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Register a new userThe free surface of a colloidal chiral fluid: waves and instabilities from odd stress and Hall viscosity
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In simple fluids, such as water, invariance under parity and time-reversal symmetry imposes that the rotation of constituent atoms are determined by the flow and that viscous stresses damp motion. Activation of the rotational degrees of freedom of a fluid by spinning its atomic building blocks breaks these constraints and has thus been the subject of fundamental theoretical interest across classical and quantum fluids. However, the creation of a model liquid which isolates chiral hydrodynamic phenomena has remained experimentally elusive. Here we report the creation of a cohesive two-dimensional chiral liquid consisting of millions of spinning colloidal magnets and study its flows. We find that dissipative viscous edge pumping is a key and general mechanism of chiral hydrodynamics, driving uni-directional surface waves and instabilities, with no counterpart in conventional fluids. Spectral measurements of the chiral surface dynamics reveal the presence of Hall viscosity, an experimentally long sought property of chiral fluids. Precise measurements and comparison with theory demonstrate excellent agreement with a minimal but complete chiral hydrodynamic model, paving the way for the exploration of chiral hydrodynamics in experiment.
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Multispecies swarms are found for microorganisms living in microfluidic environments where they can take advantage of collective motions during transport and spreading. Nevertheless, there is a general lack of physical understandings of the origins of the multiscale unstable dynamics. Here we build a computation model to study the binary suspensions of rear- and front-actuated microswimmers, or respectively the so-called pusher and puller particles, that have different populations and swimming speeds. We perform direct particle simulations to reveal that even in the scenarios of stress-balanced mixtures which produce approximately zero net extra stresses, the longtime dynamics can exhibit non-trivial density fluctuations and spatially-correlated motions. We then construct a continuum kinetic model and perform linear stability analysis to reveal the underlying mechanisms of hydrodynamic instabilities. Our theoretical predictions qualitatively agree with numerical results and explain the onsets of the observed collective motions.
In channel flows a step on the route to turbulence is the formation of streaks, often due to algebraic growth of disturbances. While a variation of viscosity in the gradient direction often plays a large role in laminar-turbulent transition in shear flows, we show that it has, surprisingly, little effect on the algebraic growth. Non-uniform viscosity therefore may not always work as a flow-control strategy for maintaining the flow as laminar.
The formation of singularities on a free surface of a conducting ideal fluid in a strong electric field is considered. It is found that the nonlinear equations of two-dimensional fluid motion can be solved in the small-angle approximation. This enables us to show that for almost arbitrary initial conditions the surface curvature becomes infinite in a finite time.
We investigate analytically the linearized water wave radiation problem for an oscillating submerged point source in an inviscid shear flow with a free surface. A constant depth is taken into account and the shear flow increases linearly with depth. The surface velocity relative to the source is taken to be zero, so that Doppler effects are absent. We solve the linearized Euler equations to calculate the resulting wave field as well as its far-field asymptotics. For values of the Froude number $F^2=omega^2 D/g$ ($omega$: oscillation frequency, $D$ submergence depth) below a resonant value $F^2_text{res}$ the wave field splits cleanly into separate contributions from regular dispersive propagating waves and non-dispersive critical waves resulting from a critical layer-like street of flow structures directly downstream of the source. In the sub-resonant regime the regular waves behave like sheared ring waves while the critical layer wave forms a street of a constant width of order $Dsqrt{S/omega}$ ($S$ is the shear flow vorticity) and is convected downstream at the fluid velocity at the depth of the source. When the Froude number approaches its resonant value, the the downstream critical and regular waves resonate, producing a train of waves of linearly increasing amplitude contained within a downstream wedge.
Imbibition, the displacement of a nonwetting fluid by a wetting fluid, plays a central role in diverse energy, environmental, and industrial processes. While this process is typically studied in homogeneous porous media with uniform permeabilities, in many cases, the media have multiple parallel strata of different permeabilities. How such stratification impacts the fluid dynamics of imbibition, as well as the fluid saturation after the wetting fluid breaks through to the end of a given medium, is poorly understood. We address this gap in knowledge by developing an analytical model of imbibition in a porous medium with two parallel strata, combined with a pore network model that explicitly describes fluid crossflow between the strata. By numerically solving these models, we examine the fluid dynamics and fluid saturation left after breakthrough. We find that the breakthrough saturation of nonwetting fluid is minimized when the imposed capillary number Ca is tuned to a value Ca$^*$ that depends on both the structure of the medium and the viscosity ratio between the two fluids. Our results thus provide quantitative guidelines for predicting and controlling flow in stratified porous media, with implications for water remediation, oil/gas recovery, and applications requiring moisture management in diverse materials.
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