By Roland Clift

ISBN-10: 012176950X

ISBN-13: 9780121769505

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**Sample text**

In the literature. the group is often simply referred to as the M-group or property group, and its inverse as the P-group. 111. 5 Shape regimes for bubbles and drops in unhindered gravitational motion through liquids. 28 2. Shapes of Rigid and Fluid Particles in any of the three groups used to construct Fig. 5. The role of p, may be significant, however, for very pure (surfactant-free) systems or for large fluid particles in high M liquids. These cases are considered in Chapters 3 and 8. 5 shows boundaries between the three principal shape regimes described above.

3-4) to (3-6) replaced by the single condition that u, = 0 at r = a. The corresponding streamlines are shown in Figs. 4a. 3 . 3 mation. 4 Streamlines for motion oi'rigid sphere through stagnant fluid at lo\\ Re: (a) Stokes's solution: (b) Oseen approximation. 35 11. Fluid Mechanics streamline curvature over a very extensive region, and there is infinite drift. On the axis of symmetry, the fluid velocity falls to half the sphere velocity almost two radii from the surface. 7 radii. From Eqs. (3-11) to (3-14),the total drag coefficient is given by "Stokes's law": C,,, = 24 'Re.

For steady flow (3-27) Ci . Vv. The final term in Eq. (3-27) dominates at large distances from the body. Since this is the region in which inertial effects are significant, Oseen suggested that the nonlinear term v . Cv be neglected. Equation (1-33) then becomes which is generally called Oseen's equation. The additional term, p U i . Vv, removes the property of "reversibility," so that solutions no longer possess fore-and-aft symmetry. For a rigid sphere, the boundary conditions are Lamb (Ll) has given an approximate solution: * = Ur2 sin2 [8 1+ 2 3Ga2 , + Re ( I -- - cos r Re s) Corresponding streamlines are shown in Figs.

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