M.Sc Thesis

M.Sc StudentRoyi Shabtay
SubjectThe Flow around and within a Viscous Liquid Droplet
Adhering to a Solid Wall
DepartmentDepartment of Aerospace Engineering
Supervisor Full Professors Frankel Itzchak
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


A droplet adhering to a solid surface under external flow may stay in place as a result of surface tension in conjunction with contact - angle hysteresis. There has been a growing interest in understanding the critical conditions for droplet-surface separation. Most of the analytical research dealing with the force balance on the adhering drop neglects the force between the droplet and the solid surface. This force is created by the flow inside the droplet. In this work we estimate the contribution of this force to the general force balance.

We investigate the internal flow within a droplet which is much more viscous than the external fluid. This type of viscous drop is typical of those appearing in the upper respiratory tract of CF or chronically ventilated patients. The high viscosity ratio causes the inner fluid motion to be slow; by the continuity of fluid velocity across the drop surface the outer flow effectively satisfies no-slip condition.

In addition to this assumption our research is based on the assumption that the surface tension effects are dominant and the droplet therefore maintains the shape of a sphere section. We consider a hemispherical drop. Under these assumptions we can separate the problem into two parts: a) The external problem of an imposed shear flow over a planar solid wall with a hemispherical protuberance; b) The inner Stokes flow generated by the now prescribed shear stress distribution over the liquid surface.

The outer flow was simulated by means of a commercially available finite - volume code (ACE programmed by CFDRC). The outer flow was thus solved for Reynolds numbers from 0.05 up to 50. The inner flow was addressed by the use of series expansions in spherical harmonics.

The results of the research show that the relative contribution of the wall to the total force acting to dislodge the droplet is slightly diminishing with the Reynolds number. However, throughout the entire range of Reynolds numbers considered it contributes over one third of the total force. It can thus be stated that the inner flow makes a significant contribution to the balance of forces acting on the droplet and should not be neglected as was formerly thought legitimate.