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The energy per unit drop volume is thus minimizing

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Unformatted text preview: the end caps, we write volume V = πr2 L and moment of inertia I = = ∆ρ π Lr4 . 2 Figure 7.3: A bubble or a drop suspended in a denser fluid, spinning with angular speed Ω. The energy per unit drop volume is thus Minimizing with respect to r: d dr E V 1 = 2 ∆ρΩ2 r − 2γ r2 E V = 1 ∆ρΩ2 r2 + 4 = 0, which occurs when r = 1 ∆ρΩ2 4π 3/2 2γ r. 4γ ∆ρΩ2 1/3 . Now r = V 1/2 πL = 4γ ∆ρΩ2 1/3 ⇒ V 3/2 L Vonnegut’s Formula: γ = allows inference of γ from L, useful technique for small γ as it avoids difficulties associated with fluid-solid contact. Note: r grows with σ and decreases with Ω. 7.2 Rolling drops Figure 7.4: A liquid drop rolling down an inclined plane. (Aussillous and Quere 2003 ) Energetics: for steady descent at speed V, M gV sin θ =Rate of viscous dissipation= 2µ Vd (∇u)2 dV , where Vd is the dissipation zone, so this sets V ⇒ Ω = V /R is the angular speed. Stability characteristics different: bioconcave oblate ellipsoids now stable. MIT OCW: 18.357 Interfacial Phenomena 25 Prof. John W. M. Bush...
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This note was uploaded on 01/23/2014 for the course MATH 18.357 taught by Professor Johnw.m.bush during the Fall '10 term at MIT.

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