Bhargav Rallabandi

Frequency dependence and frequency control of microbubble streaming flows

Steady streaming from oscillating microbubbles is a powerful actuating mechanism in microfluidics, enjoying increased use due to its simplicity of manufacture, ease of integration, low heat generation, and unprecedented control over the flow field and particle transport. As the streaming flow patterns are caused by oscillations of microbubbles in contact with walls of the set-up, an understanding of the bubble dynamics is crucial. Here we experimentally characterize the oscillation modes and the frequency response spectrum of such cylindrical bubbles, driven by a pressure variation resulting from ultrasound in the range of 1 kHz ≲f≲ 100 kHz. We find that (i) the appearance of 2D streaming flow patterns is governed by the relative amplitudes of bubble azimuthal surface modes (normalized by the volume response), (ii) distinct, robust resonance patterns occur independent of details of the set-up, and (iii) the position and width of the resonance peaks can be understood using an asymptotic theory approach. Th...

Rotation of an immersed cylinder sliding near a thin elastic coating

It is well known that an object translating parallel to a soft wall produces viscous stresses and a pressure field that deform the wall, which, in turn, results in a lift force on the object. Recent experiments on cylinders sliding near a soft incline under gravity confirmed previously developed theoretical arguments, but also reported an unexplained rotation of the cylinder at steady state (Saintyves et al. \emph{PNAS} 113(21), 2016). Here, we use the Lorentz reciprocal theorem to calculate the angular velocity of an infinite cylinder sliding near a soft incline, in the lubrication limit. Our results show that the softness-induced angular velocity of the cylinder is quadratic in the deformation of the elastic layer. This implies that a cylinder sliding parallel to a soft wall without rotation experiences an elastohydrodynamic torque that is proportional to the cube of the sliding speed. We compare the theoretical predictions of the rotation speed with experimental measurements. We then develop scaling and symmetry arguments that are generally applicable to hydrodynamically mediated interactions between soft systems, such as those in biological and geophysical settings.

Particle migration and sorting in microbubble streaming flows.

Ultrasonic driving of semicylindrical microbubbles generates strong streaming flows that are robust over a wide range of driving frequencies. We show that in microchannels, these streaming flow patterns can be combined with Poiseuille flows to achieve two distinctive, highly tunable methods for size-sensitive sorting and trapping of particles much smaller than the bubble itself. This method allows higher throughput than typical passive sorting techniques, since it does not require the inclusion of device features on the order of the particle size. We propose a simple mechanism, based on channel and flow geometry, which reliably describes and predicts the sorting behavior observed in experiment. It is also shown that an asymptotic theory that incorporates the device geometry and superimposed channel flow accurately models key flow features such as peak speeds and particle trajectories, provided it is appropriately modified to account for 3D effects caused by the axial confinement of the bubble.

Wind-Driven Formation of Ice Bridges in Straits

Ice bridges are static structures composed of tightly packed sea ice that can form during the course of its flow through a narrow strait. Despite their important role in local ecology and climate, the formation and breakup of ice bridges is not well understood and has proved difficult to predict. Using long-wave approximations and a continuum description of sea ice dynamics, we develop a one-dimensional theory for the wind-driven formation of ice bridges in narrow straits, which is verified against direct numerical simulations. We show that for a given wind stress and minimum and maximum channel widths, a steady-state ice bridge can only form beyond a critical value of the thickness and the compactness of the ice field. The theory also makes quantitative predictions for ice fluxes, which are particularly useful to estimate the ice export associated with the breakup of ice bridges. We note that similar ideas are applicable to dense granular flows in confined geometries.

Formation of sea ice bridges in narrow straits in response to wind and water stresses

Ice bridges are rigid structures composed of sea ice that form seasonally in the many straits and channels of the Canadian Arctic Archipelago. Driven primarily by atmospheric stresses, these ice bridges are formed when sufficiently thick ice “jams” during the course of its flow between land masses, resulting in a region of stationary compacted ice that is separated from a region of flowing open water (a polynya) by a static arch. Using a continuum description of sea ice that is widely used in climate modeling, we present an asymptotic theory of the process of formation of such bridges in slender channels when the motion of the ice is driven by external wind and water stresses. We show that for an arbitrary channel shape, ice bridges can only form within a range of ice properties that is determined by the channel geometry and the external stress. We then compare the results of our theory with direct numerical simulations and observational evidence. Finally, we provide simple analytical expressions for the mean velocity of the ice flow as a function of the channel shape, the properties of the ice, and the wind and water stresses along the channel.

Foam-driven fracture

Significance Hydraulic fracturing plays an important role in meeting today’s energy demands. However, the substantial use of fresh water in fracturing and wastewater returning to the surface pose risks to the environment. Alternative technology has been developed that reduces the water-related risks by injecting aqueous foam instead of water to fracture shale formations, but the mechanism is poorly understood. Here, we show, using laboratory experiments, that the injection of foam instead of water dramatically changes the fracture dynamics when the foam compressibility is important. We develop a scaling argument for the fracture dynamics that exhibits excellent agreement with the experimental results. Our findings extend to other systems involving compressible foams, including fire-fighting, energy storage using compressed foams, and enhanced oil recovery. In hydraulic fracturing, water is injected at high pressure to crack shale formations. More sustainable techniques use aqueous foams as injection fluids to reduce the water use and wastewater treatment of conventional hydrofractures. However, the physical mechanism of foam fracturing remains poorly understood, and this lack of understanding extends to other applications of compressible foams such as fire-fighting, energy storage, and enhanced oil recovery. Here we show that the injection of foam is much different from the injection of incompressible fluids and results in striking dynamics of fracture propagation that are tied to the compressibility of the foam. An understanding of bubble-scale dynamics is used to develop a model for macroscopic, compressible flow of the foam, from which a scaling law for the fracture length as a function of time is identified and exhibits excellent agreement with our experimental results.

Enhanced Boiling Heat Transfer using Self-Actuated Nano-Bimorphs

We present a new concept of a structured surface for enhanced boiling heat transfer that is capable of self-adapting to the local thermal conditions. An array of freestanding nanoscale bimorphs, a structure that consists of two adjoining materials with a large thermal expansion mismatch, is able to deform under local temperature change. Such a surface gradually deforms as the nucleate boiling progresses due to the increase in the wall superheat. The deformation caused by the heated surface is shown to be favorable for boiling heat transfer, leading to about 10% of increase in the critical heat flux compared to a regular nanowire surface. A recently developed theoretical model that accounts for the critical instability wavelength of the vapor film and the capillary wicking force successfully describes the critical heat flux enhancement for the nanobimorph surface with a good quantitative agreement.

Beyond acoustophoresis: Attractive and repulsive forces on particles

Inertial effects in microfluidics afford an interesting set of tools for the control of particle positions. The gradients of steady channel flows, as well as the gradients of acoustic field amplitudes, have been used prominently to this purpose, the latter in acoustofluidics. Here, we investigate directly the effect of an oscillating interface on the fluid surrounding it and particles suspended in the fluid. The fast oscillatory motion gives rise to strong inertial effects, while the method allows for versatile force actuation because of the variety of flow fields, frequencies, and length scales under the experimentalists control. We show in experiment and theory that the forces on particles can be evaluated analytically, on both the oscillatory and the steady, time-averaged time scales. The latter formalism generalizes streaming flow computations to particle motion, and reveals new potential strategies for manipulating particles with tunable attractive or repulsive forces, depending not only on characte...

Beyond acoustophoresis: Particle manipulation near oscillating interfaces

Inertial effects in microfluidics afford an interesting set of tools for the control of particle positions. The gradients of steady channel flows, as well as the gradients of acoustic field amplitudes, have been used prominently to this purpose, the latter in acoustofluidics. Here, we investigate directly the effect of an oscillating interface on the fluid surrounding it and particles suspended in the fluid. The fast oscillatory motion gives rise to strong inertial effects, while the method allows for versatile force actuation because of the variety of flow fields, frequencies, and length scales under the experimentalists control. We show in experiment and theory that oscillating bubbles simultaneously (i) guide particles close to the bubble interface by streaming flow, and (ii) exert strong lift forces that can be used to sort the particles by size or density. The lift forces and the ensuing particle displacement constitute an effect separate from streaming and can be understood analytically on the time...