Shape analysis based critical Eotvos numbers for buoyancy induced partial detachment of oil drops from hydrophilic surfaces

Abstract

Removal of oil drops from solid surfaces immersed in an aqueous medium is of interest in many applications. It has been shown that drop shape analysis can be used to predict conditions at which the stability limit of a lighter than water oil drop on a solid surface immersed in an aqueous bath is reached (Adv. Colloid Interface Sci. 98 (2002) 265). However the above analysis is restricted to cases where the contact angle made by the drop is below 90° and when the surface conditions result in a ‘pinned’ contact line. In this paper, it is shown that drop shape analysis can be used to predict the critical conditions at which drop stability limit is reached for drop contact angles of 90° and above, which is encountered with ‘hydrophilic’ surfaces. This critical condition can predict the occurrence of partial oil drop detachment, before complete removal due to ‘roll-up’, which occurs when the hydrophilic surface is adequately smooth which prevents ‘pinning’ of the contact line. The critical conditions at which partial drop detachment occurs can also be approximately predicted from simple force balances. It has been shown (Adv. Colloid Interface Sci. 98 (2002) 265) that for contact angles less than 90°, the critical limit based on shape analysis appears to resolve the differences that arise due to alternate expressions for capillary retention force. This paper shows that even for contact angles above 90°, the critical conditions predicted from the shape analysis resolves the differences in the predictions from the alternate force balances. Drop shape analysis used in this paper is based on the ‘Arc-length’ form of Young–Laplace or ‘drop shape’ equation, which is different from the ‘ Y vs X’ form of the above equation that is used in Adv. Colloid Interface Sci. 98 (2002) 265. The above drop shape equation is solved by a fourth order Runge–Kutta technique and it is shown that for angles less than 90°, the two forms of the drop shape equation, predict almost identical values of the critical Eotvos number. This paper highlights the competing effects of interfacial tension lowering induced drop instability and ‘roll-up’, a term that is used to describe the retraction of the contact line of an oil drop on a surface, in being the primary cause for drop detachment.