Co- and cross-flow extensions in an elliptical optical trap

The extension of a particle (translational deviation) in an isotropic harmonic potential well is linearly proportional and parallel to the applied force. In an anisotropic trapping potential, the extension is instead related to the applied force by a compliance tensor. Using the focal spot of a high numerical aperture zone plate to create an elliptical potential and microfluidics to apply a calibrated force, we measure the two-dimensional extension of a trapped spherical particle. As a function of the orientation of the elliptical potential, the extension sweeps out a circular trajectory, exhibiting extensions both parallel (coflow) and perpendicular (cross flow) to the direction of the flow. The results fit well to a compliance tensor model.