| الوصف: |
Wave propagation in a system of two arbitrary fluids separated by a contaminated interface in the form of an insoluble monolayer is investigated. The effects of four parameters (density ratio, R ; kinematic viscosity ratio, V ; Marangoni number, P ; and squared wave-Reynolds number, σ ) on the solutions of a comprehensive dispersion relation for these waves are analyzed. In the first part of the manuscript, several special cases are considered wherein the comprehensive dispersion relation is modified to a simple polynomial equation and its numerical solutions are obtained for σ ∈ [ 0 , 1 ] . A bifurcation is observed at σ = σ b in two of the solutions in each case; and the system is shown to be overdamped for σ σ b , and underdamped for σ > σ b . The relative influences of { R , V , P } on σ b are also analyzed, and it is found that in general, σ b is a strong function of { R , V } , but a weak function of P . In the second part of the manuscript, numerical solutions of the comprehensive dispersion relation are obtained for waves in a decane-water system, in the limit of { P ≫ 1 , σ ≫ 1 } ; and these solutions are classified to correspond to a transverse wave or to a longitudinal wave. The presence of a maximum/minimum in the frequency of oscillation and in the damping rate is observed for the transverse/longitudinal waves. For both the transverse and longitudinal wave modes, the relative deviation of the numerical solution (obtained from the comprehensive dispersion relation) from the respective approximate solution (obtained from a simple dispersion relation) is calculated. The relative deviation, though small, cannot be neglected because it accounts for the effects of elasticity and of capillarity/gravity; and disregarding it in the analyses will fail to yield the inherent maximum/minimum in the frequency of oscillation and in the damping rate for the transverse/longitudinal waves. |
