Cavitation in a lubrication flow between a moving sphere and a boundary

Flow-induced choking of a compliant Hele-Shaw cell

Harnessing flow–structure interactions has enabled the development of fluidic analogs of electronic circuit components, e.g., fluidic capacitors that store fluid much like an electrical capacitor stores charge. These soft components function in response to the flow; integrated into microfluidic devices, they remove the need for external actuation, thereby facilitating deployment outside of the laboratory. We describe a fluidic fuse that exploits the flow-induced deformation of a soft elastomer and identify the critical flow rate above which the flow is interrupted. This paves the way for the integration of passive flow limiters into microfluidic devices.

After centuries of striving for structural rigidity, engineers and scientists alike are increasingly looking to harness the deformation, buckling, and failure of soft materials for functionality. In fluidic devices, soft deformable components that respond to the flow have the advantage of being passive; they do not require external actuation. Harnessing flow-induced deformation for passive functionality provides a means of developing flow analogs of electronic circuit components such as fluidic diodes and capacitors. The electronic component that has so far been overlooked in the microfluidics literature—the fuse—is a passive safety device that relies on a controlled failure mechanism (melting) to protect a circuit from overcurrent. Here, we describe how a compliant Hele-Shaw cell behaves in a manner analogous to the electrical fuse; above a critical flux, the flow-induced deformation of the cell blocks the outflow, interrupting (choking) the flow. In particular, the pressure distribution within the fluid applies a spatially variant normal force to the soft boundary, which causes nonuniform deformation. As a consequence of lateral confinement and incompressibility of the soft material, this flow-induced elastic deformation manifests as bulging near the cell outflow; bulges that come into contact with the rigid cell roof interrupt the flow. We identify two nondimensional parameters that govern the central deflection and the choking of the cell, respectively. This study therefore provides the mechanical foundations for engineering passive-flow limiters into fluidic devices.

Validity of Winkler's mattress model for thin elastomeric layers: beyond Poisson's ratio

Winkler's mattress model is often used as a simplified model to understand how a thin elastic layer, such as a coating, deforms when subject to a distributed normal load: the deformation of the layer is assumed proportional to the applied normal load. This simplicity means that the Winkler model has found a wide range of applications from soft matter to geophysics. However, in the limit of an incompressible elastic layer the model predicts infinite resistance to deformation, and hence breaks down. Since many of the thin layers used in applications are elastomeric, and hence close to incompressible, we consider the question of when the Winkler model is appropriate for such layers. We formally derive a model that interpolates between the Winkler and incompressible limits for thin elastic layers, and illustrate this model by detailed consideration of two example problems: the point-indentation of a coated elastomeric layer and self-sustained lift in soft elastohydrodynamic lubrication. We find that the applicability (or otherwise) of the Winkler model is not determined by the value of the Poisson ratio alone, but by a compressibility parameter that combines the Poisson ratio with a measure of the layer's slenderness, which itself depends on the problem under consideration.

Cavitation in thin liquid layer: A review

This review tries to cover as many research fields and literatures associated with cavitation in thin liquid layer as possible. The intent was to summarize (i) list all the research fields related to cavitation in thin liquid layer that can be collected, (ii) advances in the investigation of cavitation in thin liquid layer, and (iii) draw attention to the relatively macroscopic cavitation behavior in thin liquid layer.

Dynamic self-assembly of charged colloidal strings and walls in simple fluid flows

Colloidal particles can self-assemble into various ordered structures in fluid flows that have potential applications in biomedicine, materials synthesis and encryption. These dynamic processes are also of fundamental interest for probing the general principles of self-assembly under non-equilibrium conditions. Here, we report a simple microfluidic experiment, where charged colloidal particles self-assemble into flow-aligned 1D strings with regular particle spacing near a solid boundary. Using high-speed confocal microscopy, we systematically investigate the influence of flow rates, electrostatics and particle polydispersity on the observed string structures. By studying the detailed dynamics of stable flow-driven particle pairs, we quantitatively characterize interparticle interactions. Based on the results, we construct a simple model that explains the intriguing non-equilibrium self-assembly process. Our study shows that the colloidal strings arise from a delicate balance between attractive hydrodynamic coupling and repulsive electrostatic interaction between particles. Finally, we demonstrate that, with the assistance of transverse electric fields, a similar mechanism also leads to the formation of 2D colloidal walls.

Sliding friction in the hydrodynamic lubrication regime for a power-law fluid

A scaling analysis is undertaken for the load balance in sliding friction in the hydrodynamic lubrication regime, with a particular emphasis on power-law shear-thinning typical of a structured liquid. It is argued that the shear-thinning regime is mechanically unstable if the power-law index n  <  1/2, where n is the exponent that relates the shear stress to the shear rate. Consequently the Stribeck (friction) curve should be discontinuous, with possible hysteresis. Further analysis suggests that normal stress and flow transience (stress overshoot) do not destroy this basic picture, although they may provide stabilising mechanisms at higher shear rates. Extensional viscosity is also expected to be insignificant unless the Trouton ratio is large. A possible application to shear thickening in non-Brownian particulate suspensions is indicated.

Tribonucleation of bubbles

We report on the nucleation of bubbles on solids that are gently rubbed against each other in a liquid. The phenomenon is found to depend strongly on the material and roughness of the solid surfaces. For a given surface, temperature, and gas content, a trail of growing bubbles is observed if the rubbing force and velocity exceed a certain threshold. Direct observation through a transparent solid shows that each bubble in the trail results from the early coalescence of several microscopic bubbles, themselves detaching from microscopic gas pockets forming between the solids. From a detailed study of the wear tracks, with atomic force and scanning electron microscopy imaging, we conclude that these microscopic gas pockets originate from a local fracturing of the surface asperities, possibly enhanced by chemical reactions at the freshly created surfaces. Our findings will be useful either for preventing undesired bubble formation or, on the contrary, for "writing with bubbles," i.e., creating controlled patterns of microscopic bubbles.

A mixed contact model for an immersed collision between two solid surfaces

Experimental evidence shows that the presence of an ambient liquid can greatly modify the collision process between two solid surfaces. Interactions between the solid surfaces and the surrounding liquid result in energy dissipation at the particle level, which leads to solid-liquid mixture rheology deviating from dry granular flow behaviour. The present work investigates how the surrounding liquid modifies the impact and rebound of solid spheres. Existing collision models use elastohydrodynamic lubrication (EHL) theory to address the surface deformation under the developing lubrication pressure, thereby coupling the motion of the liquid and solid. With EHL theory, idealized smooth particles are made to rebound from a lubrication film. Modified EHL models, however, allow particles to rebound from mutual contacts of surface asperities, assuming negligible liquid effects. In this work, a new contact mechanism, 'mixed contact', is formulated, which considers the interplay between the asperities and the interstitial liquid as part of a hybrid rebound scheme. A recovery factor is further proposed to characterize the additional energy loss due to asperity-liquid interactions. The resulting collision model is evaluated through comparisons with experimental data, exhibiting a better performance than the existing models. In addition to the three non-dimensional numbers that result from the EHL analysis--the wet coefficient of restitution, the particle Stokes number and the elasticity parameter--a fourth parameter is introduced to correlate particle impact momentum to the EHL deformation impulse. This generalized collision model covers a wide range of impact conditions and could be employed in numerical codes to simulate the bulk motion of solid particles with non-negligible liquid effects.

Near-contact interactions between a sphere and a plane

The hydrodynamic behavior observed for a sphere released under gravity in a Newtonian liquid is not consistent with that predicted by classical continuum theory when the sphere is near a solid wall. An irreversibility arises in the velocity of the sphere as it approaches and recedes from the plane that cannot be accounted for using continuum hydrodynamic equations alone. Earlier experiments on spheres falling from a plane were conducted under conditions such that this irreversibility could be attributed to the surface roughness of the spheres. In this investigation, we extend these studies to situations where the pressure field between the receding sphere and the plane drops to the vapor pressure of the fluid and cavitation occurs. Experimental data supports the theoretical prediction for a sphere's motion based on the irreversible effect of cavitation.