Hydrodynamic interaction short-range

In other words, it is assumed here that the particles are surrounded by a isotropic viscous (not viscoelastic) liquid, and is a friction coefficient of the particle in viscous liquid. The second term represents the elastic force due to the nearest Brownian particles along the chain, and the third term is the direct short-ranged interaction (excluded volume effects, see Section 1.5) between all the Brownian particles. The last term represents the random thermal force defined through multiple interparticle interactions. The hydrodynamic interaction and intramolecular friction forces (internal viscosity or kinetic stiffness), which arise when the macromolecular coil is deformed (see Sections 2.2 and 2.4), are omitted here. 

Figure 10.3 The influence of the finite dimension of particles in inertia-free flotation on their trajectory in the vicinity of a floating bubble. The liquid flow lines corresponding to target distances b(a,) and are indicated by dashed lines. The continuous lines are characteristic of the deviation of the trajectory of particles from the liquid flow lines under the influence of short-range hydrodynamic interaction...

This result was interpreted by the manifestation of short range hydrodynamic interactions. The role of electrostatic interaction in flotation is confirmed by investigations of the influence of added sodium dodecylsulfate (SDS). Due to SDS adsorption the charge of bubbles increases und the collision efficiency decreases. When following the capture rate it is observed, that at SDS concentrations above 10 M particle deposition completely stops while the contact angle continues to be large. Thus, electrostatic repulsion prevents the contact between particles and bubbles. 

With respect to short range hydrodynamic interactions its influence is not so general as assumed earlier. SHRI manifests itself in emulsion and bubble coalescence. Simultaneously, it is not so important for particles of rough surfaces. 

The theory of short range hydrodynamic interaction (SRHI)... 

The hydrodynamic model, with a no-slip condition on the solid substrate, and supplemented by van der Waals interaction in the precursor film, accounts for macroscopic and mesoscopic scales and provides a reference base for finer, now more specific analyses. In very thin films, the no-slip condition is not valid. Moreover, short-range contributions come into play in the disjoining pressure. 

When a liquid phase becomes very thin, both faces of this film interact. The nature of the interactions may be electrical or of shorter range of interaction [55l (attractive van der Waals forces) or even of very short range of interaction (steric repulsive forces between hydrocarbon chains in lipid bilayers or repulsive hydration forces between oriented water molecules around polar heads of molecules merging in aqueous films between two lipid drop or in soap films). When two faces of such films approach one another, repulsive and attractive forces are unbalanced, giving rise to a constraint, corresponding to a non-equilibrium value of the thickness of the liquid film h. Hydrodynamic instabilities of planar films (dielectric or aqueous) have been widely investigated in the last ten years [54] [55] r59l They are... 

---