International Journal of Dynamics of Fluids ISSN 0973-1784 Volume 3, Number 2 (2007), pp. 109–132 © Research India Publications http://www.ripublication.com/ijdf.htm Mobility of a Viscous Newtonian Drop in Shear Newtonian Flow Mauricio Giraldo 1* , Henry Power 2** and Whady F. Flórez 1*** 1 Instituto de Energía y Termodinámica, Universidad Pontificia Bolivariana Circ 1 No. 73-74, Medellín, Colombia 2 School of Mechanical, Materials and Manufacturing Engineering University of Nottingham, Nottingham, NG7 2RD, UK * E-mail: mauricio.giraldo@upb.edu.co ** E-mail: henry.power@nottingham.ac.uk *** E-mail: whady.florez@upb.edu.co Abstract Simulation of flows containing viscous drops is of great importance in industry and academy. In order to understand large scale phenomena, the basic interactions between drops must be studied, but the simulation of such cases is accompanied by a number of difficulties both mathematical and numerical. Boundary Integral, Methods leading to Fredholm integral equations of the second kind are best suited to ascertain a mathematically robust and numerically efficient formulation to model the behaviour of viscous deformable drops. In this paper, pair wise interactions at lo Reynolds number between two viscous Newtonian drops are numerically simulated in order to obtain mobility magnitudes under linear shear flow of different strengths. Simulations performed showed that under normal conditions particles would decrease their cross flow distance in time, but in situations of high capillary number (small surface tension) and low viscosity ratio, particles showed separation in the cross flow direction. The integral formulation for drop deformation has numerical singularities at the two extreme cases regarding the viscosity ratio: zero (gas bubble) and infinite (solid particle). After solving these two cases with their corresponding integral formulations it was found that drops with very low viscosity ratios behave asymptotically as bubbles, while drops with very high viscosity ratios do so as solid particles, coinciding with both mathematical and physical considerations. Keywords: Boundary-integral methods, Low-Reynolds-number flows, Multiphase and particle-laden flows, Mobility, Deformable Newtonian viscous drops.