Capillary Displacement of Viscous Liquids

Abstract

When a capillary tube is brought into contact with a wetting liquid, surface tension forces overcome gravity and the liquid spontaneously rises into the tube until an equilibrium height is reached. The early viscous dynamics of the rise typically follow the well-known Lucas-Washburn law, which is independent of gravity and neglects the displaced fluid. Here we explore the early viscous dynamics when the properties of displaced fluid are significant. Using a combination of experiments and theory, we show how the characteristic behavior of the Lucas-Washburn law is modified when the viscosity of the displaced fluid is comparable to or exceeds the wetting fluid. Additionally, we find that the effects of gravity reshape the dynamics of the capillary rise not only in the late viscous regime but also in the early viscous regime.

Spontaneous imbibition in a microchannel: analytical solution and assessment of volume of fluid formulations

“…Balancing the forces in the absence of gravity, negligible inertia and assuming w ≫ n , they obtained that the position of the meniscus, x m advances as x m ∝ √ t . The model was recently expanded to account for the viscosity of the defending gas phase in a long tube (Hultmark et al 2011), for any viscosity ratio in a vertical capillary (Walls et al 2016) and for arbitrary cross-sectioned microchannels (Berthier et al 2015). Here, we consider horizontal displacement of the meniscus with a partial slip boundary in a Hele-Shaw cell ( h ≪ w , see Fig.…”

Insight into the pressure-induced displacement mechanism for selecting efficient nanofluids in various capillaries

“…To date, much research efforts have been devoted to optimizing the two-phase displacement process, such as refining the external forces, [7][8][9] changing the composition of capillary surface, [10][11][12] and adjusting the properties of fluids 13 like viscosity and interfacial tension. Among others, adding extra chemicals (surfactant, polymer) can effectively adjust the property of injecting fluids, and meanwhile change the composition of capillary surface with their adsorption, which is thus efficient in regulating two-phase displacement process.…”

Effect of Nanoparticles on Spontaneous Imbibition of Water into Ultraconfined Reservoir Capillary by Molecular Dynamics Simulation

“…where l and t are displacement distance and time, respectively. According to the Lucas-Washburn equation, imbibition dynamics is closely related to important factors of surface tension (γ), liquid viscosity (η), the contact angle of water on the capillary wall (θ) and the radius of the capillary (R) [15][16][17][18][19][20].…”