Hydrodynamic coupling force

Another class of practically important situations arises when the particle is driven toward the interface by the macroscopic flows discussed earlier. Due to the presence of the wall, the hydrodynamic driving forces are modified, which causes the deviation of particle trajectory fi-om liquid streamlines. Hydrodynamic torques on particles and the coupling between the translational and rotational motion also appear, which make the theoretical analysis of this problem rather involved. The problem of a particle moving in a simple shear flow given by Eq. (108) was solved by Goren and O Neill [99]. It was shown that the particle velocity can be expressed as... 

Second, the dynamic equations for polymer motion and for colloid motion are qualitatively the same, namely they are generalized Langevin (e.g., Mori-Zwanzig) equations, including direct and hydrodynamic forces on each colloid particle or polymer segment, hydrodynamic drag forces, and random thermal forces due to solvent motion, all leading to coupled diffusive motion. 

Hydrodynamic brakes are similar in construction to hydrodynamic couplings. The force or torque delivered by the machine to be braked is applied to the pump... 

The earliest and simplest approach in this direction starts from Langevin equations with solutions comprising a spectrum of relaxation modes [1-4], Special features are the incorporation of entropic forces (Rouse model, [6]) which relax fluctuations of reduced entropy, and of hydrodynamic interactions (Zimm model, [7]) which couple segmental motions via long-range backflow fields in polymer solutions, and the inclusion of topological constraints or entanglements (reptation or tube model, [8-10]) which are mutually imposed within a dense ensemble of chains. 

The prime difficulty of modeling two-phase gas-solid flow is the interphase coupling, which deals with the effects of gas flow on the motion of solids and vice versa. Elgobashi (1991) proposed a classification for gas-solid suspensions based on the solid volume fraction es, which is shown in Fig. 2. When the solid volume fraction is very low, say es< 10-6, the presence of particles has a negligible effect on the gas flow, but their motion is influenced by the gas flow for sufficiently small inertia. This is called one-way coupling. In this case, the gas flow is treated as a pure fluid and the motion of particle phase is mainly controlled by the hydrodynamical forces (e.g., drag force, buoyancy force, and so... 

Shanahan and Carre [31-36, 55, 56] have done extensive theoretical work on the coating of viscoelastic surfaces and the effect of soft surfaces on hydrodynamic forces. Again, we have considered this area in a recent review [44]. This area is important in how energy is transferred or lost at the interface. Coupling changes at an inner interface can result in either an increase or decease in the energy dissipated. This has been discussed and observed for a number of acoustic systems [40, 41, 54, 57, 58]. 

Lionbashevski et al. (2007) proposed a quantitative model that accounts for the magnetic held effect on electrochemical reactions at planar electrode surfaces, with the uniform or nonuniform held being perpendicular to the surface. The model couples the thickness of the diffusion boundary layer, resulting from the electrochemical process, with the convective hydrodynamic flow of the solution at the electrode interface induced by the magnetic held as a result of the magnetic force action. The model can serve as a background for future development of the problem. 

Mode coupling theory provides the following rationale for the known validity of the Stokes relation between the zero frequency friction and the viscosity. According to MCT, both these quantities are primarily determined by the static and dynamic structure factors of the solvent. Hence both vary similarly with density and temperature. This calls into question the justification of the use of the generalized hydrodynamics for molecular processes. The question gathers further relevance from the fact that the time (t) correlation function determining friction (the force-force) and that determining viscosity (the stress-stress) are microscopically different. 

Hydrodynamic conditions in a basin may in part result from tectonic forces. Ge and Garven (1989) applied a numerical model of coupled tectonic- and gravity-induced flow to evaluate the relative importance of tectonic influence on groundwater pressure and flow in an otherwise gravity-induced flow system in a hypothetical foreland basin. Forbes et al. (1992) included an evaluation of lateral compression in their numerical reconstruction of the present-day pressure distribution in the Venture Field, Eastern Canada. 

Tenneti, S., Garg, R., Hrenya, C. M., Fox, R. O. Subramaniam, S. 2010 Direct numerical simulation of gas-solid suspensions at moderate Reynolds number quantifying the coupling between hydrodynamic forces and particle velocity fluctuations. Powder Technology 203, 57-69. 

---