Analysis on the free surface flow induced by a pair of source-sink in Stokes flow

스톡스 유동장 내의 한 쌍의 소오스-싱크에 의한 자유표면 유동해석

Two-dimensional Stokes flow due to the line source and line sink of same strength in semi-infinite flow region with free surface is analysed using complex variable theory and conformal mapping. Surface tension effects are included while gravity is neglected. From the results of analysis, flow pattern and free surface shape are obtained and velocity distribution on the free surface is determined with 2 independent parameters Ca (capillary number) and h (non-dimensionalized distance between source and sink). When the location of the sink is above the source, velocity on the free surface converges and a cusp occurs on the free surface for the value of Ca above some critical capillary number.