ABSTRACT

For contact between the surfaces, Fig. 4 (H = 0 and hence H' = 0), it follows from equation (10) that

where the subscript 0 indicates zero separation distance. Substituting equation (13) in to equation (12), the following expression for the capillary radius at zero separation distance, ro, is obtained:

where

ao = arctan (15)

and Vb is original volume of the annulus at contact. Note that for this boundary condition the radius is constant, so for all separation distances r = rn. Therefore, equation (14) is equivalent to equation (12) and the relationship between xf and Hf

becomes

Hence, as for the constant volume annulus boundary condition, the adhesion force for an annulus of constant radius can be predicted from equations (4) and (5) but with the value of x' from equation (16) instead of equation (10). Note that the capillary force of adhesion as a function of the separation distance can also be calculated for a constant meniscus radius boundary condition using equation (1) in combination with equation (14) for the radius. It should be noted that this equation does not account for the surface tension component of the capillary force. A comparison between these two approaches for a fixed radius of meniscus will be presented below.