We shall next consider the rise of a liquid between two plates of different materials for which the angles of contact are α1 and α2, the distance between the plates being a, a small quantity. Since the plates are very near one another we may use the following equation of the surface as an approximation:—
y = h1 + Ax + Bx², h2 = h1 + Aa + Ba²,
whence
cot α1 = −A, cot α2 = A + 2Ba
T(cos α1 + cos α2) = ρga(h1 + ½Aa + 1⁄3Ba²),
whence we obtain
| h1 = | t | (cos α1 + cos α2) + | a | (2cot α1 − cot α2) |
| ρga | 6 |
| h1 = | t | (cos α1 + cos α2) + | a | (2cot α2 − cot α1). |
| ρga | 6 |
Let X be the force which must be applied in a horizontal direction to either plate to keep it from approaching the other, then the forces acting on the first plate are T + X in the negative direction, and T sin α1 + ½gρh1² in the positive direction. Hence
X = ½gρh1² − T(1 − sin α1).