Droplet Tilings
ABSTRACT
Geometry in materials is a key concept which can determine material behavior in ordering, frustration, and fragmentation. More specifically, the behavior of interacting degrees of freedom subject to arbitrary geometric constraints has the potential to be used for engineering materials with exotic phase behavior. While advances in lithography have allowed for an experimental exploration of geometry on ordering that has no precedent in nature, many of these methods are low throughput or the underlying dynamics remain difficult to observe directly. Here, we introduce an experimental system that enables the study of interacting many-body dynamics by exploiting the physics of multidroplet evaporation subject to two-dimensional spatial constraints. We find that a high-energy initial state of this system settles into frustrated, metastable states with relaxation on two timescales. We understand this process using a minimal dynamical model that simulates the overdamped dynamics of motile droplets by identifying the force exerted on a given droplet as being proportional to the two-dimensional vapor gradients established by its neighbors. Finally, we demonstrate the flexibility of this platform by presenting experimental realizations of droplet−lattice systems representing different spin degrees of freedom and lattice geometries. Our platform enables a rapid and low-cost means to directly visualize dynamics associated with complex many-body systems interacting via long-range interactions. More generally, this platform opens up the rich design space between geometry and interactions for rapid exploration with minimal resources.
BIG QUESTION
“The observation that this behavior exists in an everyday substance like food coloring inspired us to ask a simple a question: how does it work?”
What are marangoni-contracted binary droplets?
Marangoni-contracted binary droplets are a class of fluids composed of a mixture of two well-chosen liquids. When the liquids are miscible and one has a higher surface tension and vapor pressure, they form an active contact angle that allows the droplets to move in the direction of steepest vapor gradients.
How do Marangoni-contracted binary droplets work?
Through a combination of extensive experimentation it was determined that droplets consisting of two miscible components in which one component has both a higher vapor pressure and higher surface tension than the other — such as water and propylene glycol — exhibit a contact angle when deposited on a high-energy surface (clean glass), but rest on a fluid film so do not suffer from contact line pinning. The droplets are stabilized by evaporation-induced surface tension gradients and can move under the influence of tiny forces, including the vapor emitted by neighboring droplets. Surprisingly, it was determined that the force law governing these interactions scales as 1/r^2 - just like gravity, but without the inertia.
Significance
Advances in material fabrication have made it possible to produce materials with an increasing range of geometries, including those with no precedent in nature. However, the relationships between geometry and state or the dynamics governing transitions between states in condensed material systems are not well understood and remain difficult to observe. Here, we use evaporating liquid droplets with a capacity for motion in response to long-range vapor-mediated interactions to create a new class of condensed matter system. The role of long-range interactions is understood by developing a simple, numerical model. A key feature of this system is the ability to rapidly fabricate nearly any 2D pattern and observe the motion of interacting elements at the macroscale.
Project Status
Ongoing work in the lab is currently exploring the use of binary droplets as bench scale system for asking fundamental questions related to many-body dynamics.
