{"title":"Migration of a Drop in Simple Shear Flow at Finite Reynolds Numbers: Size and Viscosity Ratio Effects","authors":"M. Bayareh, S. Mortazavi","country":null,"institution":"","volume":37,"journal":"International Journal of Physical and Mathematical Sciences","pagesStart":31,"pagesEnd":38,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/15647","abstract":"The migration of a deformable drop in simple shear\r\nflow at finite Reynolds numbers is investigated numerically by\r\nsolving the full Navier-Stokes equations using a finite\r\ndifference\/front tracking method. The objectives of this study are to\r\nexamine the effectiveness of the present approach to predict the\r\nmigration of a drop in a shear flow and to investigate the behavior of\r\nthe drop migration with different drop sizes and non-unity viscosity\r\nratios. It is shown that the drop deformation depends strongly on the\r\ncapillary number, so that; the proper non-dimensional number for the\r\ninterfacial tension is the capillary number. The rate of migration\r\nincreased with increasing the drop radius. In other words, the\r\nrequired time for drop migration to the centreline decreases. As the\r\nviscosity ratio increases, the drop rotates more slowly and the\r\nlubrication force becomes stronger. The increased lubrication force\r\nmakes it easier for the drop to migrate to the centre of the channel.\r\nThe migration velocity of the drop vanishes as the drop reaches the\r\ncentreline under viscosity ratio of one and non-unity viscosity ratios.\r\nTo validate the present calculations, some typical results are\r\ncompared with available experimental and theoretical data.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 37, 2010"}