Linear flow, general

For the case of a thread breaking during flow, the analysis is complicated because the wavelength of each disturbance is stretched along with the thread. This causes the dominant disturbance to change over time, which results in a delay of actual breakup. Tomotika (1936) and Mikami et al. (1975) analyzed breakup of threads during flow for 3D extensional flow, and Khakhar and Ottino (1987) extended the analysis to general linear flows. Each of these works uses a perturbation analysis to describe an equation for the evolution of a disturbance. 

Illustration Effect of flow type on shear induced collisions in homogenous linear flows. The collision frequency for a general linear flow [Eq. (15)] is obtained following Smoluchowski s (1917) approach as (Bidkar and Khakhar, 1990)... 

For general linear flows, the limit case of axisymmetric flows [ det(D ) =... 

The dynamics of rigid, isolated spheroids was first analyzed for the case of shear flow by Jeffery[95]. When subject to a general linear flow with velocity gradient tensor G, the time rate of change of the unit vector defining the orientation of the symmetry axis of such a particle will have the following general form,... 

Problem 7-9. Motion of a Force- and Torque-Free Axisymmetric Particle in a General Linear Flow. We consider a force- and torque-free axisymmetric particle whose geometry can be characterized by a single vector d immersed in a general linear flow, which takes the form far from the particle y°°(r) = U00 + r A fl00 + r E00, where U°°, il, and Ex are constants. Note that E00 is the symmetric rate-of-strain tensor and il is the vorticity vector, both defined in terms of the undisturbed flow. The Reynolds number for the particle motion is small so that the creeping-motion approximation can be applied. 

In this section, we consider the problem of a nonrotating sphere in a general linear flow of an unbounded fluid, namely,... 

Instead, in this section, we consider the deformation of a drop in a general linear flow, lor ( a 1, where the shape remains approximately spherical. We assume that the density of the drop is equal to that of the suspending fluid and that the surface tension is constant on the drop surface - that is, there are no thermal gradients and no surfactants present. The fact that the drop is neutrally buoyant means that it does not translate relative to the surrounding fluid. Thus, at large distances from the drop, we can assume that the fluid undergoes a general linear flow of the form... 

We have already seen that this general linear flow includes simple shear, uniaxial extension, and other flows of interest. 

Problem 8-11. The Effect of Surfactant on Drop Deformation in a General Linear Flow. 

The class of general linear flows represented by (9-192) includes simple shear flow as a special case,... 

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