We consider picoliter sized water droplets immersed in a fluid with different viscosity. At these small scales, inertial effects are negligible, and the dynamics are governed by the Stokes equations. With the large surface to volume ratio of these drops, the dynamics at the interface become extremely important and it is very natural to consider integral equations for this Stokes flow problem. The integral equations are defined on the interfaces only, require no meshing of the volume, and naturally incorporate the interfacial conditions. A high order discretization based on integral equations can be made using an accurate surface representation and quadrature method with special attention in dealing with singularities. We consider a representation for each drop surface in terms of a spherical harmonics expansion, the surface counterpart to a Fourier series for a closed curve. We focus on strategies for updating these representations dynamically with particular attention on accuracy and efficiency. A special quadrature method for dealing with multiple drops and close interactions is considered. Moreover, high distortions of the surface point distribution may arise, especially for long time simulations; for this reason, an adaptive reparametrization procedure has been implemented. The next step in the project is to add an insoluble surfactant and study the effect on drop deformation.