Flow Classification

Flow is classified broadly as shear fiow and extensional fiow. A catalog of various types of shear fiows has been given by Bird et al. [4]. In the present book, the discussion is restricted mainly to simple shear flow that occurs when a fluid is held between two parallel plates. Simple shear flow could be of the steady or unsteady type. Thus, flow is classified here under three headings  

The definitions of important rheological parameters under each of the three headings are given below. 

Ruid deformation under steady simple shear flow can be aptly described by considering the situation in Fig. 2.1 wherein the fluid is held between two large parallel plates separated by a small gap dxi and sheared as shown. 

The lower plate is moving at a constant velodty Vi while the upper plate is moving at a constant velocity of + dvi under the action of a force/applied to it A thin layer of fluid acQacent to each plate moves at the same velocity as the plate, as aiining the no-slip condition at the solid boundary. Molecules in the fluid layers between these two plates move at velocities whidi are intermediate between Vi and Vi -F dvi. Under steady-state conditions, the force/required to produce the motion becomes constant and is related to the velocity. The velocity profile of the fluid within the gap is given by tfvi = if where if is a constant. 

The velocity gradient (dvjdx, which is termed the shear rate -y can also be written as 

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Tanner, R. I., A test particle approach to flow classification for viscoelastic fluids. AIChE J. 22, 910-918 (1976). 

The problem of two-phase-flow classification is complicated by the inevitable differences due to individual interpretations of visual observations, and also by differences in terminology. Fig. 1, taken from the work of Govier et al. (G6), shows the variation in terminology used for vertical gas-liquid flow patterns. It includes a classification of flow regimes proposed by Govier et al. based on pressure-drop behavior rather than visual observations, as illustrated in Fig. 2. In the definitions adopted by the writer, which follow, an attempt has been made to select the most... 

There are some other flow classifications, for example, with respect to specific properties of the boundary of the flow region fluid flow with free boundaries [385], fluid flow with interface [226, 501], and flow along a permeable boundary [524], This classification also allows one to describe properties of various flows and suggest methods for studying these flows. 

Chella, R. and Ottino, J.M. (1985) Stretching in some classes of fluid motions and asymptotic mixing efficiencies as a measure of flow classification. Ardt. Rat. Mech. Anal.,... 

Tucker s Flow Classification for Fiber Suspension in Thin Cavities... 

A kinematic flow classification can be based on Q. If the flow is extensional Ck = 0, for viscometric flow = 1 and for flow which is rigid rotational - oo similarly, a rheological flow classification based on can be formulated. When the flow is viscometric = 0, if the flow has extensional characteristics > 0, and for a flow which has rigid rotational characteristics < 0. This seems to be the most satisfactory flow classification yet devised the distinction between a kinematic and a rheological classification is particularly useful and significant. The criticism of this classification made by Huilgol is false, as Astarita has shown. 

With this presentation on pneumatic conveying, the basic design consideration and analysis is reviewed. Further analysis of such systems is possible. One theme that has received much attention is the area of flow classification with several diflerent phase diagram approaches. 

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