In this paper, we present a numerical model based on the widely used ¯nite element formulation to analyze in detail the e®ect of surface active agents on capillary–gravity wave parameters such as phase velocity and wave amplitude. Moreover, the e®ect of a physicochemical parameter, which is the ratio of surface concentration to surface tension is also considered. For a number of °uid samples covering a range of concentrations from 0 to 0.01 molar, the phase speed of waves propagating on the surface of the liquid is found to decrease monotonically as the concentration of the solution considered is increased up to a limit of 0.004 molar. This is attributed to the corresponding increase in capillary number. It is shown numerically that the Marangoni e®ects contribute to the interfacial dynamics for °uid with physicochemical parameter value greater than 0.5. Moreover, a grid re- ¯nement study shows accuracies and convergence orders of the numerical model.
کلید واژگان :Multiphase °ow; transient analysis; physicochemical parameter; Marangoni e®ect; thin ¯lm °ow.
ارزش ریالی : 600000 ریال
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