Understanding the mobilisation of trapped globules of non-wetting phase during two-phase flow has been the aim of numerous studies. However, the driving forces for the mobilisation of the trapped phases are still not well understood. Also, there is little information about what happens within a globule before, at the onset and during mobilization. In this work, we used micro-particle tracking velocimetry in a micro-fluidic model in order to visualise the velocity distributions inside the trapped phase globules prior and during mobilisation. Therefore, time-averaged and instantaneous velocity vectors have been determined using fluorescent microscopy. As a porous medium, we used a polydimethylsiloxane (PDMS) micro-model with a well-defined pore structure, where drainage and imbibition experiments were conducted. Three different geometries of trapped non-wetting globules, namely droplets, blobs and ganglia were investigated. We observed internal circulations inside the trapped phase globules, leading to the formation of vortices. The direction of circulating flow within a globule is dictated by the drag force exerted on it by the flowing wetting phase. This is illustrated by calculating and analyzing the drag force (per unit area) along fluid-fluid interfaces. In the case of droplets and blobs, only one vortex is formed. The flow field within a ganglion is much more complex and more vortices can be formed. The circulation velocities are largest at the fluid-fluid interfaces, along which the wetting phase flows and decreases towards the middle of the globule. The circulation velocities increased proportionally with the increase of wetting phase average velocity (or capillary number). The vortices remain stable as long as the globules are trapped, start to change at the onset of mobilization and disappear during the movement of globules. They reappear when the globules get stranded. Droplets are less prone to mobilization; blobs get mobilised in whole; while ganglia may get ruptured and get mobilised only partially.
Microscopic velocity field measurements inside a regular porous medium adjacent to a low Reynolds number channel flow. Physics of Fluids, 31(4), [042001].
We present simulations and experiments of drainage processes in a micro-model. A direct numerical simulation is introduced which is capable of describing wetting phenomena on the pore scale. A numerical smoothed particle hydrodynamics model was developed and used to simulate the two-phase flow of immiscible fluids. The experiments were performed in a micro-model which allows the visualization of interface propagation in detail. We compare the experiments and simulations of a quasistatic drainage process and pure dynamic drainage processes. For both, simulation and experiment, the interfacial area and the pressure at the inflow and outflow are tracked. The capillary pressure during the dynamic drainage process was determined by image analysis.
Modeling coupled systems of free flow adjacent to a porous medium by means of fully resolved Navier–Stokes equations is limited by the immense computational cost and is thus only feasible for relatively small domains. Coupled, hybrid-dimensional models can be much more efficient by simplifying the porous domain, e.g., in terms of a pore-network model. In this work, we present a coupled pore-network/free-flow model taking into account pore-scale slip at the local interfaces between free flow and the pores. We consider two-dimensional and three-dimensional setups and show that our proposed slip condition can significantly increase the coupled model’s accuracy: compared to fully resolved equidimensional numerical reference solutions, the normalized errors for velocity are reduced by a factor of more than five, depending on the flow configuration. A pore-scale slip parameter $$\beta _{{{{\rm pore}}}}$$
β
pore
required by the slip condition was determined numerically in a preprocessing step. We found a linear scaling behavior of $$\beta _{{{{\rm pore}}}}$$
β
pore
with the size of the interface pore body for three-dimensional and two-dimensional domains. The slip condition can thus be applied without incurring any run-time cost. In the last section of this work, we used the coupled model to recalculate a microfluidic experiment where we additionally exploited the flat structure of the micromodel which permits the use of a quasi-3D free-flow model. The extended coupled model is accurate and efficient.
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