Droplet motion in microfluidic networks: Hydrodynamic interactions and pressure-drop measurements

Abstract

We present experimental, numerical, and theoretical studies of droplet flows in hydrodynamic networks. Using both millifluidic and microfluidic devices, we study the partitioning of monodisperse droplets in an asymmetric loop. In both cases, we show that droplet traffic results from the hydrodynamic feedback due to the presence of droplets in the outlet channels. We develop a recently-introduced phenomenological model [W. Engl, Phys. Rev. Lett. 95, 208304 (2005)] and successfully confront its predictions to our experimental results. This approach offers a simple way to measure the excess hydrodynamic resistance of a channel filled with droplets. We discuss the traffic behavior and the variations in the corresponding hydrodynamic resistance length L_{d} and of the droplet mobility beta , as a function of droplet interdistance and confinement for channels having circular or rectangular cross sections.

Microfluidic breakups of confined droplets against a linear obstacle: The importance of the viscosity contrast

“…Building on earlier works [12,18], we assume that the speed v of a slug flowing in a channel of constant cross section hw varies with q the total flow rate as v = q hw , and that the flows of the slug and the continuous phase satisfy Darcy's law, with an effective viscosity η ef f d for the slug [19]. Hence, the pressure drop p over a portion ℓ of the slug reads…”

Encoding and controlling of two droplet trains in a microfluidic network with the loop-like structure

“…In this section, we derive the mathematical relationship between the outlet patterns (the intervals of droplets) and the parameters including microstructure size, tuning flow rates and so on. With mathematical analysis, theory model can be looked as a useful numerical simulation method to understand and manage the microfluidic droplet-related traffic problems (Schindler and Ajdari 2008;Cybulski and Garstecki 2010;Jousse et al 2006;Sessoms et al 2009;Behzad et al 2010;Sessoms et al 2010;Smith and Gaver 2010;Glawder et al 2011). The analytical results here can provide effective reference for encoding and encounter of droplets.…”

“…In addition, a droplet may either split into smaller daughter droplets at large capillary numbers (Song et al 2003;Link et al 2004) or choose to enter the channel that has the instantaneous maximum flow rate (Sessoms et al 2009;Engl et al 2005) when reaching a junction in microchannels. Salkin et al (2013) found that the breakup of droplets is affected by the additional presence of droplets in downstream channels and the slug-to-slug interactions, so it is with the breakup of bubbles at a microfluidic T-junction , and the flow resistance due to droplets or bubbles should be considered for the design of microfluidic devices.…”

“…Although many studies assume a constant one and can obtain the essential characteristics of the droplet dynamics as an approximation for analysis (Schindler and Ajdari 2008;Cybulski and Garstecki 2010;Bithi and Vanapalli 2010;Garstecki 2010), droplets motion will still result in nonlinear change of the flow resistance of microchannels and affect the flow rates of the channels and later choices of droplets at the junctions in turn. Actually, this problem is a complex nonlinear feedback regulation one (Sessoms et al 2009;Engl et al 2005), which brings great difficulties to the setup of theoretical models even for the droplet dynamics in the simple microfluidic devices Garstecki et al 2005), and more research work including the usage of innovative analytical methods should be done.…”

“…1b can be an expansion structure for encoding research of two droplet trains. Meanwhile, we impose two controllers to add the flexible manipulation; the controllers can be dilution or concentration modules and the imposed controlling flow rates can be called tuning flow rates (Sessoms et al 2009;Yamada et al 2008). We do mathematical analysis and establish an effective and robust theoretical solution to study the droplet dynamics correspond to the expansion structure (Fig.…”