The Symmetric Sessile Drop

Abstract

We consider a connected drop of liquid of prescribed volume V resting on a horizontal plane П in a vertical gravity field directed toward П,and we suppose the plane to be of homogeneous material so that the contact angle γ will be constant, 0≤γ≤π. Wente has proved [186] that under these conditions any equilibrium surface is generated by an interval of disks centered on a line segment orthogonal to П, so we may restrict attention to that case (see Fig. 3.1). According to (1.51), at a point on the free surface L where the fluid is below L, the height u(x, y) of L above П will satisfy

$$ divTu = ku + \lambda $$

(3.1)

for some constant (Lagrange multiplier) λ.