Coupled oscillations in a 1D emulsion of Belousov–Zhabotinsky droplets

Abstract

We experimentally and computationally study the dynamics of interacting oscillating Belousov-Zhabotinsky (BZ) droplets of $120 mm diameter separated by perfluorinated oil and arranged in a onedimensional array (1D). The coupling between BZ droplets is dominated by inhibition and is strongest at low concentrations of malonic acid (MA) and small droplet separations. A microfluidic chip is used for mixing the BZ reactants, forming monodisperse droplets by flow-focusing and directing them into a hydrophobized 100 mm diameter capillary. For samples composed of many drops and in the absence of well defined initial conditions, the anti-phase attractor, in which adjacent droplets oscillate 180 outof-phase, is observed for strong coupling. When the coupling strength is reduced the initial transients in the phase difference between neighboring droplets persist until the BZ reactants are exhausted. In order to make quantitative comparison with theory, we use photosensitive Ru(bipy) 3 2+ -catalyzed BZ droplets and set both boundary and initial conditions of arrays of small numbers of oscillating BZ droplets with a programmable illumination source. In these small collections of droplets, transient patterns decay rapidly and we observe several more complex attractors, including ones in which some adjacent droplets are in-phase. Excellent agreement between experiment and numerical simulations is achieved.

Testing Turing’s theory of morphogenesis in chemical cells

“…Because the system is closed and the BZ reactants are not replenished, the reaction lasts no more than about 100 oscillations until the final uniform equilibrium state is approached. However, the system evolves sufficiently slowly that it can adiabatically exhibit the dynamical instabilities predicted by Turing for open systems (17,18,23). Stationary Turing patterns have been notoriously difficult to produce experimentally, primarily because, for the activatorinhibitor dynamics that typically provides the necessary feedback, the inhibitor must diffuse significantly more rapidly than the activator (6).…”

“…The transport of the micelles is much slower than the transport of bromine; hence, the criterion for the stationary Turing instability is met. The distinction between the micelles used previously (24,25) and the emulsions we study here (17,18) is that the micelles are in dynamic equilibrium; they merge and split on a timescale much shorter than the period of a BZ oscillation and a length scale much shorter than the wavelength of the chemical wave. Therefore, on the timescale and length scale appropriate for a continuum description of the reaction-diffusion system, the BZ microemulsion can be considered to be homogeneous in composition.…”

“…We report an experimental reaction-diffusion system ideally suited for testing Turing's ideas in synthetic "cells" consisting of microfluidically produced surfactant-stabilized emulsions (17,18) in which aqueous droplets containing the Belousov-Zhabotinsky (BZ) oscillatory chemical reactants (19) are dispersed in oil. In contrast to biology, here the chemistry is understood, rate constants are known, and interdrop coupling is purely diffusive.…”

“…1 and Fig. S1) consists of a monodisperse emulsion of drops of aqueous BZ solution, whose diameter ranges from 20 to 200 μm dispersed in a continuous phase of oil (17,18). The drops are surfactant-stabilized to prevent coalescence (22) (SI Methods).…”

Towards heterotic computing with droplets in a fully automated droplet-maker platform

“…However, one grand aim is to exploit the computational potential of molecules from parallel assemblies, to interacting ensembles, down to the individual molecule without direct addressing. While most 'conventional' implementations are mostly done in a bulk solution, water-in-oil (W/O) droplets have been increasingly used to compartmentalize the BZ reaction in recent years [6][7][8]. Such compartmentalized chemistry has also been employed to implement chemical computers: Tompkins et al [9] used W/O droplets encapsulating the BZ reaction to test Turing's theory of chemical morphogenesis.…”