Session J05: Microscale Flows: General (8:00am - 8:45am CST)

Sedimentation of elastic circular microfibres

We study the gravitational sedimentation of a thin, flexible filament bent into the shape of a loop in a viscous fluid depending on its stiffness. In the Stokesian regime, with a vanishing Reynolds number elastic forces, gravity, and hydrodynamic drag on the filament balance out to zero. We account for hydrodynamic interactions using the local slender-body theory (resistive-force theory), in which the local velocity is linearly related to the local hydrodynamic drag force. We model the elastic forces according to the Euler-Bernoulli beam theory. Depending on the relative strength of gravity and stiffness of the loop, we observe various regimes of motion. We analyse the stability of a circular solution known for an infinitely stiff loops when increasing the fibre elasticity. By linear stability analysis, we identify a single dimensionless parameter (stiffness vs gravity) that controls the dynamics and find the threshold value determining the stability of a sedimenting loop. We verify this stability criterion in simulations and analyse the transition towards the unstable region. Our results give intuitive grounding to the preference for horizontal orientation seen in sedimenting red blood cells and in DNA loops which break at locations corresponding to large stress in our model.   

The Nanoscale Caterpillar - or how to achieve precise motion with random sticky feet

Beating equilibrium diffusion is a paradigm challenge that biological or artificial systems of small particles have to face to achieve complex functions. Some cells (like leucocytes) use ligand-receptor contacts (sticky feet) to crawl and roll along vessels. Sticky DNA (another type of sticky feet) is coated on colloids to design programmable interactions and long-range assembly features. The dynamics of such sticky motion are complex as sticky events (attaching/detaching) often occur on very short time scales that affect the overall motion of the particle on much longer time scales, and makes predictions challenging. Furthermore, the equilibrium statistics of these systems (how many feet are attached in average) are extremely entangled and inaccessible experimentally. Here we present advanced modeling and experimental results on a model system, and we find predictions in several cases (with different geometries of sticky feet). We rationalize what parameters control average feet attachment, long term diffusion and how they can be compared to other existing systems. We investigate furthermore how various motion modes (rolling, sliding or skipping) may be favored compared to each other.   

Geometrical effect of lubricant-containing cavity on lubricant depletion under external flow

Lubricant-infused surface (LIS) has been widely investigated owing to its extensive potential to be applied to various industrial fields. However, the outermost lubricant layer of LIS can be easily depleted by external shear force, which induces a significant loss of its promising properties. In this work, the shear-induced depletion of impregnated lubricant from a single cavity was investigated with varying the geometry of lubricant-containing cavity. The effect of cavity geometry on depletion dynamics of impregnated lubricant was experimentally investigated by directly visualizing the temporal variation of lubricant menisci. The internal circulating vortex flow during lubricant depletion was measured using a particle image velocimetry (PIV). Temporal evolution of internal vortex flow in response to the liquid menisci variation was also analyzed simultaneously. As a result, a correlation between cavity geometry, internal flow structure and lubricant depletion was newly established. The present results would provide valuable insight for designing a robust LIS system for effective and sustainable applications.   

Closing the lid: Fluid dynamics of telescopic cardboard boxes

Cardboard boxes are an important form of packaging for products in the food, electronics, and medical industries. Here, we focus on the fluid dynamics of a basic process: closing the lid of telescopic cardboard boxes. The characteristic slow vertical sliding motion of the lid is controlled by viscous flow in a thin film of air in the gap separating the lid and the base of the box. If the lid and base fit tightly, it is difficult for the consumer to remove the lid. By contrast, if the lid is loose, it can accidentally open and damage the content. A properly sized lid provides an appropriate tradeoff between safety and convenience. Yet, the time, and hence cost, required to close the lid before shipment or storage may still be significant. We discuss this process and the dependence of the closing dynamics on physical and geometric parameters.   

Diffusion Into Dead-End Pores of Non-Uniform Cross-Section

Understanding micron-scale fluid flows is critical to perfecting the manufacturing and use of microfluidic technologies for medical and engineering applications. In particular, microchannels with dead-end pores are ubiquitous in natural and industrial settings, and ongoing research focuses on fluid and chemical transport in and out of these pores. In the present work, we detail a repeatable and accessible experimental protocol developed to study the passive diffusion process of a dissolved solute into dead-end pores of rectangular and trapezoidal geometries. Custom microchannels with pores of specified geometries are rapidly produced using inexpensive materials and a commercial craft cutter. The experimental data is compared directly to both detailed 3D numerical simulations as well as to analytical solutions of an effective 1D diffusion equation: the Fick-Jacobs equation. The role of the pore geometry on the passive diffusion process will be highlighted. Ongoing and future directions will be discussed.   

Interfacial flow around thermally forced colloids measured by correlated displacement velocimetry

We have developed a method to measure nanoscale flow field around interfacially trapped colloidal particles undergoing Brownian motion. By this method, we map the flow field generated by particle displacements, which are decomposed into interfacial hydrodynamic multipoles, including thermally induced force monopole and dipole flows, whose forms differ significantly from their bulk fluid counterparts. Analysis of the detailed flow structures provide key insights essential to understanding the interfacial response. Importantly, the flow structure around micron size colloids shows that the interface is incompressible for scant surfactant near the ideal gaseous state with surface pressures smaller than 0.1 mN m. Furthermore, the measured flow fields also contain information about the mechanical properties of the interface in a range that is inaccessible with other measurement techniques, e.g., surface viscosities less than 10$^{\mathrm{-10}}$ Pa m s. This measurement reveals flow reorganization for nearly surfactant-free systems, and can be applied to probe interfacial flows in systems to which surface active substances are deliberately added.   

Enhanced Transport Due to Driven and Active Colloids at Fluid Interfaces

We examine the hydrodynamics of driven or active colloids trapped at fluid interfaces and their impact on mass transport rates. We assume that the colloids are adhered to the interface by a pinned contact line and thus in a fixed orientation with respect to the interface. However, they are free to translate along the interface and rotate about an axis normal to the interface. Far-field flows generated by these colloids are of primary importance to long-ranged hydrodynamic interactions that drive transport of other passive material on or near the interface. We introduce a “library” of such flows, which vary depending on the mechanism of colloid motion, colloid orientation, and the properties of the interface. We then quantify transport of passive material by computing the “drift,” or fluid tracer displacements, arising from each of these modes for a colloid moving along a specified trajectory. We also estimate the resulting tracer diffusivity due to a dilute layer of active or driven colloids moving along random trajectories. We find conditions for viscous fluid interfaces in which lateral dispersion of passive material on or near the interface may be greatly enhanced by driven or active colloids.   

Transient behavior of an optically induced electrothermal micro-vortex: Modelling and PIV analysis

Optical, electrical and hybrid micro-manipulation techniques such as optical tweezers, dielectrophoresis and rapid electrokinetic patterning (REP) have proven to be of great importance in studying synthetic and biological particles. In this work, we study the flow field around a dynamically changing optically activated REP micro-vortex using computational modelling and particle image velocimetry (PIV). In-situ reconfigurable REP traps have potential to enhance our real-time micro-manipulation capabilities. A colloidal suspension of 1$\mu $m polystyrene beads (0.1 mM aq. KCl) sandwiched between two parallel-plate indium tin-oxide coated glass electrodes was subjected to an AC electric field (3.6 Vrms, 500 kHz). A laser (980 nm) spot was focused at the liquid-electrode interface and was scanned back and forth in a line at varying rates, to create the vortex. The resulting flow velocity was measured by a time-resolved PIV analysis. A model was created with COMSOL Multiphysics to visualize flow in dynamic REP vortices. Both the analysis methods show that fluid velocity oscillated with the laser spot however, with increasing scanning rate the mean as well as the deviation in velocity decreased. At scanning rates above 15 Hz, the oscillations in fluid velocity were indiscernible.   

Direct numerical simulations of semi-dilute and concentrated suspensions of non-conductive particles in an electric field.

The electrical manipulation of particles dispersed in a host fluid is known to be the basic concept of electrorheological (ER) fluids. Under the action of an electric field, the ER fluids in which non-conductive but electrically active particles are suspended in an electrically insulating fluid, are known to undergo dielectrophoretic (DEP) interactions and exhibit a dramatic viscosity enhancement. It is well-known that DEP interactions between the particles lead to a rapid formation of particle chains along the field direction. The fibrillated structures are responsible for the unique rheological properties of ER suspensions and tend to be thicker with volume fraction. However, the response of ER suspensions to an electric field at high concentrations has yet to be fully studied. In this study, we perform large-scale Stokesian dynamics simulations to study the semi-dilute and concentrated suspension of non-conductive particles in an electric field. It is found that the kinetics of pattern formation changes above a volume fraction of 0.35 at which a suspension directly undergoes mesoscale structure formation. The electric stress field of suspension is presented for a range of volume fractions. Lastly, the effect of confinement on suspension dynamics is discussed.   

Colloidal particle dynamics during the particle accumulation stage

Colloidal polystyrene particles in a very dilute (volume fractions $=$ $O$(10$^{\mathrm{-5}}$--10$^{\mathrm{-3}})$ suspension become attracted to, and accumulate in, the high shear regions near the wall, depleting particles from the bulk, in combined Poiseuille and electroosmotic ``counterflow.'' This has been observed in $H \quad =$ 34 $\mu $m deep channels when the pressure and voltage gradients are in the same direction. The particles then assemble into streamwise structures that we call ``bands''. Two-color experiments, where 1{\%} of the $a \quad \approx $ 250 nm radius particles are tracers labeled with a different fluorophore, are used to investigate the initial particle accumulation stage at different streamwise locations. The near-wall particle concentration increases linearly over time by at least two orders of magnitude, consistent with the exponential growth in the average image grayscales reported previously. These results are used to estimate the wall-normal attractive ``lift'' forces that drive particle concentration, and compared to recent models. There appears to be an ``entrance length'', where the near-wall particle concentration does not become independent of streamwise position until $O$(10$^{\mathrm{3}}H)$ downstream of the inlet, which may depend on the number of suspended particles upstream.   

Colloidal particle dynamics during the steady-state bands stage

Polystyrene particles in a very dilute (volume fractions $=$ $O$(10$^{\mathrm{-5}}$--10$^{\mathrm{-3}}))$ suspension become concentrated near the wall, then assemble into streamwise structures called ``bands'' which only exist within a few $\mu $m of the wall, when subject to pressure and voltage gradients in the same direction. These bands, which attain steady-state within $O$(10$^{\mathrm{2}}$ s), have cross-sectional dimensions of a few $\mu $m, \textit{vs.} a channel depth $H \quad =$ 34 $\mu $m, and a length comparable to that of the channel of a few cm. Tracer particles were used to track the dynamics of $a \quad \approx $ 250 nm radius particles within and between the bands in this steady-state stage at different streamwise locations. The time scales of band formation appear to scale linearly with streamwise position past an ``entrance length'' region. The particles within the bands ``lag'' the flow, as do the much fewer particles between the bands, though their velocities are closer to the expected flow velocities. The time scales for achieving steady-state bands are compared with the time scales of near-wall particle concentration. Results over different wall-normal extents suggest that the particle concentration within the bands may be underestimated in these evanescent-wave visualizations because they visualize the ``edge'' of the bands.