Alexandros Fragkopoulos

Biofilm formation in geometries with different surface curvature and oxygen availability

Bacteria in the natural environment exist as interface-associated colonies known as biofilms . Complex mechanisms are often involved in biofilm formation and development. Despite the understanding of the molecular mechanisms involved in biofilm formation, it remains unclear how physical effects in standing cultures influence biofilm development. The topology of the solid interface has been suggested as one of the physical cues influencing bacteria-surface interactions and biofilm development. Using the model organism Bacillus subtilis, we study the transformation of swimming bacteria in liquid culture into robust biofilms in a range of confinement geometries (planar, spherical and toroidal) and interfaces (air/water, silicone/water, and silicone elastomer/water). We find that B. subtilis form submerged biofilms at both solid and liquid interfaces in addition to air-water pellicles. When confined, bacteria grow on curved surfaces of both positive and negative Gaussian curvature. However, the confinement geometry does affect the resulting biofilm roughness and relative coverage. We also find that the biofilm location is governed by oxygen availability as well as by gravitational effects; these compete with each other in some situations. Overall, our results demonstrate that confinement geometry is an effective way to control oxygen availability and subsequently biofilm growth.

Dynamic assembly of ultrasoft colloidal networks enables cell invasion within restrictive fibrillar polymers

Significance Decoupling stiffness, pore size, and cell infiltration is a critical hurdle in biomaterials design. Here, by adding ultrasoft colloidal hydrogels to polymerizing fibrin, the particles are driven into a percolated three-dimensional tunnel-like structure throughout the fibrin network. The colloidal particles remain embedded, in stark contrast to the fate of a sacrificial porogen. Yet, cells use the long-time flow behavior of the colloidal network within the tunnels to migrate. Importantly, the colloidal volume fraction, ϕ, defines the critical physical dimensions of the network, which can thus be tuned. Additionally, the stiffness of the constituent particles affects the viscous flow of the colloidal network, affecting cell migration rates. This simplistic approach makes its potential applicability in clinical settings highly tractable. In regenerative medicine, natural protein-based polymers offer enhanced endogenous bioactivity and potential for seamless integration with tissue, yet form weak hydrogels that lack the physical robustness required for surgical manipulation, making them difficult to apply in practice. The use of higher concentrations of protein, exogenous cross-linkers, and blending synthetic polymers has all been applied to form more mechanically robust networks. Each relies on generating a smaller network mesh size, which increases the elastic modulus and robustness, but critically inhibits cell spreading and migration, hampering tissue regeneration. Here we report two unique observations; first, that colloidal suspensions, at sufficiently high volume fraction (ϕ), dynamically assemble into a fully percolated 3D network within high-concentration protein polymers. Second, cells appear capable of leveraging these unique domains for highly efficient cell migration throughout the composite construct. In contrast to porogens, the particles in our system remain embedded within the bulk polymer, creating a network of particle-filled tunnels. Whereas this would normally physically restrict cell motility, when the particulate network is created using ultralow cross-linked microgels, the colloidal suspension displays viscous behavior on the same timescale as cell spreading and migration and thus enables efficient cell infiltration of the construct through the colloidal-filled tunnels.

Shrinking instability of toroidal droplets

Significance Liquid doughnuts or tori exhibit an inherent instability consisting in the shrinking of their “hole.” For sufficiently thick tori, this behavior is the only route for the torus to become spherical and thus minimize the area for a given volume. Of note, this shrinking instability is not completely understood. In this work, we experimentally determine the flow field of toroidal droplets as they shrink and account for our observations by solving the relevant equations of motion in toroidal coordinates. We find that four modes, out of the many possible ones, are needed to successfully account for all of the relevant features in the experiment. These results highlight the rich fluid mechanics that results in the presence of interfaces with nonconstant mean curvature. Toroidal droplets are inherently unstable due to surface tension. They can break up, similar to cylindrical jets, but also exhibit a shrinking instability, which is inherent to the toroidal shape. We investigate the evolution of shrinking toroidal droplets using particle image velocimetry. We obtain the flow field inside the droplets and show that as the torus evolves, its cross-section significantly deviates from circular. We then use the experimentally obtained velocities at the torus interface to theoretically reconstruct the internal flow field. Our calculation correctly describes the experimental results and elucidates the role of those modes that, among the many possible ones, are required to capture all of the relevant experimental features.

Toroidal-droplet instabilities in the presence of charge

Neutral toroidal droplets can break via the surface-tension-driven Rayleigh-Plateau instability. They can additionally exhibit a shrinking instability, which is also driven by surface tension, whereby the handle progressively disappears. We find that charging a toroidal droplet can qualitatively change the behavior and cause the droplet to expand. We successfully model the transition from shrinking to expanding, considering the pressure balance across the interface of the torus. However, despite the change in behavior, charged toroidal droplets end up breaking into spherical droplets. We quantify how the wavelength of the fastest unstable mode associated to this breakup depends on the applied voltage and compare the results with theoretical expectations for charged cylindrical jets.

Charge-Induced Saffman-Taylor Instabilities in Toroidal Droplets

We show that charged toroidal droplets can develop fingerlike structures as they expand due to Saffman-Taylor instabilities. While these are commonly observed in quasi-two-dimensional geometries when a fluid displaces another fluid of higher viscosity, we show that the toroidal confinement breaks the symmetry of the problem, effectively making it quasi-two-dimensional and enabling the instability to develop in this three-dimensional situation. We control the expansion speed of the torus with the imposed electric stress and show that fingers are observed provided the characteristic time scale associated with this instability is smaller than the characteristic time scale associated with Rayleigh-Plateau break-up. We confirm our interpretation of the results by showing that the number of fingers is consistent with expectations from linear stability analysis in radial Hele-Shaw cells.

Teaching Rayleigh–Plateau instabilities in the laboratory

The breakup of a liquid jet into spherical droplets via the Rayleigh–Plateau instability is a common and fundamental part of fluid mechanics. However, teaching this instability in a laboratory setting is challenging, requiring sophisticated methods to generate and study the jet dynamics. Recently, toroidal droplets were shown to break into one or more spherical droplets in the thin-drop limit via the Rayleigh–Plateau instability. We propose a simple experimental setup to generate toroidal droplets that break up on the order of tens of seconds, allowing for easy video capture using a basic CCD camera. With this setup, it is possible to quantify the Rayleigh–Plateau instability in a pedagogical laboratory setting. In addition, the role of curvature on jet breakup can be explored using thick toroidal droplets. We envision this setup as a powerful teaching tool for one of the most fundamental fluid dynamics processes.