Asymptotic of the velocity of a dilute suspension of droplets with interfacial tension

In this work, we derive the asymptotic expansion of the velocity field of a small deformable droplet immersed in an incompressible Newtonian fluid. Using an appropriate physical scaling of the surface tension with respect to the droplet volume we show that the first order of the asymptotic can be expressed in terms of the velocity field in absence of the droplet and a new kind of moment tensor [2]. Moreover, we determine explicitly this tensor for ellipses and ellipsoids.