Droplet breakup in flow past an obstacle: A capillary instability due to permeability variations

¹ Department of Physics and SEAS, Harvard University - Cambridge, MA 02138, USA
² Departments of Chemical Engineering and Mathematics, MIT - Cambridge, MA 02139, USA
³ Department of Mechanical and Aerospace Engineering, Princeton University - Princeton, NJ 08544, USA

^a protiere@ida.upmc.fr

Received: 27 September 2010
Accepted: 16 November 2010

Abstract

In multiphase flow in confined geometries an elementary event concerns the interaction of a droplet with an obstacle. As a model of this configuration we study the collision of a droplet with a circular post that spans a significant fraction of the cross-section of a microfluidic channel. We demonstrate that there exist conditions for which a drop moves completely around the obstacle without breaking, while for the same geometry but higher speeds the drop breaks. Therefore, we identify a critical value of the capillary number above which a drop will break. We explain the results with a one-dimensional model characterizing the flow in the narrow gaps on either side of the obstacle, which identifies a surface-tension–driven instability associated with a variation in the permeability in the flow direction. The model captures the major features of the experimental observations.