Comparison of velocity field characteristics of gas invasion via viscous fingering and elastic fracturing in visco-elasto-plastic fluids.

Viscous fingering (VF) and elastic fracture (EFr) are prevalent phenomena when gas invades into complex fluids. In this study, compressed nitrogen gas was injected into a complex fluid called magnesium lithium phyllosilicate (MLPS) suspension through a single-point injection in a rectangular Hele-Shaw cell. In the case of gas invasion into the MLPS suspension via VF, the affected area is confined to the tips of the independently growing fingers after splitting. Within the affected region, the velocity is primarily parallel to the growth direction of fingers, while the perpendicular component is mainly distributed on the outer sides of the whole bubble and within a more limited range. The gas-liquid interface can be divided into moving and static boundaries, where the length of the moving boundary is much smaller than the perimeter of the bubble. On the moving boundary, the parallel velocity component to the growth direction is significantly greater than the perpendicular component in terms of both the influence range and magnitude. The included angles between the velocity direction and the growth direction are concentrated within a narrow range, showing a significant positive correlation among the velocities. Conversely, when a bubble invades via EFr, the disturbed area is larger, with the parallel velocity component primarily located at the tip and the perpendicular component distributed in a "butterfly" shape around the middle of the bubble. The moving boundary length is comparable to the bubble perimeter. On the moving boundary, the perpendicular component exerts a non-negligible influence, and the distribution of included angles is more uniform, resulting in a significant negative correlation among the velocities. Based on the above characteristics of the velocity field, quantitative indicators, such as the ratio of the affected area, the ratio of moving boundary length to the perimeter, the velocity component ratio, the coefficient of uniformity, and the relative correlation length, are proposed. Based on the velocity field, these indicators demonstrate universal applicability in distinguishing between the two different invasion patterns observed in complex fluids.