The considerable interest in two-dimensional (2D) materials and complex molecular topologies calls for a robust experimental system for single-molecule studies. In this work, we study the equilibrium properties and deformation response of a complex DNA structure called a kinetoplast, a 2D network of thousands of linked rings akin to molecular chainmail. Examined in good solvent conditions, kinetoplasts appear as a wrinkled hemispherical sheet. The conformation of each kinetoplast is dictated by its network topology, giving it a unique shape, which undergoes small-amplitude thermal fluctuations at subsecond timescales, with a wide separation between fluctuation and diffusion timescales. They deform elastically when weakly confined and swell to their equilibrium dimensions when the confinement is released. We hope that, in the same way that linear DNA became a canonical model system on the first investigations of its polymer-like behavior, kinetoplasts can serve that role for 2D and catenated polymer systems.

Knots in DNA occur in biological systems, serve as a model system for polymer entanglement, and affect the efficacy of modern genomics technologies. We study the motion of complex knots in DNA by stretching molecules with a divergent electric field that provides an elongational force. We demonstrate that the motion of knots is nonisotropic and driven towards the closest end of the molecule. We show for the first time experimentally that knots can go from a mobile to a jammed state by varying an applied strain rate, and that this jamming is reversible. We measure the mobility of knots as a function of strain rate, demonstrating the conditions under which knots can be driven towards the ends of the molecule and untied.

We perform single-molecule experiments and simulations to study the swelling of complex knots in linearly extended DNA molecules. We induce self-entanglement of DNA molecules in a microfluidic T-junction using an electrohydrodynamic instability and then stretch the molecules using divergent electric fields. After the chain is fully extended, the knot appears as a region of excess fluorescent brightness, and we shut off the field and observe the knot swelling over time. We find (1) the knot topologies created by the instability are more complex than what is expected from equilibrium simulations of knot formation, (2) the knot swells at a time scale comparable to the end-to-end relaxation of the chain, which indicates that the swelling is dictated by the chain’s global dynamics, and (3) knots are long-lived when the DNA is in the coiled state. These findings demonstrate the rich physics involved in the relaxation of knotted polymers which has not been examined heretofore.

The entanglement of ring polymers remains mysterious in many aspects. In this Letter, we use electric fields to induce self-entanglements in circular DNA molecules, which serve as a minimal system for studying chain entanglements. We show that self-threadings give rise to entanglements in ring polymers and can slow down polymer dynamics significantly. We find that strongly entangled circular molecules remain kinetically arrested in a compact state for very long times, thereby providing experimental evidence for the severe topological constraints imposed by threadings.

We report theoretical and experimental studies to describe buoyancy-driven fluid drainage from a porous medium for configurations where the fluid drains from an edge. We first study homogeneous porous systems. To investigate the influence of heterogeneities, we consider the case where the permeability varies transverse to the flow direction, exemplified by a V-shaped Hele-Shaw cell. Finally, we analyse a model where both the permeability and the porosity vary transverse to the flow direction. In each case, a self-similar solution for the shape of these gravity currents is found and a power-law behaviour in time is derived for the mass remaining in the system. Laboratory experiments are conducted in homogeneous and V-shaped Hele-Shaw cells, and the measured profile shapes and the mass remaining in the cells agree well with our model predictions. Our study provides new insights into drainage processes such as may occur in a variety of natural and industrial activities, including the geological storage of carbon dioxide.

We perform single-molecule DNA experiments to investigate the relaxation dynamics of knotted polymers and examine the steady-state behavior of knotted polymers in elongational fields. The occurrence of a knot reduces the relaxation time of a molecule and leads to a shift in the molecule's coil-stretch transition to larger strain rates. We measure chain extension and extension fluctuations as a function of strain rate for unknotted and knotted molecules. The curves for knotted molecules can be collapsed onto the unknotted curves by defining an effective Weissenberg number based on the measured knotted relaxation time in the low extension regime, or a relaxation time based on Rouse/Zimm scaling theories in the high extension regime. Because a knot reduces a molecule's relaxation time, we observe that knot untying near the coil-stretch transition can result in dramatic changes in the molecule's conformation. For example, a knotted molecule at a given strain rate can experience a stretch-coil transition, followed by a coil-stretch transition, after the knot partially or fully unties.

Knotting is a prevalent phenomenon which occurs in long polymer chains. We perform Brownian dynamics simulations and single-molecule DNA experiments to investigate knot untying in elongational fields that is induced by the knot being convected off the chain. The change in knot size as the knot moves off the chain and unties causes a change in the effective Weissenberg number, which in turn leads to a change in chain extension. Large-scale chain conformational changes are observed in both simulations and experiments for complex knots at low Weissenberg numbers (Wi). We investigate the knot untying time and untying-induced change in extension for a range of knot types and field strengths. Simulations predict a quadratic relationship between the change in extension due to knot untying and initial knot size for Wi ≥ 1.5. Due to the changes in chain extension as a knot unties, the untying process can be diffusion- or convection-driven.

We characterize the different morphologies adopted by a drop of liquid placed on two randomly oriented fibers, which is a first step toward understanding the wetting of fibrous networks. The present work reviews previous modeling for parallel and touching crossed fibers and extends it to an arbitrary orientation of the fibers characterized by the tilting angle and the minimum spacing distance. Depending on the volume of liquid, the spacing distance between fibers and the angle between the fibers, we highlight that the liquid can adopt three different equilibrium morphologies: 1) a column morphology in which the liquid spreads between the fibers, 2) a mixed morphology where a drop grows at one end of the column or 3) a single drop located at the node. We capture the different morphologies observed using an analytical model that predicts the equilibrium configuration of the liquid based on the geometry of the fibers and the volume of liquid.