Drops on lubricated polymer brushes and gels
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Abstract
In this thesis, we engage with the physics of drops deposited on polymer brushes and gels that can also be swollen by a lubricant. We discuss results from simulation, theory, and experiment at three different levels: equilibrium, approach towards equilibrium, and steady state dynamics.
At the level of equilibrium, we use Molecular Dynamics (MD) simulations using the Many-body Dissipative Particle Dynamics (MDPD) model. We tune our model to emulate a water drop on a PDMS substrate. To characterize the brush, we find the point where it is saturated with lubricant and the corresponding brush height. In addition, we calculate the surface tension for different lubricant fractions. We show that the contact angle should theoretically be independent of the swelling of the brush. Afterwards, we show that drops deposited on lubricated polymer brushes undergo a cloaking transition, where the drop becomes covered by a film of lubricant. The transition sets in after a particular amount of lubricant is infused in the brush, a result which is supported by a theoretical thermodynamic analysis of the system. For spherical drops on dry brushes we reveal the presence in MDPD of a line tension that promotes the spreading of the drop. On lubricated brushes, the relation is not as transparent, though we do see a dependence of contact angles on the size of the drop. We also find that the brush in the area of the wetting ridge is swollen to a height that is close to the height at saturation, especially after the cloaking transition sets it. We complement our results for spherical drops with an analysis of cylindrical drops to eliminate the effect of line tension. In terms of the cloaking transition the results for both spherical and cylindrical drops are consistent. However, we see opposite behavior for the contact angle as a function of the lubricant fraction in the brush, which is indicative of a possible dependence of line tension on the swelling of the brush.
To study the approach towards equilibrium, our experimental collaborators ran experiments where a glycerol drop was deposited on PDMS gels swollen with high viscosity silicone oils. There, the lubricant separates from the gel so that the wetting ridge has a liquid component. We show that as the ridge grows, it does so in a geometrically similar fashion, maintaining the same shape. The separation height between the apex of the wetting ridge and the gel is followed through time and shown to depend on both the degree of swelling and the viscosity of the oil. We support the experimental findings with a theoretical model based on diffusion, and find that the results agree very well with the experiments for saturated gels, but not so much for undersaturated ones. To follow the approach towards equilibrium in terms of cloaking, we perform experiments where a drop is pending from a swollen gel, and follow the evolution of the shape with time. Unfortunately, few conclusions could be drawn from the experiments due to a lack of reproducibility. In addition, we perform numerical simulations using the MDPD model to follow the cloaking away from equilibrium. We find that the cloak front progresses on the drop linearly with time, with the rate increasing with the fraction of oil. Additionally, the cloak creeps onto the drop as it thickens simultaneously, and continues to get thicker after it covers the entire drop. We also find that the distribution of lubricant throughout the brush is consistent with our assumption that the time scale is set through the diffusion of lubricant across the brush.
Finally, we address the steady state dynamics of drops moving on lubricated polymer brushes. The results of our experimental collaborators for water drops on PDMS brushes reveal an asymptotic power law relation between the dissipated power and the velocity of the drop. Our numerical simulations also show such a power law, albeit with different exponents. The exponent in the experiments is the same for two preparation methods of the brush. Meanwhile, in simulation, the exponent depends weakly on the swelling of the brush. To understand the discrepancy and the dissipation mechanisms that influence the exponent, we quantify the height of the wetting ridge and the flow field inside the drop. The analysis rules out slip as a major contributor to dissipation, but neither viscous dissipation in the drop nor viscoelastic dissipation in the brush can be ruled out at this stage. Instead, we find that the viscoelastic dissipation can remain relevant even at high velocities since the wetting ridge does not vanish at any velocity; in addition, the flow field inside the drop is complex with the possible presence of multiple vortices, and can possibly explain the observed exponents.