Swimming near Deformable Membranes*

Active particles often do not swim in a bare, infinite fluid but interact with the soft surfaces surrounding them, as seen in cases like active proteins or bacteria moving near a biomembrane. These particles generate flow fields that couple to the membrane, leading to non-trivial forces. In this work, we use the Lorentz reciprocal theorem and the method of images to derive an analytical expression for the hydroelastic force resulting from the coupling between an active particle, modeled as a symmetric force dipole, and a nearby elastic, bendable membrane. Compared to the repulsive force found near a rigid interface, we discover that in the limit of small deformations, the bending-induced force is opposite in sign and becomes attractive. Furthermore, the interaction strength increases quadratically with the dipole moment.