RESUMEN
Motivated by a developmental gas embolotherapy technique for selective occlusion of blood flow to tumors, we examined the transport of a pressure-driven semi-infinite bubble through a liquid-filled bifurcating channel. Homogeneity of bubble splitting as the bubble passes through a vessel bifurcation affects the degree to which the vascular network near the tumor can be uniformly occluded. The homogeneity of bubble splitting was found to increase with bubble driving pressure and to decrease with increased bifurcation angle. Viscous losses at the bifurcation were observed to affect the bubble speed significantly. The potential for oscillating bubble interfaces to induce flow recirculation and impart high stresses on the vessel endothelium was also observed.
RESUMEN
A pressure driven 2-D channel flow at very low Reynolds numbers (Stokes flow) with a bubble sticking and sliding along one of the walls is studied computationally using the boundary element method (BEM). The moving three phase contact lines are modeled using a Tanner law wherein the contact line speed is linearly proportional to the deviation of the contact angle from its equilibrium value. Results are presented with and without the effect of contact angle hysteresis. Including contact angle hysteresis allows us to predict the stick-slide behavior of bubbles, which in turn affects the long term evolution and dynamics of the bubbles. It is shown that the initial rapid contraction or expansion of the bubbles to achieve local equilibrium with the surrounding pressure field results in cusps and bulges in the wall normal stress profiles. The wall shear stress also increases (with opposite signs upstream and downstream of the bubble) as the fluid rushes in or out of the channel inlet and outlet. In the long term, bubbles slowly expand as they slide along the channel wall. Contact lines are found to correspond to peaks in the wall normal and shear stress profiles at all times. The effectiveness of bubbles in occluding flow through the channel is also examined.