A soap film, each of whose two faces has surface tension , is held on a wire frame so…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Fluid statics and the continuum picture · Fluid statics and the continuum picture

Fluid Dynamics, Ch Interfaces: capillary statics and the stress conditions at a surface

Problem

A soap film, each of whose two faces has surface tension γ=0.025 N m−1\gamma = 0.025\,\mathrm{N\,m^{-1}}, is held on a wire frame so that it takes up a saddle shape, with air (fluid 2) outside on the side the frame's normal n^\hat{\mathbf{n}} points into, and air (fluid 1) inside a wire loop pumped to a slightly different pressure. At a marked point on the film the two principal radii of curvature are R1=4.0 cmR_1 = 4.0\,\mathrm{cm} (the surface curves towards fluid 2 along this direction) and R2=−10.0 cmR_2 = -10.0\,\mathrm{cm} (the surface curves away from fluid 2, i.e. towards fluid 1, along the perpendicular direction). ((a)) Write the Young-Laplace law for the pressure jump across the film at this point in terms of γ\gamma, R1R_1 and R2R_2. ((b)) Evaluate p1−p2p_1 - p_2 at that point.

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