 6 are then about half the value of D at which onset of repulsion (A curves) is first noted. 6 thus corresponds to some 3Rg for both polymers in the present investigation, a value comparable to that obtained for hydrodynamic layer thickness of PEO absorbed on latex particles in water, for similar molecular weights, from light scattering studies. 

Keywords Block copolymers Director Hydrodynamics Layer normal Layered systems Liquid crystals Macroscopic behavior Multilamellar vesicles Onions Shear flow Smectic A Smectic cylinders Undulations... 

Within the interstices of the brush border is a hydrodynamic layer of unstirred water , which must act, to some extent, to modify the kinetics of the transport processes (Chapter 5). The significance of this layer as a diffusion barrier, is, however, a matter of dispute (458). 

The first is the concept of a hydrodynamic layer of thickness <5H, within which all velocity gradients occur. In practice one uses values that differ by 5 per cent from their values at infinite distance from the electrode surface, given that the components tend asymptotically to their values in bulk solution. It has been demonstrated that11... 

In Chap. 2, the concept of the diffusion layer was established. It is a thickness, within which a large fraction of diffusional changes take place, and at a distance of several times this thickness, practically no more diffusional changes are observed. This layer will here be given the symbol 8b (D for diffusion). In fluid dynamics, there is a similar layer, within which most of the velocity changes occur. This is the hydrodynamic layer 8. It turns out that for diffusive mass transfer, 8b is usually much smaller than <5/,. This is fortunate, because it justifies to some extent the linearised velocity profiles often assumed near walls, making analysis easier. These relations are very lucidly discussed in a classic paper by Vielstich [560]. 

Stagnant hydrodynamic layer - hydrodynamic boundary layer... 

The values thus estimated (Table 3.4) are in reasonable agreement with the hydrodynamic layer thicknesses on polystyrene latex measured by photon correlation spectrometry and ultracentrifugation [224]. 

After a distance (the entry length) from the entrance, the hydrodynamic layers from each wall merge, and the flow regime established is laminar in form (Compton and Coles, 1983 Albery and Bruckenstein, 1983) in which separate... 

It should be realized that hydrodynamic techniques measure an effective thickness obtained by comparing the tangential flow along a polymer-covered surface with that along a bare surface. The effective thickness thus found is usually called the hydrodynamic layer thickness. The exact shape of the flow velocity profile is Important, and this depends on the shape of the surface in question, and on its orientation with respect to the flow field. Detailed data Interpretation is therefore only possible if simple geometries are chosen such as smooth cylindrical channels or spherical colloidal particles. 

Figure 5.23. Theoretical hydrodynamic layer thickness as a function of chain length. The figure gives d as computed from the complete volume fraction profile (solid curve), from the loops and trains only (dotted curve), and from the tails only (dashed curve). Parameters = L It = 0.5, (p = 10 , hexagonal lattice. Redrawn from ref. f.

When the hydrodynamic thickness is plotted as a function of the adsorbed amount T, a steep Increase is found as F approaches saturation. This Is schematically Illustrated in fig. 5.24, both for a good solvent and for a poor solvent. In the good solvent saturation corresponds to a relatively low F, whereas in a poor solvent higher adsorbed amounts can be accomodated. The key feature of the two drawn curves in fig. 5.24 Is that a small increase In F on a crowded surface (saturation) leads to a considerable increase of the hydrodynamic layer thickness because the additional segments are forced to form tails. Another Important aspect is that d at given F and solvency hardly depends on the chain length 2). However, In order to obtain the same F for short and long chains, quite different bulk concentrations are usually required. 

Figure 5.24. The hydrodynamic layer thickness d as a function of the adsorbed amount r (schematic), and the effect of changes in the solvency under various experimental conditions, as symbolized the arrows. For explanation see text.

Figure 5.25. The hydrodynamic layer thickness as a function of adsorbed amount F for (a) PEO/H2O/PSL and (b) PE0/H20/S102. In both cases a range of molecular weights was used. The data in diagram (a) were obtained by PCS ). those in diagram (b) by viscosity measurements on dispersions .

The dependence of planarizarion rate on hydrodynamic layer thickness. (From Ref. (31).)... 

In this equation, D is the diffusion coefficient of the solute, h is the hydrodynamic layer thickness, V is the volume of medium, and C is the solute concentration in the bulk of the solution. Water is the usual solvent used for these studies. 

Helmholtz layer contains the second water molecule layer. From the Helmholtz double layer toward the bulk electrolyte are the diffusion layer and the hydrodynamic layer. In the diffusion layer, the concentration of species changes from that of the bulk electrolyte to that of the electrode surface. The diffusion layer does not move, but its thickness will decrease with increasing bulk electrolyte flow rate to allow higher reaction rates. The diffusion layer thickness is inversely proportional to the square root of the flow rate. The hydrodynamic layer or Prandtl layer has the same composition as the bulk electrolyte, but the flow of the electrolyte decreases from that of the bulk electrolyte to the stationary diffusion layer. 

The Schmidt number for the mass transfer is analogous to the Prandtl number for heat transfer. Its physical implication means the relative thickness of the hydrodynamic layer and mass-transfer boundary layer. The ratio of the velocity boundary layer (S) to concentration boundary layer (Sc) is governed by the Schmidt number. The relationship is given by... 

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