Relation between surface tension and viscous forces during thin film formation in a microchannel

Question

Hi guys,

I am trying to study (understand) thin film formations on micro channel wall surfaces. In a recent paper published:

https://hal.archives-ouvertes.fr/IJLRDA/hal-01312931v1, ; (From the paper text in quotes.)

" Film thickness is governed by the balance between surface tension and viscous stresses. As the former tends to minimize the interface curvature and pushes the droplet interface closer to the wall, the latter tends to open up the gap between the droplet and the wall."

I am not able to understand how come surface tension minimize interface curvature (this means it increases radius of drop but in reality surface tension tends to minimize the surface area of contact, therefore it tends to relax to a circle/ sphere).

Can anyone help me understand things better. Thanks!!

Answer 1

There is no contradiction. Ignoring external forces, the free surface (not the contact surface - else the contact would be a point only!) is minimized subject to a volume constraint and constraints depending on the bounding material (wall, frame). It also tends to minimize the mean curvature (an integral over local curvature), since the pressure difference across a fluid interface is proportional to the mean curvature.

Of course it cannot alter the size of a droplet but it locally a droplet is fairly flat, compared to a wiggly surface, which has higher local curvature. The integrated curvature will become smaller if the wiggles are smoothed out, resulting in a spherical surface. Without the wall and ignoring gravitation it would form a perfect sphere. The effect of the wall depends on the material (of both fluid and wall) ; different materials lead to different contact angles between wall and fluid surface.