Rise of a single bubble through an idealized porous medium

Direct numerical simulations using a Volume-of-Fluid method is employed to study buoyancy-driven rise of a single gas bubble through an idealized porous medium made of a staggered array of parallel cylinders. The main studied parameters are the pore-to-bubble diameter ratio $D_p/D$ and Bond number $Bo$, which are varied in range 2.5--7 and 0.1--4, respectively. The simulations are run at Galilei number $Ga$ of 40 and 100. We present the results in terms of the trajectory of the bubbles as well as variations of their velocity and deformability in time. Comparisons have been made with free-rising bubbles at identical $(Ga,Bo)$ combinations.The results show the trajectories to be meaningfully sensitive to the initial location and with considerable lateral drift when both Bond number and pore diameter are small. This is a result of strong and frequent deflections, which also cause the ratio of mean vertical velocity to that of the corresponding free-rising bubble to fall below 30\% in certain range of parameters. In the case with $(Ga,Bo)=(100,4)$, where the corresponding free-rising bubble takes a zigzag path due to its inherent wake instability, we observe a transition from geometry-driven to wake-driven path oscillations at $D_p/D\approx3.5$ based on an analysis of the dominant wavelengths. The shape of a bubble interface during rise is dominated by high deformations after the cylinder collisions and low deformations due to slow down of velocity leading to a range of behaviors depending on the ratio of capillary and collision time scales.