Computational Analysis of a Three-Dimensional Liquid Bridge Between Two Right Circular Cylinders

Alexander Virozub, Nir Haimovich, and Simon Brandon. Chemical Engineering, Technion, Haifa, 32000, Israel

Capillary forces acting between two solid bodies, joined by a liquid bridge, are important in many processes such as particle agglomeration, flocculation of slurries, coating of liquid films on solids, generation of highly porous materials, textile wetting and cleaning processes, liquid aerosol filtration, fiber agglutination and soldering.

Several reports exist in the literature regarding the calculation of forces associated with liquid bridges between plates and/or spheres (see e.g. [1-4]). However, to the best of our knowledge, little attention has been given to modeling interactions between liquid droplets and cylindrical solid bodies such as fibers, whiskers or wires. A recent relevant publication [5] is concerned with the theoretical and experimental investigation of the detachment of liquid droplets from a single fiber. However, the model involves significant simplifications, e.g. of the liquid-solid and liquid-gas interface shapes. Moreover, the analysis in [5] does not address the important case of interaction between two mutually wetted cylinders.

In this contribution we will discuss a static analysis of a liquid bridge connecting two right circular cylinders held in a fixed position one with respect to the other. Brakke's Surface Evolver program [6] is used to calculate the resultant equilibrium shape of the liquid bridge for different values of contact angle, volume of liquid, as well as the relative distance and angle between the two cylinders. Results to be presented include the dependence of forces and torques, acting on the cylinders, on relevant parameters; possible practical implications of these results will be discussed. For example, we will show that the torque exerted on the cylinders typically acts to align them parallel one with respect to the other.

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[2] T.-Y. Chen, J. A. Tsamopoulos, and R. J. Good, J. Coll. Int. Sci., 151, 49-69, (1992).

[3] C. D. Willett, M.J. Adams, S. A. Johnson, and J.P.K. Seville, Langmuir, 16, 9396-9405, (2000).

[4] Y. I. Rabinovich, M. S. Esayanur, and B. M. Moudgil, Langmuir, 21, 10992-10997, (2005).

[5] B. J. Mullins, A. Pfrang, R. D. Braddock, T. Schimmel, and G. Kasper, J. Coll. Int. Sci., 312, 333-340, (2007).

[6] K. A. Brakke, Experimental Mathematics, 1, 141-165, (1992).