arXiv subjects

Michael Rennick

Publications and source records attributed to Michael Rennick.

4 recordsLinked to original sources

arXiv2026

N-Component Free Energy Lattice Boltzmann Method with Reduction Consistency and Global Momentum Conservation

We present a free energy lattice Boltzmann model capable of simulating fluid systems with an arbitrary number of immiscible components in principle. Our method is strictly reduction consistent, ensuring that absent fluid components do not spontaneously nucleate. We introduce a novel discretization of the surface tension force that globally conserves momentum to machine precision, and we enforce reduction consistency through a flux correction that is independent of the mobility. The method is benchmarked with a range of static and dynamic problems, including: liquid lenses, Janus droplets, quaternary phase separation, and six-component layered Poiseuille flow, and we obtain excellent agreement with theoretical predictions throughout. Finally, we demonstrate the applicability of the proposed method through patterned liquid surfaces and microfluidic emulsion droplet generation.

physics.flu-dyn↗

arXiv2025

Topology Controls the Phase Separation Dynamics of Many Component Fluid Mixtures

Fluid mixtures, ranging from the cellular cytoplasm to synthetic DNA nanostar systems, can spontaneously compartmentalize into many ($N$) coexisting liquid phases through liquid-liquid phase separation. While such systems exhibit a remarkable diversity of spatial organizations, the physical principles governing their non-equilibrium dynamics remain poorly understood. Here, combining simulations and analytical theory, we show that the coarsening dynamics of many component phase separation are fundamentally linked to mathematical coloring problems. For planar phase organization, relevant to synthetic droplet monolayers and simple biological structures, we identify distinct topological constraints for $N=2$, $N=3$, and $N=4$, with no further change for $N>4$, consistent with the four-color theorem. These constraints govern the coarsening dynamics, and, using chromatic graph theory, we derive a theoretical model for $N\geq 3$ that quantitatively captures the diffusive-like coarsening. By contrast, classical theories based solely on Ostwald ripening underestimate the observed dynamics. We further show that tuning interfacial tensions modifies the set of admissible phase arrangements, enabling highly heterogeneous coarsening dynamics across different phases. For unconfined systems with nonplanar phase organization, different coloring constraints apply, with no analogue of the four-color theorem, and coalescence suppression emerges only when the number of phases exceeds $N\gtrsim 7$. More broadly, our work establishes coloring theory as a topological framework for understanding and predicting the dynamics of many component phase-separating fluids.

physics.flu-dyn↗

arXiv2025

The Diffuse Solid Method for Wetting and Multiphase Fluid Simulations in Complex Geometries

We develop a diffuse solid method that is versatile and accurate for modeling wetting and multiphase flows in highly complex geometries. In this scheme, we harness N + 1-component phase field models to investigate interface shapes and flow dynamics of N fluid components, and we optimize how to constrain the evolution of the component employed as the solid phase to conform to any pre-defined geometry. Implementations for phase field energy minimization and lattice Boltzmann method are presented. Our approach does not need special treatment for the fluid-solid wetting boundary condition, which makes it simple to implement. To demonstrate its broad applicability, we employ the diffuse solid method to explore wide-ranging examples, including droplet contact angle on a flat surface, particle adsorption on a fluid-fluid interface, critical pressure on micropillars and on Salvinia leaf structures, capillary rise against gravity, Lucas-Washburn's law for capillary filling, and droplet motion on a sinusoidally undulated surface. Our proposed approach can be beneficial to computationally study multiphase fluid interactions with textured solid surfaces that are ubiquitous in nature and engineering applications.

physics.flu-dyn↗

arXiv2022

Three-Dimensional Printed Liquid Diodes with Tunable Velocity: Design Guidelines and Applications for Liquid Collection and Transport

Directional and self-propelled flow in open channels has a variety of applications, including microfluidic and medical devices, industrial filtration processes, fog-harvesting and condensing apparatuses. Here, we present versatile three-dimensional (3D)-printed liquid diodes that enable spontaneous unidirectional flow over long distances for a wide range of liquid contact angles. Typically, we can achieve average flow velocities of several millimeters per second over a distance of tens to hundreds of millimeters. The diodes have two key design principles. First, a sudden widening in the channels' width, in combination with a small bump, the pitch, ensure pinning of the liquid in the backward direction. Second, an adjustable reservoir, the bulga, is introduced to manipulate the liquid velocity with differing expansion angles. Using a combination of experiments and lattice Boltzmann simulations, we provide a comprehensive analysis of the flow behavior and speed within the channels with varying contact angles (CA), pitch heights and bulga angles. This provides guidelines for the fabrication of bespoke liquid diodes with optimal design for their potential applications. As a feasibility investigation, we test our design for condensation of water from fog and subsequent transport uphill.

physics.flu-dyn↗