Mechanisms of Deagglomeration in Viscous Media

A flow field is laminar, when it is governed by the viscous properties. That applies to very slow fluid velocities or very high viscosities, which are typical for polymer composites or highly concentrated suspensions (e.g. paints). There are three ideal types of laminar flow uniform flow (e.g. experienced by settling particles), shear flow (e. g in rheometers or pipes), and elongational flow (e.g. in nozzles and diffusers). Only the latter two are relevant for deagglomeration. 

Particles that move in a laminar flow field with velocity gradient y experience shear and normal stresses which vary along/across the surface and induce particle rotation and deformation. The rotation of spheres is stable with an angular velocity of CO = 1/2 X 7 (Jeffery 1922 Trevelyan and Mason 1951), whereas aspherical particles or agglomerates rotate in a quasi-periodic or even chaotic manner (Blaser 

In any case, rotation means fluctuating hydrodynamic forces on the surface elements of the particle. The maximum stress for spherical particles can be calculated as (Raasch 1962)  

In elongational flow, the velocity gradient is parallel to the direction of flow. This leads to a stretching of particles by tensile stress and may eventually lead to rupture. In contrast to laminar shear, there is no permanent rotational motion the particle thus experiences a quasi-static load. 

Turbulence occurs in any sufficiently rapid flow when the fluid inertia exceeds its molecular friction. It is the typical flow regime when suspensions of relatively low viscosity are dispersed—e.g. by stirring or in nozzles. Turbulent flow is characterised by multiscale eddy structures that erratically move through the flow field and cause local fluctuations in velocity and pressure. The velocity fluctuations can be quantified by the effective velocity difference Am over a distance Ar (Kolmogorov 1958). For the inertial subrange of microturbulence, it amounts to  

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