Lattice Boltzmann Modelling of Droplet Dynamics on Fibres and Meshed Surfaces

Abstract

Fibres and fibrous materials are ubiquitous in nature and industry, and their interactions with liquid droplets are often key for their use and functions. These structures can be employed as-is or combined to construct more complex mesh structures. Therefore, to optimise the effectiveness of these structures, the study of the wetting interactions between droplets and solids is essential. In this work, I use the numerical solver lattice Boltzmann method (LBM) to systematically study three different cases of droplet wetting, spreading, and moving across fibres, and droplets impacting mesh structures.

First, I focus on partially wetting droplets moving along a fibre. For the so-called clamshell morphology, I find three possible dynamic regimes upon varying the droplet Bond number and the fibre radius: compact, breakup, and oscillation. For small Bond numbers, in the compact regime, the droplet reaches a steady state, and its velocity scales linearly with the driving body force. For higher Bond numbers, in the breakup regime, satellite droplets are formed trailing the initial moving droplet, which is easier with smaller fibre radii. Finally, in the oscillation regime (favoured in the midrange of fibre radius), the droplet shape periodically extends and contracts along the fibre.

Outside of the commonly known fully wetting and partial wetting states, there exists the pseudo-partial wetting state (where both the spherical cap and the thin film can coexist together), which few numerical methods are able to simulate. I implement long-range interactions between the fluid and solid in LBM to realise this wetting state. The robustness of this approach is shown by simulating a number of scenarios. I start by simulating droplets in fully, partial, and pseudo-partial wetting states on flat surfaces, followed by pseudo-partially wetting droplets spreading on grooved surfaces and fibre structures. I also explore the effects of key parameters in long-range interactions. For the dynamics demonstration, I simulate droplets in the pseudo-partial wetting state moving along a fibre in both the barrel and clamshell morphologies at different droplet volumes and fibre radii.

Finally, I focus on the dynamics of droplets impacting square mesh structures. I systematically vary the impact point, trajectory, and velocity. To rationalise the results, I find it useful to consider whether the droplet trajectory is dominated by orthogonal or diagonal movement. The former leads to a lower incident rate and a more uniform interaction time distribution, while the latter is typically characterised by more complex droplet trajectories with less predictability. Then, focussing on an impact point, I compare the droplet dynamics impacting a single-layer structure and equivalent double-layer structures. From a water-capturing capability perspective (given the same effective pore size), a double-layer structure performs slightly worse. A double-layer structure also generally leads to shorter interaction time compared to a single-layer structure.