tailieunhanh - Stability of liquid films down an inclined plane

In this paper, the problem of linear stability of viscous liquid films down an inclined plane is solved by finite difference method. It is applicable for moderate values of Reynolds and wave numbers. The obtained results by this method is compared with ones of some papers and with experimental data. | Vietnam Journal of Mechanics, VAST, Vol. 28, No. 4 (2006), pp. 219 - 224 S_T ABILITY OF LIQUID FILMS DOWN AN INCLINED PLANE PHAN THI THU PHUONG AND TRAN VAN TRAN Hanoi University of Natural Sciences Vietnam National University, Hanoi Abstract. In this paper, the problem of linear stability of viscous liquid films down an inclined plane is solved by finite difference method. It is applicable for moderate values of Reynolds and wave numbers. The obtained results by this method is compared with ones of some papers and with experimental data. 1. INTRODUCTION The flow of liquid films down an inclined wall has been often met in Nature, in chemical and food processing industries. This kind of flows may be also observed when very hot solid surfaces need to be cooled safely and effectively. The problem of linear stability of liquid films on inclined plane has been studied early from the work of Kapitza [2]. In later works of many authors, the problem was solved for long wave disturbances at small Reynolds numbers by seeking the solut ion in some kinds of series. For vertical films as shown by experiments and by some theoretical works, instability may occur at very low Reynolds numbers . In last decades of the previous century, nonlinear stability of liquid films down an inclined plane as well as linear stability of heated inclined liquid films had been investigated intensively. The purpose of this paper is to take attempt to solve the stability problem for flows with free surface by numerical method. It is expected that this method will be useful in solving more complicated problem related to flows of the above mentioned kind. 2. PROBLEM DESCRIPTION A viscous liquid layer of thickness H on a solid surface with an inclination angle () , flows down under the gravity action. We call this undisturbed laminar uniform two-dimensional flow as a basic, whose stability is considered here. We also suppose that the liquid film is bounded by a gas on the free surface so that the .