Forced Wetting Transition and Bubble Pinch-Off in a Capillary Tube

Abstract

Immiscible fluid-fluid displacement in partial wetting continues to challenge our microscopic and macroscopic descriptions. Here, we study the displacement of a viscous fluid by a less viscous fluid in a circular capillary tube in the partial wetting regime. In contrast with the classic results for complete wetting, we show that the presence of a moving contact line induces a wetting transition at a critical capillary number that is contact angle dependent. At small displacement rates, the fluid-fluid interface deforms slightly from its equilibrium state and moves downstream at a constant velocity, without changing its shape. As the displacement rate increases, however, a wetting transition occurs: the interface becomes unstable and forms a finger that advances along the axis of the tube, leaving the contact line behind, separated from the meniscus by a macroscopic film of the viscous fluid on the tube wall. We describe the dewetting of the entrained film, and show that it universally leads to bubble pinch-off, therefore demonstrating that the hydrodynamics of contact line motion generate bubbles in microfluidic devices, even in the absence of geometric constraints.

Restoring universality to the pinch-off of a bubble

“…1), the ratio of which determines the apparent contact angle as θap = 2hr /w ≈ 30 • , which is small enough for the long-wave approximation to be valid (40,41). This observation is further confirmed in our earlier work, showing an excellent match between the experimentally observed profiles and the theoretical prediction (37). Of course, the longwave approximation ultimately breaks down as the slope of the meniscus near the point of singularity diverges, leading to a crossover to the late-time self-similar regime.…”

“…1). This can be analyzed using a long-wave approximation (37), which assumes that the flow is mainly parallel to the tube axis. Near the point of pinch-off, we postulate that the shape of the profile becomes self-similar:R(ξ) =r (z ,τ )/τ α , and ξ = (z −z0)/τ β with α and β as constants ( Fig.…”

“…At low flow rates, the meniscus deforms slightly and moves downstream at a constant velocity U = 4Q/(πd 2 ). When the imposed flow rate is higher than a critical value, however, a wetting transition occurs: the meniscus loses its quasi-static geometry and air starts invading the tube in the form of an extending axial finger, leaving a film of the viscous liquid on the walls (37). Fig.…”

Comprehensive comparison of pore-scale models for multiphase flow in porous media

“…Thin Films and Corner Flow. The complex nature of interfacial flows in the presence of solid surfaces lends an inherently 3D nature to fluid-fluid displacement processes, even in quasi-1D geometries such as capillary tubes (48) and quasi-2D geometries such as Hele-Shaw cells (46). In a patterned micromodel, these 3D effects include the propagation of thin films along the top and bottom walls and the surfaces of the posts, and in the corners where the walls and posts meet (2,47).…”

Connectivity enhancement due to film flow in porous media

“…The complicated geometry of pores and throats in the medium renders the problem too demanding from the numerical point of view and analytical solutions are only available for very simple geometries [44]. In order to develop a reasonable growth model, one has to understand the basic mechanisms behind the pore-scale dynamics [26], including effects from the contact line dynamics [45], and how those mechanisms interact to yield the macroscopic properties of the flow. Understanding the relative importance of nontrivial flow mechanisms such as film flow is important to allow a precise judgment on whether or not a given flow condition can be appropriately described by a growth model such as IP or DLA (both models, in their standard formulations, do not incorporate film flow phenomena).…”