caa a22 4500 469100362 CHVBK 20180323133043.0 cr unu---uuuuu 170328e19920101xx s 000 0 eng 10.1007/BF01054178 doi (NATIONALLICENCE)springer-10.1007/BF01054178 Chivilikhin S. St. Petersburg aut Plane capillary flow of a viscous fluid with mutiply connected boundary in the Stokes approximation [Elektronische Daten] [S. Chivilikhin] A study is made of the process of relaxation to the equilibrium configuration of an isolated volume of a viscous incompressible Newtonian fluid under the influence of capillary forces. The fluid has the form of an infinite cylinder of arbitrary shape with a smooth compact and, in general, multiply connected boundary. In the course of relaxation, internal cavities collapse, and the cylinder acquires asymptotically a circular configuration. The quasisteady Stokes approximation [1] is used to describe the flow. First proposed by Frenkel' [2], this approximation has been used in the calculation of a dynamic boundary angle [3], the collapse of a circular cylinder [4], and the collapse of a hollow cylinder [5]. The analogy between the hydrodynamic equations in the Stokes approximation and the equations of elasticity theory made it possible [6] to describe the relaxation of a simply connected cylinder by a method close to the one employed by Muskheleshvili [7]. In the present paper, the approach of the author [8] based on work of Grinberg [9] and Vekua [10] is developed. It is shown that the true pressure distribution gives a minimum of the integral of the square of the pressure over the region for fixed integral of the pressure over the boundary. An explicit expression for the pressure is obtained in the form of the projection of a generalized function with support on the boundary onto the subspace of harmonic functions. The velocity field on the boundary of the region is calculated. An upper bound is found for the law of decrease of the perimeter of the region and for the time during which the number of connected components of the boundary remains unchanged. Plenum Publishing Corporation, 1992 Fluid Dynamics Kluwer Academic Publishers-Plenum Publishers 27/1(1992-01-01), 88-92 0015-4628 27:1<88 1992 27 10697 https://doi.org/10.1007/BF01054178 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01054178 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Chivilikhin S. St. Petersburg aut NATIONALLICENCE 773 0- Fluid Dynamics Kluwer Academic Publishers-Plenum Publishers 27/1(1992-01-01), 88-92 0015-4628 27:1<88 1992 27 10697 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer