This dissertation investigates fluid-structure interactions at low Reynolds numbers, with a focus on soft materials, offering insights for applications in microrheometry, tribology, and soft robotics. After reviewing fluid-elastic interactions, particularly the forces and torques arising when objects move near deformable soft materials, we discuss three different studies.

The first study develops an analytical framework to calculate the lift force generated by a soft substrate in Stokes flow. Using Lorentz's reciprocal theorem, the study links the lift force to the substrate’s linear response function. The framework is applied to both elastic and viscoelastic materials, revealing how the lift force scales with Poisson's ratio and substrate thickness. This approach enables the characterization of soft materials through lift force measurements without direct contact.

The second study explores the coupling between rotation and translation in the lubricated motion of a submerged cylinder on a soft substrate. The study finds strong coupling when substrate deformation is comparable to fluid film thickness, with behavior transitioning to near-Hertzian contact at large deformations. The effects of external torque are also examined, revealing various rotational and translational states, including back-spinning and top-spinning motions, relevant to soft material systems.

The third study examines the lubricated contact of soft, patterned surfaces on a cylindrical geometry. The study identifies three key dimensionless parameters governing the system and analyzes their impact on contact pressure and friction coefficient. The findings challenge conventional understanding by showing that increasing surface roughness can reduce the friction coefficient in soft, wet contacts. This work provides a framework for incorporating friction coefficients into haptic feedback systems in robotics.

This dissertation advances the understanding of fluid-elastic interactions in soft materials, offering theoretical models and insights applicable across multiple scientific and engineering domains.