The linear stability of thermocapillary liquid layers for Upper Convected Maxwell (UCM) fluid is investigated. Elastic instability is found. The rate of perturbation growth increases with the wave number. For UCM fluid, the critical Marangoni number does not exist, which is different from Newtonian fluid. Instead, a critical wave number is found above which unstable elastic waves appear. The critical wave number decreases with elastic number and Marangoni number. When elastic number approaches zero, the fluid becomes Newtonian fluid with the critical wave number tending to infinity. The wave speed of elastic wave stays constant for different wave numbers and propagating directions. However, the growth rate reaches its maximum in a specific direction. Energy analysis shows the work done by perturbation stress contributes most to the perturbation energy of elastic wave.
; 何蒙
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