Viscous Solitons on Film Flows Falling Down a Vertical Wall

概要

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We study liquid film flows falling down a vertical wall, focusing our attention to the limit of high viscosity. For highly viscous liquids (small Kapitza number), it is possible to find a limit in which both Reynolds number R and Weber number W vanish;the governing equations are then reduced to the Stokes equation with free-surface boundary conditions. Theoretical analysis with regularized long-wave expansion yields the modified Benjamin-Bona-Mahony equation as a reduced equation describing one-dimensional surface dynamics. The surface dynamics exhibits a soliton-like behavior: two solitary waves are seen to collide elastically in our numerical calculation. This phenomenon arises in highly viscous situation (described by the Stokes equation), which is opposite to that of inviscid "water waves" (described by the Euler equation). As a step toward comparison with real experiments, a preliminary calculation of two-dimensional surface dynamics (three-dimensional flows) is also presented.
日本学術会議「機械工学委員会・土木工学・建築学委員会合同IUTAM分科会」の論文