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Register a new userFront pinning in capillary filling of chemically coated channels
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The dynamics of capillary filling in the presence of chemically coated heterogeneous boundaries is investigated, both theoretically and numerically. In particular, by mapping the equations of front motion onto the dynamics of a dissipative driven oscillator, an analytical criterion for front pinning is derived, under the condition of diluteness of the coating spots. The criterion is tested against two dimensional Lattice Boltzmann simulations, and found to provide satisfactory agreement as long as the width of the front interface remains much thinner than the typical heterogeneity scale of the chemical coating.
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The motion of an air-fluid interface through an irregularly coated capillary is studied by analysing the Lucas-Washburn equation with a random capillary force. The pinning probability goes from zero to a maximum value, as the interface slows down. Under a critical velocity, the distribution of waiting times $tau$ displays a power-law tail $sim tau^{-2}$ which corresponds to a strongly intermittent dynamics, also observed in experiments. We elaborate a procedure to predict quantities of experimental interest, such as the average interface trajectory and the distribution of pinning lengths.
We show how the capillary filling of microchannels is affected by posts or ridges on the sides of the channels. Ridges perpendicular to the flow direction introduce contact line pinning which slows, or sometimes prevents, filling; whereas ridges parallel to the flow provide extra surface which may enhances filling. Patterning the microchannel surface with square posts has little effect on the ability of a channel to fill for equilibrium contact angle $theta_e lesssim 30^{mathrm{o}}$. For $theta_e gtrsim 60^{mathrm{o}}$, however, even a small number of posts can pin the advancing liquid front.
When a very thin capillary is inserted into a liquid, the liquid is sucked into it: this imbibition process is controlled by a balance of capillary and drag forces, which are hard to quantify experimentally, in particularly considering flow on the nanoscale. By computer experiments using a generic coarse-grained model, it is shown that an analysis of imbibition forced by a controllable external pressure quantifies relevant physical parameter such as the Laplace pressure, Darcys permeability, effective pore radius, effective viscosity, dynamic contact angle and slip length of the fluid flowing into the pore. In determining all these parameters independently, the consistency of our analysis of such forced imbibition processes is demonstrated.
We study the impact of wall corrugations in microchannels on the process of capillary filling by means of three broadly used methods - Computational Fluid Dynamics (CFD), Lattice-Boltzmann Equations (LBE) and Molecular Dynamics (MD). The numerical results of these approaches are compared and tested against the Concus-Finn (CF) criterion, which predicts pinning of the contact line at rectangular ridges perpendicular to flow for contact angles theta > 45. While for theta = 30, theta = 40 (no flow) and theta = 60 (flow) all methods are found to produce data consistent with the CF criterion, at theta = 50 the numerical experiments provide different results. Whilst pinning of the liquid front is observed both in the LB and CFD simulations, MD simulations show that molecular fluctuations allow front propagation even above the critical value predicted by the deterministic CF criterion, thereby introducing a sensitivity to the obstacle heigth.
Capillary phenomena are involved in many industrial processes, especially those dealing with composite manufacturing. However, their modelling is still challenging. Therefore, a finite element setting is proposed to better investigate this complex issue. The variational formulation of a liquid-air Stokes system is established, while the solid substrate is described through boundary conditions. Expressing the weak form of Laplaces law over liquid-air, liquid-solid and air-solid interfaces, leads to a natural enforcement of the mechanical equilibrium over the wetting line, without imposing explicitly the contact angle itself. The mechanical problem is discretized by using finite elements, linear both in velocity and pressure, stabilized with a variational multiscale method, including the possibility of enrichment of the pressure space. The moving interface is captured by a Level-Set methodology, combined with a mesh adaptation technique with respect to both pressure and level-set fields. Our methodology can simulate capillary-driven flows in 2D and 3D with the desired precision: droplet spreading, droplet coalescence, capillary rise. In each case, the equilibrium state expected in terms of velocity, pressure and contact angle is reached.
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