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 φ decreases with U. By matching the interior of the drop to the contact line, we calculate φ 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.