In the cases discussed so far, there is no preferential interaction between the fluid components and the capillary boundary. This interaction is found to have little effect on the breakup morphology for Λ > 2.5, but the liquid-surface interaction can be expected to be important in more confined threads. In contrast to Fig. 7, where there is no energetic preference of the thread fluid for the tube wall, Figs. 9(a) and 9(c) show the evolution in the fluid breakup (Λ = 2.09) for the cases where the fluid thread preferentially wets the tube wall and dewets the wall, respectively. Figure 9(b) indicates the energetically neutral case where neither fluid has a preferential affinity for the tube wall. Specifically, the equilibrium contact angles of the thread fluid on a plane surface having the interaction of the tube boundary are 35º, 90º, and 145º for Figs. 9(a)–9(c);, respectively [29]. These simulations are for the case of an impulsive thread perturbation (ε = 0.1), although the type of perturbation is less important for this moderate confinement case. The contact angles of the plugs directly reflect this variation in the relative energies between the fluids and the substrate. Although thread breakup occurs regardless of the relative surface energy, there is a dramatic change in the kinetics of thread breakup and plug formation arising from the fluid-tube wall interaction. First, we notice that the breakup time is greatly increased relative to the neutral wall case when either the thread or annular fluid has a higher affinity for the wall. In particular, the time scales tred for thread rupture in Figs. 9(a)–9(c) approximately equal to 56, 38, and 50, respectively. This corresponds to about 47% and 32% increases in the thread rupture time relative to the "neutral" wall boundary condition for the case where the thread preferentially wets the surface and the wall fluid preferentially wets the surface, respectively. Unexpectedly, a high affinity of the thread fluid for the wall greatly decelerates the rate of thread breakup. We at first hypothesized that segregation of the tube fluid to the boundary caused a slowing of the dynamics by modifying the effective tube radius to a smaller value (thus reducing the rate of capillary breakup), but the extent of this segregation (a couple of a percent enrichment of the thread volume fraction at the wall) seems to be too small to account for the observed effect. Thus, the origin of this effect remains obscure. The stabilization of the thread rupture by the wetting of the encapsulating fluid can be more readily rationalized. The formation of plugs is clearly difficult under these circumstances and supporting this view we see that the capsules capsules persist to long times in the simulations shown in Fig. 9(c) with this boundary interaction. (Notably we found that the capsules became plugs more rapidly in this case if the tube was made shorter, i.e., L = 100). These results indicate that fluid surface interactions can have a large influence on thread breakup kinetics in moderately confined geometries. This important and subtle effect will require systematic computational and experimental investigation.
FIG. 9. Influence of surface interaction on thread breakup of confined threads. As in Fig. 7, we consider the LB simulation of thread of radius 9.55±0.06 (in units of lattice spacing) that is confined to a tube of radius 20 and having length 600. (a) The thread fluid (white) preferentially wets the tube wall. (b) Fluids have the same affinity for the capillary wall. (c) The tube wall preferentially wets the annular fluid. Note that the rate of thread breakup and plug formation is slowed relative to the neutral boundary when either fluid preferentially wets the wall. These studies are performed at a fixed quench depth (interfacial width) and Λ, and future work must consider the variation of these parameters to deduce the quantitative effect of fluid-surface interaction on the rate of thread breakup.