Bhargav Rallabandi

How fast Arctic ice spreads out and how quickly the floes travel from coarsely resolved environmental data can be predicted by simulating sea ice as a granular medium driven by stochastic winds and using measurements of the local wind and ice properties as input parameters.

Tangential interactions between particles play a central role in suspension rheology. We show that surface roughness significantly enhances the strength of hydrodynamic interactions between closely separated particles in relative sliding motion. Using numerical solutions of the lubrication equation, we show that tangential forces due to sliding motion between rough spheres scale inversely with the separation distance, as opposed to the weaker logarithmic scaling for smooth spheres. A fully analytic theory identifies these features as the consequence of asperity-scale squeeze flows, quantitatively recovering the numerical results. These singular hydrodynamic forces are associated with similarly singular torques. The need to resolve the hydrodynamic singularity couples the particles’ rotation to their translation, and forces them to roll without slip, recovering a kinematic constraint that is central to understanding dense suspension rheology. Despite their purely hydrodynamic origin and occurring without contact, these features resemble several aspects of rolling and sliding contact friction.

Physical Review . Polynyas—persistent regions of open water within polar sea ice—play a critical role in polar ocean-atmosphere interactions. We combine theoretical modeling and numerical simulations to investigate the dynamics and thermodynamics of wind-driven, latent-heat-generated polynya formation adjacent to straight and curved coastlines. Under the assumption of negligible ice internal pressure, we propose a one-dimensional, continuum, mass- and momentum-conserving theory characterizing the offshore distribution of ice velocity and the spatiotemporal evolution of ice concentration. Finite-element simulations incorporating realistic sea-ice rheology validate the theoretical predictions, demonstrating strong agreement in steady-state polynya widths and ice dynamics. These results align qualitatively with observational climate data. Furthermore, we generalize the framework to two dimensions, enabling quantitative predictions of leeward polynya formation around a model circular island. The proposed theoretical framework advances mechanistic understanding of polynya formation and provides a foundation for improving their representation in climate models.

Wicking of fluid in paper-based microfluidic devices can be greatly enhanced by engineering macroscopic grooves into the surface of the paper. We developed a quantitative model of this enhancement by resolving the coupled flow in the paper matrix and the groove. While the groove enhances wicking by providing a low-resistance conduit for flow, we find that the degree of enhancement depends strongly on the poorer wettability of the groove as well as the effect of gravity. We obtain an analytical prediction of imbibed length as a function of time, generalizing the Lucas-Washburn law to microporous wicks with engineered macroscopic surface grooves. The prediction is shown to be in quantitative agreement with previous experiments of upward wicking in both single- and multigrooved paper channels. The model also rationalizes the experimental finding that wide grooves may slow down imbibition despite their larger cross-sectional area and, thus, identifies optimal groove widths.

Microswimmers and active colloids often move in confined systems, including those involving interfaces. Such interfaces, especially at the microscale, may deform in response to the stresses of the flow created by the active particle. We develop a theoretical framework to analyse the effect of a nearby membrane on the motion of an active particle whose flow fields are generated by force-free singularities. We demonstrate our results on a particle represented by a combination of a force dipole and a mass dipole, while the membrane resists deformation due to tension and bending rigidities. We find that the deformation either enhances or suppresses the motion of the active particle, depending on its orientation and the relative strengths between the fundamental singularities that describe its flow. Furthermore, the deformation can generate motion in new directions.

We study the interaction between a pair of particles suspended in a uniform oscillatory flow. The time-averaged behaviour of particles under these conditions, which arises from an interplay of inertial and viscous forces, is explored through a theoretical framework relying on small oscillation amplitude. We approximate the oscillatory flow in terms of dual multipole expansions, with which we compute time-averaged interaction forces using the Lorentz reciprocal theorem. We then develop analytic approximations for the force in the limit where Stokes layers surrounding the particles do not overlap. Finally, we show how the same formalism can be generalised to the situation where the particles are free to oscillate and drift in response to the applied flow. The results are shown to be in agreement with existing numerical data for forces and particle velocities. The theory thus provides an efficient means to quantify nonlinear particle interactions in oscillatory flows.

The transport of sea ice over the polar oceans plays an important role in climate. This transport is driven predominantly by turbulent winds, leading to stochastic motion of ice floes. Observed diffusivities and velocity distributions of sea ice deviate by orders of magnitude from Brownian models, making it challenging to predict ice transport. We fully resolve these gaps through stochastic granular simulations that account for interactions between ice floes as they respond to a noisy wind. Using only directly measured quantities as model inputs, we reproduce the dispersion, diffusivity, velocity distribution, and power spectra of sea ice observed in the Fram Strait with remarkable quantitative accuracy. We understand these features as direct consequences of collisions between floes, which rapidly dissipate the energy injected by wind. A kinetic theory provides insights into these dynamics in terms of environmental properties, and makes predictions in close agreement with observations. The ideas and tools developed here pave the way for a new predictive understanding of global sea ice transport in terms of local floe-scale processes.

We study the lubricated contact of sliding soft surfaces that are locally patterned but globally cylindrical, held together under an external normal force.

The interaction between deformable surfaces and oscillatory driving is known to produce complex secondary time-averaged flows due to inertial and elastic nonlinearities. Here, we revisit the problem of oscillatory flow in a cylindrical tube with a deformable wall, and analyse it under a long-wave theory for small deformations, but for arbitrary Womersley numbers. We find that the oscillatory pressure does not vary linearly along the length of a deformable channel, but instead decays exponentially with spatial oscillations. We show that this decay occurs over an elasto-visco-inertial length scale that depends on the material properties of the fluid and the elastic walls, the geometry of the system, and the frequency of the oscillatory flow, but is independent of the amplitude of deformation. Inertial and geometric nonlinearities associated with the elastic deformation of the channel drive a time-averaged secondary flow. We quantify the flow using numerical solutions of the perturbation theory, and gain insight by developing analytic approximations. The theory identifies a complex non-monotonic dependence of the time-averaged flux on the elastic compliance and inertia, including a reversal of the flow. Finally, we show that our analytic theory is in excellent quantitative agreement with the three-dimensional direct numerical simulations of Pande et al. (Phys. Rev. Fluids, vol. 8, no. 12, 2023, 124102).

We study the lubricated contact of sliding soft surfaces that are locally patterned but globally cylindrical, held together under an external normal force. The local patterns represent either naturally occurring surface roughness or engineered surface textures. Three dimensionless parameters govern the system: a speed, and the amplitude and wavelength of the pattern. Using numerical solutions of the Reynolds lubrication equation, we investigate the effects of these dimensionless parameters on key variables such as contact pressure and the coefficient of friction of the lubricated system. For small roughness amplitudes, the coefficient of friction increases with roughness. However, our findings reveal that increasing surface roughness beyond a critical value can decrease the friction coefficient, a result that contradicts conventional intuition and classical studies on the lubrication of rigid surfaces. For very large roughness amplitudes, we show that the coefficient of friction drops even below the corresponding smooth case. We support these observations with a combination of perturbation theory and physical arguments, identifying scaling laws for large and small speeds, and for large and small roughness amplitudes. This study provides a quantitative understanding of friction in the contact of soft, wet objects and lays theoretical foundations for incorporating the friction coefficient into haptic feedback systems in soft robotics and haptic engineering.