Influence of wetting conditions on drainage in porous media: A microfluidic study

This paper presents some experimental results on two-phase flows in model two-dimensional (2D) porous media with different wetting properties. Standard microfluidic techniques are used to fabricate the 2D micromodels that consist of a network of straight microchannels having heterogeneous sizes. The invasion mechanism is analyzed quantitatively for partial and total wetting conditions, and for various stable viscosity ratios and capillary pressure heterogeneity. For capillary numbers ranging from ${10}^{-7}$ to ${10}^{-2}$, we observe a transition between capillary fingering and a stable front. The capillary fingering regime exhibits differences between partial and complete wetting systems: The front width in complete wetting is larger. Simple models are proposed to account for these regimes and indicate that the differences between the systems are likely to be due to the flow of the displaced fluid in the complete wetting situation.

Figure 1

Example of a design. The real size of the porous domain is 1.3 cm. The wavelength $\lambda$ of the lattice is 250 $\mu$m.

Figure 2

Images taken during the invasion step with the water-dodecane system (water is the injected fluid) in grid a for two different flow rates (top, ${\text{Ca}}_i=2.3\times {10}^{-7}$; bottom, $2.2\times {10}^{-5}$). From left to right, the pictures are taken at $t=43,$ 74, 174, and 265 s (top) and $t=3,$ 6, 9, 12, 18 s (bottom).

Figure 3

Typical pictures of menisci located upstream from the front during the invasion process. The system under study is the water-dodecane system seeded with latex beads under total wetting conditions in channels of width 80 $\mu$m. Hydrophobic PDMS grid a. ${\text{Ca}}_i=2.{10}^{-5}$. From left to right, the pictures correspond to time $t$, $t+11$s, $t+22$ s. These pictures illustrate the back and forth displacements of the menisci. The streamlines that could be seen in the rightmost panel are another feature of the flow. The latter fluctuates and exhibits some intermittent recirculations, with rather high velocities. The channel width is equal to $80\mu$m.

Figure 4

$〈{\text{Ca}}_l〉$ as a function of ${\text{Ca}}_i$ obtained with the water-dodecane system for the two micromodels used. Grid a, $\epsilon =0.1$ (squares); grid b, $\epsilon =0.035$ (triangles). The dashed lines correspond to $〈{\text{Ca}}_l〉={\text{Ca}}_i$ and the dashed-dotted one to $〈{\text{Ca}}_l〉=N_w{\text{Ca}}_i$.

Figure 5

Variations of $〈{\text{Ca}}_l〉$ as a function of ${\text{Ca}}_i$ in grid a ($\epsilon =0.1$), for various viscosity ratios $M={\eta }_1/{\eta }_2$, where ${\eta }_1$ and ${\eta }_2$ are the viscosities of the displacing and displaced fluids, respectively. $M=0.5$ ($◯$), 0.7 (+), 2 ($\square$), 5 ($*$), 10 ($•$), 30 ($\blacksquare$), and 100 ($♦$).

Figure 6

Scheme of the pressure field in the case of partial wetting. The colored phase is the invading fluid.

Figure 7

Variations of the modified measured mean local capillary number as a function of the imposed one for various viscosity ratios and in the two micromodels (grids a and b), in complete wetting situations. The dashed and dotted lines correspond to $\widetilde{〈{\text{Ca}}_l〉}={\widetilde{\text{Ca}}}_i$ and to $\widetilde{〈{\text{Ca}}_l〉}=N_w{\widetilde{\text{Ca}}}_i$ and are similar for the two models. The full lines correspond to the capillary regime, the horizontal one standing for the coinjection situation and the other for $\widetilde{〈{\text{Ca}}_l〉}=c{\widetilde{\text{Ca}}}_i^{0.5}$.

Figure 8

Example of an invasion at very low capillary number (${\text{Ca}}_i=5\times {10}^{-7}$) under total wetting conditions. The micromodel used is made of channels of uniform width, which might explain why the chosen path is a straight one. Note that the menisci curvatures at the nodes of the network do not increase when going upstream. They remain smaller than that of the most advanced meniscus.

Figure 9

Plot of the modified measured mean local capillary number $\widetilde{〈{\text{Ca}}_l〉}$ as a function of the imposed one $\widetilde{{\text{Ca}}_i}$. The symbols correspond to experiments performed in the partial wetting situation (see Ref. [9] for the details). The full line correspond to the model in the uniform pressure situation in the displaced fluid, where the capillary regime is given by $\widetilde{〈{\text{Ca}}_l〉}=0.27\widetilde{{\text{Ca}}_i}$.

Figure 10

Images of the invasion process for grid a. (Left) The pictures correspond to the total wetting case, the PDMS chip is hydrophobic and water is pushing dodecane. (Right) The pictures correspond to the partial wetting case, the PDMS chip is “hydrophilic,” FC40 is pushing water, $\theta \simeq {140}^{\circ }$. In both cases ${\text{Ca}}_i=2\times {10}^{-5}$.