Stability analysis of a thermocapillary spreading film with slip-model

Thin liquid films spreading on a solid substrate due to thermocapillary stresses are susceptible to rivulet instability at the advancing solid-liquid-vapor contact line. The unstable front is related to the presence of a capillary ridge at the contact line. In this work, the dynamics and stability of thermocapillary-driven films are analyzed using a detailed slip-model to alleviate the stress singularity at the moving contact line. The slip-model is well suited to model partially wetting fluids due to the possibility of defining the contact angle explicitly. The effect of motion of the contact line on the dynamic contact angle and subsequently on the dynamics and stability of the film is explored. The apparent contact angle is a result of the static contact angle and motion of the contact line. It is shown that one can obtain exactly the same base profile with and without taking into account the effect of motion on the contact angle with suitable change of parameters but the linear stability of the two profiles is different. Further the transient growth is found to be somewhat different but small for both configurations. Analysis of the ε -pseudospectra indicates a highly non-normal system for the case of dynamic contact angle.