Search for: All records

Viscous fingering, a classic hydrodynamic instability, is governed by the the competition between destabilising viscosity ratios and stabilising surface tension or thermal diffusion. We show that the channel confinement can induce ‘diffusion’-like stabilising effects on viscous fingering even in the absence of interfacial tension and thermal diffusion, when a clear oil invades the mixture of the same oil and non-colloidal particles. The key lies in the generation of long-range dipolar disturbance flows by highly confined particles that form a monolayer inside a Hele-Shaw cell. We develop a coarse-grained model whose results correctly predict universal fingering dynamics that is independent of particle concentrations. This new mechanism offers insights into manipulating and harnessing collective motion in non-equilibrium systems. 

Free surface flows driven by boundary undulations are observed in many biological phenomena, including the feeding and locomotion of water snails. To simulate the feeding strategy of apple snails, we develop a centimetric robotic undulator that drives a thin viscous film of liquid with the wave speed$$V_w$$. Our experimental results demonstrate that the behaviour of the net fluid flux$$Q$$strongly depends on the Reynolds number$$Re$$. Specifically, in the limit of vanishing$$Re$$, we observe that$$Q$$varies non-monotonically with$$V_w$$, which has been successfully rationalised by Pandeyet al.(Nat. Commun., vol. 14, no. 1, 2023, p. 7735) with the lubrication model. By contrast, in the regime of finite inertia ($${Re} \sim O(1)$$), the fluid flux continues to increase with$$V_w$$and completely deviates from the prediction of lubrication theory. To explain the inertia-enhanced pumping rate, we build a thin-film, two-dimensional model via the asymptotic expansion in which we linearise the effects of inertia. Our model results match the experimental data with no fitting parameters and also show the connection to the corresponding free surface shapes$$h_2$$. Going beyond the experimental data, we derive analytical expressions of$$Q$$and$$h_2$$, which allow us to decouple the effects of inertia, gravity, viscosity and surface tension on free surface pumping over a wide range of parameter space. 

Abstract Examples of fluid flows driven by undulating boundaries are found in nature across many different length scales. Even though different driving mechanisms have evolved in distinct environments, they perform essentially the same function: directional transport of liquid. Nature-inspired strategies have been adopted in engineered devices to manipulate and direct flow. Here, we demonstrate how an undulating boundary generates large-scale pumping of a thin liquid near the liquid-air interface. Two dimensional traveling waves on the undulator, a canonical strategy to transport fluid at low Reynolds numbers, surprisingly lead to flow rates that depend non-monotonically on the wave speed. Through an asymptotic analysis of the thin-film equations that account for gravity and surface tension, we predict the observed optimal speed that maximizes pumping. Our findings reveal how proximity to free surfaces, which ensure lower energy dissipation, can be leveraged to achieve directional transport of liquids. 

Partially wetting droplets under an airflow can exhibit complex behaviours that arise from the coupling of surface tension, inertia of the external flow and contact-line dynamics. Recent experiments by Hooshanginejad et al. ( J. Fluid Mech. , vol. 901, 2020) revealed that a millimetric partially wetting water droplet under an impinging jet can oscillate in place, split or depin away from the jet, depending on the magnitude (i.e. $$5\unicode{x2013}20\ {\rm m}\ {\rm s}^{-1}$$ ) and position of the jet. To rationalise the experimental observations, we develop a two-dimensional lubrication model of the droplet that incorporates the external pressure of the impinging high-Reynolds-number jet, in addition to the capillary and hydrostatic pressures of the droplet. Distinct from the previous model by Hooshanginejad et al. ( J. Fluid Mech. , vol. 901, 2020), we simulate the motion of the contact line using precursor film and disjoining pressure, which allows us to capture a wider range of droplet behaviours, including the droplet dislodging to one side. Our simulations exhibit a comparable time-scale of droplet deformations and similar outcomes as the experimental observations. We also obtain the analytical steady-state solutions of the droplet shapes and construct the minimum criteria for splitting and depinning. 

When a mixture of viscous oil and non-colloidal particles displaces air between two parallel plates, the shear-induced migration of particles leads to the gradual accumulation of particles on the advancing oil–air interface. This particle accumulation results in the fingering of an otherwise stable fluid–fluid interface. While previous works have focused on the resultant instability, one unexplored yet striking feature of the experiments is the self-similarity in the concentration profile of the accumulating particles. In this paper, we rationalise this self-similar behaviour by deriving a depth-averaged particle transport equation based on the suspension balance model, following the theoretical framework of Ramachandran ( J. Fluid Mech. , vol. 734, 2013, pp. 219–252). The solutions to the particle transport equation are shown to be self-similar with slight deviations, and in excellent agreement with experimental observations. Our results demonstrate that the combination of the shear-induced migration, the advancing fluid–fluid interface and Taylor dispersion yield the self-similar and gradual accumulation of particles. 

The means by which aquatic animals such as freshwater snails collect food particles distributed on the water surface are of great interest for understanding life at the air–water interface. The apple snail Pomacea canaliculata stabilizes itself just below the air–water interface and manipulates its foot such that it forms a cone-shaped funnel into which an inhalant current is generated, thereby drawing food particles into the funnel to be ingested. We measured the velocity of this feeding current and tracked the trajectories of food particles around and on the snail. Our experiments indicated that the particles were collected via the free surface flow generated by the snail’s undulating foot. The findings were interpreted using a simple model based on lubrication theory, which considered several plausible mechanisms depending on the relative importance of hydrostatic pressure, capillary action and rhythmic surface undulation.