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 con
tact 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.
We study the direct incoherent energy transfer from an immobile excited donor molecule to acceptor molecules, which are all attached to polymer chains, randomly arranged in a viscous solvent. The decay forms are found explicitly, in terms of an optim
al-fluctuation method, for arbitrary conformations of polymers.
