Self-Excited Wave on an Interface in a Chemical Reaction

Ryuji Takaki and Kimie Sannomiya

Tokyo University of Agriculture and Technology, Fuchu, Tokyo 183, Japan

(Received April 26, 1989; Accepted July 3, 1989)

Keywords: Surface Wave, Hele-Shaw Cell, Self-Excitation, Nonlinear Wave

Abstract. A hydrodynamical analysis is made of a self-excited wave on the interface between two immiscible liquids, an aqueous solution of a certain surfactant and nitrobenzene with KI, which are confined in a annular tube and undergo a chemical reaction at the interface. The reaction of the surfactant and the iodine ion is considered to modulate the surface tension of the interface, causing the surface wave self-excitation. The Hele-Shaw cell approximation is applied to describe flows of both liquids with the kinematical and the pressure boundary conditions at the interface. The surface tension coefficient g is assumed to vary with the surface elevation speed u_n, as g=g₀(1-cu). The shallow water approximation is applied, and exact solutions are obtained. It is shown that discontinuity points in the solution are inevitable, and that a special treatment at these points gives values of the amplitude and the propagation speed of the wave. These theoretical values agree with experimental ones.