Modeling Memory-Dependent Colloidal Hydrodynamic Interactions in a Viscoelastic Medium with Experimental Validation of Coupled Translational-Rotational Dynamics

The design and study of complex fluids for engineered soft materials is partly enriched by physical interactions among their numerous constituents that span several length- and time-scales. Under flow, the interplay of conservative and hydrodynamic forces engenders an exotic microstructure that determine a material’s rheology. Whereas prior studies have either reconciled this with fluid-mediated forces in Newtonian solvents or to macromolecular structure in viscoelastic materials, there currently exists a gap in bridging these two ideas.

In this work, we use micro-hydrodynamic theory and optical tweezers experiments to study the transmission of fluid-mediated forces between colloidal-scale particulates in a viscoelastic medium. We measure the induced angular displacement of a colloidal probe due to a nearby, moving particle. First, we reproduce established theory that describes the probe’s rotation in a Newtonian solvent due to pair hydrodynamic forces, ranging from near-field lubrication to far-field interactions. Then, we extend this analysis to include memory effects that arise from macromolecular rearrangement in the surrounding fluid, demonstrating excellent agreement with the experimental data across pair-separation distance and time. We anticipate that our results will inform new constitutive models and advanced simulation tools to design increasingly heterogeneous fluids with targeted mechanical performance.