Microscopic Water Droplets in Oil

Michael Siegel is at present Professor at New Jersey Institute of Technology, USA. Thanks to a grant from the Knut and Alice Wallenberg Foundation, he will be Visiting Professor in Numerical Analysis Group at the Department of mathematics, KTH Royal Institute of Technology, Stockholm.

A relatively new area of nano-research is microfluidics. One of its applications consists in suspending microscopic, i.e. less than 30 thousandth of a millimeter in diameter, droplets of water containing biological or other samples in oil. Droplets’ surface is coated with an active substance in order to keep them apart.

Mathematical modeling of such microfluidic systems requires advanced numerical methods in order to perform computer simulations. One of the difficulties of such modeling stems from the variability of the water droplets, which tend to move around and undergo deformations. This is difficult to simulate with accurate and fast results. Another problem stems from changing concentration of the active substance causing fluctuations in surface tension. Changes in the concentration of the active substance may be influenced by the degree to which it dissolves in oil.

The proposed project will develop an algorithm modeling systems with low degree of diffusion of the active substance in oil. A layer of highly concentrated active substance separating water droplets from oil is present in such systems. New numerical methods for effective simulations of such systems will be developed as well. Additional difficulties arise when water droplets come near each other. One of the project’s goals is to develop an algorithm, which can effectively handle this case combined with applying the so-called fast summation method in order to make the calculations faster.

Photo: New Jersey Institute of Technology