Cornered drops and rivulets

We present theoretical and experimental results for a drop of viscous liquid running down an inclined plane at speed U. For U > U-cr the rear of the drop forms a corner whose opening half-angle phi decreases with U. By matching the interior of the drop to the contact line, we calculate phi analytically. We find that above a second critical speed U-riv this solution no longer exists and instead a slender rivulet comes out of the tip of the corner. To compute the width of the rivulet, we match it to the front of the drop, where it is rounded. Our theoretical results on the opening angle, the rivulet width and the drop velocity are in good agreement with experiment.