Shear-induced diffusivity

The velocity, viscosity, density, and channel-height values are all similar to UF, but the diffusivity of large particles (MF) is orders-of-magnitude lower than the diffusivity of macromolecules (UF). It is thus quite surprising to find the fluxes of cross-flow MF processes to be similar to, and often higher than, UF fluxes. Two primary theories for the enhanced diffusion of particles in a shear field, the inertial-lift theory and the shear-induced theory, are explained by Davis [in Ho and Sirkar (eds.), op. cit., pp. 480-505], and Belfort, Davis, and Zydney [/. Membrane. Sci., 96, 1-58 (1994)]. While not clear-cut, shear-induced diffusion is quite large compared to Brownian diffusion except for those cases with very small particles or very low cross-flow velocity. The enhancement of mass transfer in turbulent-flow microfiltration, a major effect, remains completely empirical. 

These equations describe the coupled phenomena between diffusion and viscous stresses, existing, for example, in diffusion of small molecules in polymer matrix. Other possible couplings occur in shear-induced diffusion and shear-induced separation. 

TABLE 8.1 Coefficient Coefficients in Equation 8.1 for Different Mechanisms Brownian Diffusion Shear-Induced Diffusion Inertial Lift ... 

Although this picture is remarkably generic, the mechanisms responsible for the formation of a particle-lean layer adjacent to the wall depend on the properties of the material under consideration. For the case of solid particle dispersions, wall depletion, particle migration, and solid-liquid separation are the most frequent sources of solvent layer lubrication. Wall depletion occurs whenever dispersions are brought into contact with smooth and solid surfaces because the suspended particles cannot penetrate rigid boundaries [147]. Particle migration is due to various forces arising from fluid inertia, fluid elasticity, and shear-induced diffusivity effects [165]. Solid-liquid separation, which frequently occurs in flocculated suspensions like... 

The shear induced diffusivity D, is about 60 times the molecular diffusivity D. ... 

Three mechanisms are important for the backtransport of particles from a membrane. For small solutes and submicron colloids. Brownian Diffusion (determined by the Stokes-Einstein equation (Sethi and Wiesner (1997)) dominates backtransport of the colloids from the membrane into the bulk solution. Inertial Lift, which is caused by the presence of a wall is important for large particle sizes and high shear rates. Shear Induced Diffusion is an orthokinetic mechanism also more important for larger colloids. 

Chellam S., Wiesner M.R. (1998), Evaluation of crossflow filtration models based on shear-induced diffusion and particle adhesion Complications induced by feed suspension polydispersity. 

A unique interaction between fluid mechanics and transport exists for filtration processes. Such processes perform better than expected based on the predicted impact of concentration boundary layers. The improvement in performance, a rare occurrence for membrane processes, arises from a combination of hydrodynamic diffusion and inertial lift [51]. Hydrodynamic interactions between particles or colloids that accumulate in the concentration boundary layer lead to shear-induced diffusion away from the membrane surface. Shear-induced diffusion can be significantly larger than molecular diffusion and thereby reduce surface concentrations. For sufficiently large particles at high shear rates, inertial lift becomes the dominant mechanism for particle movement away from the membrane. 

The diffusion of NPs in blood flow can be due to (1) Brownian diffusion caused by the bombardment of fluid molecules and (2) shear-induced diffusion due to the presence of red blood cells (RBCs) in shear flow. The Brownian diffusion coefficient, Dpr, can be calculated using the Stokes-Einstein equation ... 

The shear-induced diffusion effect and the transition to irreversibility... 

One of the most beautiful results manifesting the effect of flow on diffusion is the shear-induced diffusion effect, which is the quantitative manifestation of the transition to irreversibility in a set of particles obeying the classical reversible equations of motion. Recently, this effect was studied in a series of experiments and numerical simulations were the transition from a dynamical reversible behavior to a dynamical irreversible chaotic behavior of a suspension of non-Brownian particles was directly observed (Drazer, 2002 Pine, 2005). The importance of these experiments lies in the fact that they shed light on the origin of the thermodynamic irreversibility and its relation to the chaotic dynamics of a system (Guasto Gollub, 2007 Pine, 2005). 

To close this section, we want to emphasize that the explanation of the experiments and simulations on shear-induced diffusion shows the validity of the theoretical approach and its importance, because it was shown that the shear-induced diffusion and the transition to irreversibility are fully compatible with the thermodynamic irreversibility as obtained from the second principle and the generalized Gibbs entropy postulate. 

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