| Summary: | <p>A small amount of liquid trapped between two solid surfaces can pull them together because of the effects of surface tension. This effect is called capillary adhesion, and is thought to be important in many small-scale scenarios, including helping insects to adhere. In this thesis, we study aspects of capillary adhesion using mathematical modelling.</p>
<p>We begin by considering whether the forces generated through capillary adhesion with a fixed volume of liquid can be enhanced by splitting a liquid bridge into many smaller bridges. By carefully calculating the bridge shape (and when bridges can span a given gap), capillary adhesion of rough surfaces is shown to be significantly enhanced compared to smooth surfaces. It is also shown that roughness may lead to a steady-state resistance to shear, which is compared quantitatively to experiments in insects.</p>
<p>Next, we turn to study solid-solid contact in the presence of capillary adhesion. Equilibria are found for impermeable and permeable elastic spheres in contact with a flat, rigid substrate. When saturated, a porous sphere can naturally secrete its own adhering liquid as its pore space is compressed by deformation. Numerical results and scaling laws are found to describe the equilibria with and without an applied force; results without a force are compared to experiments on hydrogel beads in contact.</p>
<p>We then investigate in more detail the effect of surface deformation on capillary adhesion through a model of a thin membrane under tension. Calculating the equilibrium adhesion forces shows that an increase in adhesion of more than an order of magnitude can be achieved compared to a comparable undeformable system; this is supported by experimental results. The dynamics of adhesion are investigated via a lubrication model. The slow drainage of a liquid-filled dimple explains why adhesion may not always be achieved in practice unless sufficient time is allowed to adhere. We also investigate how the deformability may be exploited to detach in a controllable manner.</p>
<p>Finally, we study how detachment occurs using a dynamic two-dimensional model of a loaded plate attached to a rigid substrate by a liquid bridge. Using a linear stability analysis, the motion of the plate is shown to decouple into two modes — separation and tilting — with the tilting mode growing fastest. As the plate tilts it may contact the substrate, depending on the width of the plate. We characterize how plate width and initial condition may determine whether a plate ultimately detaches or adheres and show that tilting may lead to anomalous detachment: plates that should stick, detach.</p>
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