Colloids arId Surfices, 67 (1991) 119- 138 Elscvier Science Publishers B.V.. Amsterdam 119 zyxwvuts Capillary meniscus interaction between a microparticle and a wall zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA V.N. Paunov”, P.A. Kralchevsky”, N.D. Denkov”, LB. Ivanova and K. Nagayamab “Laboratory of T}rer~~todynnmics arid Physico-Chemical Hydrodyrzamics, University of Sofia, Faculty of zyxwvutsrqpon C ile nristry, SoJia 1126, Bulgaria bNagayanla Protein Away Project, ERATO. JRDC, 18-1 Higashiarai, Tsukuba 305. Japalt (Received 3 January 1992: accepted 13 March 1992) Abstract An analytical expression for the shape of the capillary menis, R formed around a vertical cylinder or spherical particle near a vertical wall is derived by using the method of matched asymptotic expansions. The forces of capillary interaction bctwccn the particle (cylinder) and the wall arc calculated. The resulting expressions are valid when the distance bctwecn the particle (cylinder) and the wall, as well as the particle radius, are much smaller than the capillary length. This range corresponds to colloidal and micron-size particles. The theory predicts attraction bctwccn such a particlc and the wall. The results can be useful for a better understanding of proccsscs such as surface coagulation and two-dimensional ordering of colloidal particles or protein molcculcs attached to a fluid intcrfacc. Kq+\~ords: Asymptotic expansions; capillary meniscus forces: microparticlcs. 1. Introduction The deformation of a liquid-fluid interface due to trapped small particles gives rise to capillary forces exerted on the particles. Usually these forces are attractive and lead to formation of clusters. Such effects were observed long ago and are utilized in some extraction and separation flotation pro- cesses (see for example Refs [ 1,2]). The capillary meniscus interactions were studied experimentally by Minsch [3] and Camoin et al. [4]. These forces can be among the main factors leading to formation of two-dimensional clusters and ordered structures observed with micron-size particles [S-7] as well as with protein molecules [S-lo]. Despite the well-established importancs of the capillary meniscus forces, there are only a few theo- Corrqmdence 10: I.B. Ivanov, Laboratory of Thermo- dynamics and Physic+Chemical Hydrodynamics, University of Sofia. Faculty of Chemistry, Sofia 1126, Bulgaria. retical works devoted to them. Nicolson [ 111 derived an analytical expression for the capillary force between two floating bubbles by using the superpo- sition approximation to solve the Laplace equation of capillarity. A similar approximate method was applied by Chan et al. [ 121 to floating spheres and horizontal cylinders. For the latter case alternative approaches were proposed by Gifford and Striven [13] and by Fortes [14]. The theoretical works [ zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJI 1 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLK l- 141 are based on solutions of the Laplace equa- tion for capillary menisci of translational or rota- tional symmetry, where the Laplace equation reduces to an ordinary differential equation. A recent development in this field is the analyti- cal solution of the Laplace partial diflerential equa- tion in bipolar coordinates proposed in Refs [15,16] for the case of small particles and small meniscus slope. This solution provides expressions for calculating the capillary meniscus force between two vertical cylinders, between two spheres par- Ol66-6622/92/SO5.00 0 1992 - Elsevicr Science Publishers B.V. All rights rcscrvcd.