By Pierre-Gilles de Gennes
The learn of capillarity is in the middle of a veritable explosion. what's provided here's no longer a finished overview of the newest study yet really a compendium of rules designed for the undergraduate scholar and for readers drawn to the physics underlying those phenomena.
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Extra info for Capillarity and wetting phenomena : drops, bubbles, pearls, waves
Wieselsburger [25, 26]. -J. 6 Homotopy Analysis Method—The Viscous Drag Coefficient Computed for Arbitrary Reynolds Numbers As revealed by the above mentioned perturbation approaches, and explicitly demonstrated by Fig. 11, the drag coefficient, predicted by them is only in conformity with the experimental results, provided the Reynolds number is small, ideally R < 1 and realistically certainly R < 5. None of the presented perturbation drag formulae is valid for R > 1—more generally for realistic values of R up to R < 2000.
Can be found. 114) with respect to q, then setting q = 0 and finally dividing the resulting equation by m!. This yields the boundary value problems for ψm (r, μ), m = 1, 2, 3, . 121) + in which χm = 1, 2. 119) are all linear and can be solved consecutively, starting with an estimate for ψ0 . 119) for ψ1 , etc. In this way an infinite number of functions ψm , m = 1, 2, . . can be determined. 118) is found. Obviously, this procedure is only useful, provided the sum +∞ m=1 ψm (r, μ) is convergent.
33)1 provided B = 23 aν. With this choice the boundary condition at the surface of the sphere is only approximately satisfied. The final result is 28 11 Creeping Motion Around Spheres at Rest in a Newtonian Fluid U a3 2r 2 + sin2 θ 4 r Ur 3 + aν(1 + cos θ) exp − (1 − cos θ) − 1 . 77) ‘Oseen−let As is known from potential theory, the terms in the first line of this expression are due to doublets (dipoles) at infinity and the origin of the coordinates. Consequently, the third term due to the particular solution of the Oseen equation is characteristically called ‘Oseen-let’.
Capillarity and wetting phenomena : drops, bubbles, pearls, waves by Pierre-Gilles de Gennes