Capillary Bridges and Capillary-Bridge Forces：毛细管桥和毛细管桥力.pdf

Capillary Bridges and Capillary-Bridge Forces 469 Chapter 11 in the book: P.A. Kralchevsky and K. Nagayama, “Particles at Fluid Interfaces and Membranes” (Attachment of Colloid Particles and Proteins to Interfaces and Formation of Two-Dimensional Arrays) Elsevier, Amsterdam, 2001; pp. 469-502. CHAPTER 11 CAPILLARY BRIDGES AND CAPILLARY-BRIDGE FORCES The importance of capillary bridges has been recognized for many systems and phenomena like consolidation of granules and soils, wetting of powders, capillary condensation and bridging in the atomic-force-microscope measurements, etc. The capillary bridge force is oriented normally to the plane of the three-phase contact line and consists of contributions from the capillary pressure and surface tension. The toroid (circle) approximation can be applied to quantify the shape of capillary bridges and the capillary-bridge force. More reliable results can be obtained using the exact profile of the capillary bridge, which is determined by the Plateau sequence of shapes: (1) nodoid with “neck”, (2) catenoid, (3) unduloid with “neck”, (4) cylinder, (5) unduloid with “haunch”, (6) sphere and (7) nodoid with “haunch”. For the shapes (1-5) the capillary-bridge force is attractive, it is zero for sphere (6) and repulsive for the nodoid (7). Equations connecting the radius of the neck/haunch with the contact angle and radius are derived. The procedures for shape calculations are outlined for the cases of bridges between a plane and an axisymmetric body, and between two parallel planes. In the asymptotic case, in which the contact angle belongs to the range 70 90, the elliptic integrals reduce to