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تسجيل مستخدم جديدShape of pendant droplets under a tilted surface
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For a pendant drop whose contact line is a circle of radius $r_0$, we derive the relation $mgsinalpha={piover2}gamma r_0,(costheta^{rm min}-costheta^{rm max})$ at first order in the Bond number, where $theta^{rm min}$ and $theta^{rm max}$ are the contact angles at the back (uphill) and at the front (downhill), $m$ is the mass of the drop and $gamma$ the surface tension of the liquid. The Bond (or Eotvos) number is taken as $Bo=mg/(2r_0gamma)$. The tilt angle $alpha$ may increase from $alpha=0$ (sessile drop) to $alpha=pi/2$ (drop pinned on vertical wall) to $alpha=pi$ (drop pendant from ceiling). The focus will be on pendant drops with $alpha=pi/2$ and $alpha=3pi/4$. The drop profile is computed exactly, in the same approximation. Results are compared with surface evolver simulations, showing good agreement up to about $Bo=1.2$, corresponding for example to hemispherical water droplets of volume up to about $50,mu$L. An explicit formula for each contact angle $theta^{rm min}$ and $theta^{rm max}$ is also given and compared with the almost exact surface evolver values.
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