# Energy invariance in capillary systems

## TL;DR

This paper explores the invariance of capillary surface energy during boundary reconfiguration, combining theoretical analysis and experiments to demonstrate minimal dissipative losses under certain conditions, enabling low-energy liquid manipulation.

## Contribution

It introduces a theoretical framework for energy-invariant equilibria of capillary surfaces with arbitrary boundaries and experimentally verifies minimal energy dissipation during boundary reconfiguration.

## Key findings

- Energy invariance holds during boundary reconfiguration with low dissipation.
- Lubricant-impregnated surfaces eliminate contact-angle hysteresis.
- Dissipative losses are small if actuation is slow compared to relaxation times.

## Abstract

We demonstrate the continuous translational invariance of the energy of a capillary surface in contact with reconfigurable solid boundaries. We present a theoretical approach to find the energy-invariant equilibria of spherical capillary surfaces in contact with solid boundaries of arbitrary shape and examine the implications of dynamic frictional forces upon a reconfiguration of the boundaries. Experimentally, we realise our ideas by manipulating the position of a droplet in a wedge geometry using lubricant-impregnated solid surfaces, which eliminate the contact-angle hysteresis and provide a test bed for quantifying dissipative losses out of equilibrium. Our experiments show that dissipative energy losses for an otherwise energy-invariant reconfiguration are relatively small, provided that the actuation timescale is longer than the typical relaxation timescale of the capillary surface. We discuss the wider applicability of our ideas as a pathway for liquid manipulation at no potential energy cost in low-pinning, low-friction situations.