Session M6: Microfluidics: Capillary II

Dynamics of a small number of droplets moving in microfluidic Hele-Shaw cells

We investigate both theoretically and experimentally the dynamics of a small number of droplets moving in microfluidic Hele-Shaw cells. We derive simplified equations in the limit of large friction against the wall. These equations provide a quantitative description of the dynamics observed in the experiments. Similar conclusions hold for the influence of the walls.   

Multiple bubble propagation modes in Hele-Shaw cells of variable depth

Experimental investigations of long air bubbles displacing viscous oil in axially uniform rectangular channels have shown that symmetric partial occlusion of the cross-section can induce a variety of bubble morphologies, which may find practical application in microdevices. For sufficiently high steady flow rates, the bubbles switch from centred to asymmetric configurations,\footnote{de L\'{o}zar et al., {\emph{Phys. Fluids}} {\bf 21}, 101702, (2009)} and spatial oscillations can develop behind the tip in intermediate regimes.\footnote{Pailha et al., {\emph{Phys. Fluids}} {\bf{24}}, 021702, (2012)} We show that all observed morphologies are reproduced in a two-dimensional depth-averaged model, similar to that describing Saffman--Taylor fingering, but with a spatially varying channel height. The resulting equations are solved numerically, using the finite-element library \texttt{oomph-lib}\footnote{Heil \& Hazel, {\emph{Lect. Notes Comput. Sci. Eng.}} {\bf{53}}, (2006)} and we present the results of a bifurcation analysis that complements the existing experimental data. The qualitative agreement between 2D model and 3D experiments indicates that the complex behaviour arises solely from the enforced change in transverse curvature of the air-oil interface.   

Modeling sessile droplets on hydrophobic surfaces with spatially varying contact angle

We present a mathematical model that we have developed in order to numerically investigate droplets deposited on hydrophobic surfaces with spatially varying contact angle, $\theta\left(\mathbf{r}\right)$. If a gradient in $\theta$ is induced on the surface it is possible to guide the flow. The model solves the Navier-Stokes equation on a time-dependent domain $\Omega(t)$ by the use of the Finite Element Method with a moving mesh (Arbitrary Lagrangian-Eulerian, ALE). A Navier slip boundary condition at the fluid-solid interface has been implemented, and at the free surface the Young-Laplace equation is used. Results for 1) drops deposited on an inclined plane will be presented, along with 2) results for a drop oscillating in a ``potential well'' made from rapidly (but smoothly) changing the contact angle. In case 1) we examined the internal flow field of the drop and, according to the model, a rotating flow builds up as the overall velocity increases. In case 2) the drop oscillates in a damped way since viscous friction damps out the energy. There seem to be a non-linearity between the strength of the potential and the amplitude, decay length, and frequency of the oscillations. We suspect this is due to some preferred internal oscillatory state/eigenmode of the drop.   

Modification of the effective contact angle by means of particle collection and the generation of armored bubbles

We report on an experimental work where hydrophobic particles are collected by a moving water-air meniscus in a capillary tube. The results show that under certain conditions the collected particles can position themselves on a granular monolayer at the liquid-air interface and move with it. A continuation in the particle collection by the meniscus results in the decrease of the effective liquid-water contact angle (CA) in the capillary tube. At zero CA an ``air finger'' with its walls covered by particles forms. The finger displays stick-slip behavior in its motion due to solid friction of the particles with the wall. This friction eventually provokes its pinch-off which results in the formation of a cylindrical armoured bubbles.   

Capillary Rise in Tubes with Interior Corners

The classic problem of sudden capillary rise in tubes (i.e. channels) with one or more interior corner is revisited from the perspective of a first tier advancing bulk meniscus of constant curvature that feeds second tier advancing corner flows. Asymptotic solutions are presented for the visco-capillary limit that extends the Lucas-Washburn solution to such geometries. These ``compound capillary'' flows are common but overlooked due to the relatively small impact on overall flow rate for typical geometries such as the square tube. However, for more acute sections, the second tier corner flows are significant and cannot be ignored. Such geometries may be exploited for a variety of applications including passive phase separations. Supportive experimental data are presented using both micro-scale terrestrial and macro-scale drop tower tests.   

Thermocapillary Levitation of Nanoliter-Volume Droplets and Extension to Two-Phase Systems

The development of a novel method of droplet levitation to be employed in lab-on-a-chip (LOC) applications relies upon the mechanism of thermocapillary convection (due to the temperature dependence of surface tension) to drive a layer of lubricating gas between droplet and substrate. The fact that most droplets of interest in LOC applications are aqueous in nature, coupled with the fact that success in effecting thermocapillary transport in aqueous solutions has been limited, has led to the development of a technique for the controlled encapsulation of nanoliter-volume water droplets within a shell of inert silicone oil. Previously, microliter-volume single-phase silicone-oil droplets have been levitated. This work aims to extend this technique to nanoliter-volume single- and compound-phase oil and water droplets as well as ascertain how the fluid-fluid interface affects the internal convective currents driven by the surface flow in compound-phase systems.   

Microfluidic dissolution of CO$_{2}$ bubbles in viscous oils

We experimentally study the interrelation between the dissolution of carbon dioxide bubbles and microfluidic multiphase flows. Individual bubbles are generated in silicone oils at the junction of a hydrodynamic focusing section. High-speed imaging is used to track individual bubbles and monitor their shape and velocity as they experience a reduction in size due to gas diffusion. The early diffusive behavior is analyzed using computational routines developed to reconstruct the evolving 3D volume of elongated bubbles from their 2D contour. In particular, we examine the fast initial diffusive behavior, which is characterized as a function of the oil molecular weight - from low to high viscosity - gas inlet pressure, flow rates, and microgeometries.   

Phase-locked confocal micro-PIV measurement of three dimensional flow structure of transient droplet formation mechanism in T-shaped micro junction

This paper aims to investigate a mechanism of microdroplet formation at a micro T-shaped junction using a ``phase-locked multicolor confocal micro-PIV (Particle Image Velocimetry)'' technique. The multicolor system can measure dynamic behavior of each phase of multiphase flow separately and simultaneously. The phase-locking technique is necessary to reconstruct three-dimensional flow field from two-dimensional confocal micro-PIV measurement data. We successfully obtained each temporal phase of periodic phenomenon non-invasively by detecting passage of droplet from transmitted light of optical proximity sensor. Additionally, the phase-locking technique also enables picking up same condition of formation frequency, size and translational velocity of droplet to minimize instability of droplet formation phenomenon. As a result, three-dimensional flow structure of the droplet formation was successfully reconstructed and the droplet formation mechanism was investigated by the flow interaction between each phase.   

Formation of partially wetting droplets in square microchannels

We experimentally study the formation and evolution of partially wetting droplets in microchannels made of glass and silicon. Droplets are steadily generated by focusing water in an external phase of silicone oil using square channels. To probe the influence of the capillary number on droplet and wetting dynamics in confined geometries, the oil viscosity is varied over four decades. At low capillary numbers, we observe the formation of contact lines and the nucleation of dewetting patches in the thin film surrounding elongated droplets. By contrast, small and lubricated droplets are produced at large capillary numbers. The dynamic wetting properties of microfluidic segmented flows are compared with measurements performed using a contact angle goniometer.