Liquid interfaces in viscous straining flows ... - Itai Cohen Group

Liquid interfaces in viscous straining flows 1870.810 1r(z = h/2)0.60.4[r(z = h/2) – r c ]/r c10 010 –110 –210 –310 10 –4 10 –2 10 010 –6 10 –4 10 –2 10 –6(Q c – Q)/Q c0.20–6 (Q c – Q)/Q cFigure 6. Evolution of the hump radius at z = h/2 as a function of (Q c − Q)/Q c . The insetshows how the radius at half-height reaches its saturation value.8060κ10 210 110 010 –1κ4020κ 010 –210 –30 0.02 0.04 0.06 0.08 0.10h00 0.02 0.04 0.06 0.08 0.10hFigure 7. Mean curvature at the hump tip versus the hump height. Inset shows the same dataon a semi-log plot. When the deflection is sufficiently large, the hump height h has a lineardependence on ln(κ). The dashed line indicates the logarithmic fit which intercepts h =0 at κ 0 .is given by a balance of Laplace pressure and reservoir pressure p 0 .Forp 0 =0.01,the shape is nearly a flat spherical cap. When the interface is only weakly perturbedfrom the Q = 0 shape, both κ and h increase linearly with Q, and therefore κ ∝ h.This linear regime persists until h ≈ 0.02. Beyond this point, κ increases much morerapidly than h. This large increase of κ relative to the increase in h is approximatedwell by a simple mathematical expression, as is evident from the inset for figure 7. In