Feedback control of photoresponsive fluid interfaces

Abstract

Photoresponsive surfactants provide a unique microfluidic driving mechanism. Since they switch between two molecular shapes under illumination and thereby affect surface tension of fluid interfaces, Marangoni flow along the interface occurs. To describe the dynamics of the surfactant mixture at a planar interface, we formulate diffusion-advection-reaction equations for both surfactant densities. They also include adsorption from and desorption into the neighboring fluids and photoisomerization by light. We then study how the interface responds when illuminated by spots of light. Switching on a single light spot, the density of the switched surfactant spreads in time and assumes an exponentially decaying profile in steady state. Simultaneously, the induced radial Marangoni flow reverses its flow direction from inward to outward. We use this feature to set up specific feedback rules, which couple the advection velocities sensed at the light spots to their intensities. As a result two neighboring spots switch on and off alternately. Extending the feedback rule to light spots arranged on the vertices of regular polygons, we observe periodic switching patterns for even-sided polygons, where two sets of next-nearest neighbors alternate with each other. A triangle and pentagon also show regular oscillations, while heptagon and nonagon exhibit irregular oscillations due to frustration. While our findings are specific to the chosen set of parameters, they show how complex patterns at photoresponsive fluid interfaces emerge from simple feedback coupling.

Spatial organization of active particles with field-mediated interactions

“…The homogeneous and stationary solution to Eqs. (19), (20), (21) is characterized by the following values of the fields…”

“…We set ρ 1 = ρ − ρ h , ψ 1 = ψ − ψ h and φ 1 = φ − φ h and we expand Eqs. (19), (20), (21) to linear order in the ρ 1 , φ 1 , ψ 1 fields. We expand the fields in Fourier modes ∼ e ik·x and we arrive at a linear system for the Fourier components with k = k .…”

“…The functions ρ n , ψ n and φ n are expected to be products of slow dynamics envelopes and fast growing patterns. These considerations allow us to write differential operators with the chain rule, namely, (20), (21) to successive orders to get a closed set of equations. In the canonical case of the Swift-Hohenberg equation [32,33], the closed relation for the lowest order amplitude is obtained to order O(ε 3 ).…”

“…From the evolution equations of the fields, we compute φ × ∂ t ψ + ψ × ∂ t φ (where ∂ t ψ is given in Eq. (20) and ∂ t φ is given in Eq. (21)) to reconstruct a time derivative of a correlation, which is 0 in steady state.…”

Steering droplets on substrates using moving steps in wettability

“…These experiments essentially demonstrated an early use of structured light to create motion on the micron scale, an approach which has recently become the focus of intense research. [3][4][5] Light-driven fluid motion [6][7][8][9][10] is an especially favorable control mechanism because of its high precision and controllability through the established experimental methods in optics. 11 Notably, it can be used in combination with or as an alternative to electrowetting techniques.…”