Liquid mixing and sculpting using light-actuated photosurfactants

This study utilises chromocapillary stresses induced by light-actuated photosurfactants to demonstrate theoretically that a stable uniform liquid layer wetting a substrate can be sculpted and stirred on the microscale. A mathematical model is presented for two photosurfactant species that can switch from trans to cis states. Switching takes place in the bulk and on the interface, and convection–diffusion–reaction equations describe the local concentrations there. Under uniform light illumination (e.g. blue light) the equilibrium concentrations of trans and cis are non-uniform with layer depth, and a quiescent state with a flat interface exists. A non-uniform light intensity along the layer is superimposed to drive the system out of equilibrium, and induce interfacial deformations and flow in the bulk. This is carried out asymptotically for small-intensity non-uniformities and the first-order non-uniform solutions are found in semi-analytic form. The solutions show that a local increase in intensity increases the surface tension locally by sweeping surfactant off the interface to generate an inward trapping flow (known as a ‘Marangoni tweezer’ in experiments). Light intensities with a sinusoidal variation along the interface are also considered to show that vortical mixing motions are set up. Additionally, the liquid sculpting problem is analysed and a class of inverse problems are solved to predict the distribution of the light intensity required to produce a desired target interfacial shape. Finally, a parametric study is carried out to evaluate the effect of Biot, Damköhler and Marangoni numbers on the maximum light-induced interfacial velocity.