Executive Summary : | Liquid layers flowing down on a substrate find application in many technological and natural processes. Under certain conditions, these films exhibit instability. In certain applications, these instabilities are desirable, whereas in others they need to be suppressed. Hence it is important to understand the stability characteristics of liquid layers flowing down on a substrate from the most fundamental point of view. In most applications, the substrate is not perfectly flat. The undulations on the substrate may be introduced on purpose (e.g. in heat transfer applications), whereas in other cases it may be unavoidable. Moreover, in applications such as cooling of an electronic board, the non-planar substrate is expected to show substantial non-uniformity in temperature these practical situations. A complete picture of the combined effect of waviness of the substrate and non-homogeneous wall temperature on the different modes of instability of film flow is still elusive. Especially experimental studies on such systems is very rare, if not nil. Recognizing this research gap in the literature, the proposal puts forward an experimental work on instabilities on film flowing down on non-isothermal wavy bottom. Analytical treatment of the problem is also planned. An experimental setup to study the stability characteristics of a liquid film flowing down on a non-uniformly heated wavy incline will be designed, developed and installed. The effect of buoyancy and thermocapillarity on the modes of instability will be focused. Detailed stability map in the space of various parameters involved, such as the geometric features of the corrugation, wall heat flux, equilibrium water height, inclination, etc. will be presented. Analytical linear stability analysis based on long-wave approximation, non-linear stability analysis, non-modal transient growth analysis of the problem will be carried out. The analytical/numerical results will provide further insight into the interplay between various mechanisms underlying the flow physics. Additional factors such as solutal Marangoni effect and the effect of viscosity, non-Newtonian behavior, etc. will also be investigated both numerically and experimentally, if time permits. Finally the possibility of using the results to develop an active feedback control scheme for the film stability for various application will be explored. |