Symmetry of small clusters of levitating water droplets

Observation of a chemical reaction in a levitating microdroplet cluster and droplet-generated music

Ordered clusters of water droplets levitating over a heated water surface can be used as chemical microreactors and computational devices. Here we show that a chemical reaction between melamine and cyanuric acid can occur during coalescence of pairs of droplets containing these reagents and lead to the sedimentation of the product, crystals of melamine cyanurate. In rotating droplets, the crystals flash with frequencies dependent mostly on the rotational velocity of the droplets defined by the rotor of the velocity field of the air-vapor flow above the heated water surface. With the Machine Learning (ML) approach, we trace the brightness and frequencies of individual crystals and convert the frequencies into musical notes thus making a "micro-orchestra" of the levitation cluster.

Inversion of Stabilized Large Droplet Clusters

We investigate the spontaneous rearrangement of microdroplets in a self-assembled droplet cluster levitating over a thin locally heated water layer. The center-to-periphery droplet diameter ratio (the "inversion coefficient") controls the onset of the inversion. Larger droplets can squeeze between smaller ones due to increased drag force on them from the air-vapor flow. In smaller clusters, the rotation of the droplets plays an important role since larger droplets rotating with the same angular velocity (dependent on the rotor of the airflow field) have higher viscous friction force with the liquid layer. It is desirable to avoid cluster inversion in experiments where individual droplet positions should be traced.

Branched droplet clusters and the Kramers theorem

Scaling laws inherent for polymer molecules are checked for the linear and branched chains constituting two-dimensional (2D) levitating microdroplet clusters condensed above the locally heated layer of water. We demonstrate that the dimensionless averaged end-to-end distance of the droplet chain r[over ¯] normalized by the averaged distance between centers of the adjacent droplets l[over ¯] scales as r[over ¯]/l[over ¯]∼n^{0.76}, where n is the number of links in the chain, which is close to the power exponent ¾, predicted for 2D polymer chains with excluded volume in the dilution limit. The values of the dimensionless Kuhn length b[over ̃]≅2.12±0.015 and of the averaged absolute value of the bond angle of the droplet chains |θ|[over ¯]=22.0±0.5^{0} are determined. Using these values we demonstrate that the predictions of the Kramers theorem for the gyration radius of branched polymers are valid also for the branched droplets' chains. We discuss physical interactions that explain both the high value of the power exponent and the applicability of the Kramers theorem including the effects of the excluded volume, surrounding droplet monomers, and the prohibition of extreme values of the bond angle.

Levitation conditions for condensing droplets over heated liquid surfaces

We report experimental studies and develop mathematical models of levitation of microscale droplets over an evaporating liquid layer. The maximum size of droplets is estimated from the balance between gravity and Stokes force due to the action of upward Stefan flow generated by evaporation. Mathematical models of diffusion around levitating droplets allow us to determine Stefan flow velocity at the liquid layer surface. These results are then used to determine the dependence of levitation height on droplet size. Experimental data for a range of conditions are shown to collapse onto a single curve predicted from the model.

Scaling in Colloidal and Biological Networks

Scaling and dimensional analysis is applied to networks that describe various physical systems. Some of these networks possess fractal, scale-free, and small-world properties. The amount of information contained in a network is found by calculating its Shannon entropy. First, we consider networks arising from granular and colloidal systems (small colloidal and droplet clusters) due to pairwise interaction between the particles. Many networks found in colloidal science possess self-organizing properties due to the effect of percolation and/or self-organized criticality. Then, we discuss the allometric laws in branching vascular networks, artificial neural networks, cortical neural networks, as well as immune networks, which serve as a source of inspiration for both surface engineering and information technology. Scaling relationships in complex networks of neurons, which are organized in the neocortex in a hierarchical manner, suggest that the characteristic time constant is independent of brain size when interspecies comparison is conducted. The information content, scaling, dimensional, and topological properties of these networks are discussed.