Thermocapillary Flow Near a Cold Wall

The thermocapillary feedback mechanism important at the edge of weld pools and other materials processes is examined through a model problem A pool of liquid with a at horizontal free surface is bounded on one side by a vertical solid wall which is maintained at a cold temperature to unit depth and at a warmer temperature below far away the uid is at the warmer temperature Surface tension is a decreasing function of temperature so that the surface thermal gradient drives ow toward the corner When convection is vigorous the ow compresses the thermal gradient which is driving the ow this positive feedback results in small local length scales and high velocities near the corner This problem is examined through a detailed scaling analysis and through numerical simulation for a range of parameters The results show that for vigorous convection the ow in the cold corner is locally determined Typeset using REVTEX