arXiv subjects

Thomas Appleford

Publications and source records attributed to Thomas Appleford.

3 recordsLinked to original sources

arXiv2026

Droplet Deformation and Emulsion Rheology in Two-Dimensional Odd Stokes Flow

We study the deformation of a two-dimensional viscous droplet in simple shear in the presence of odd viscosity. We derive an analytical solution for the droplet shape and surrounding flow field within the framework of odd Stokes flow, allowing for differences in both even and odd viscosity between the droplet and the surrounding fluid. This solution yields closed-form expressions for the macroscopic apparent even and odd viscosities of a dilute emulsion. We show that, provided all viscosity differences remain moderate, the steady-state Taylor deformation parameter satisfies $D_T^\infty = \text{Ca} + \mathcal{O}(\text{Ca}^2)$ so that the leading-order droplet deformation is unchanged from the classical (even-viscous) result. Nevertheless, pronounced effects emerges beyond leading order, where our direct numerical simulations reveal odd-viscous differences to the droplet deformation. In addition, we show that the flow is influenced only by the difference in odd viscosity between the droplet and the medium and not on their individual values. Our analysis clarifies how odd viscosity might modify the effective rheology of dilute emulsions and provides a framework for interpreting droplet-based measurements of odd-viscous response. Key words: odd viscosity $|$ droplets $|$ emulsions $|$ surface tension $|$ chiral fluids

cond-mat.soft↗

arXiv2026

Biogenic bubbles enable microbial escape from physical confinement

Immotile microbes inhabit nearly every environment on Earth, from soils and sediments to food matrices -- yet how they disperse through these physically confining environments is poorly understood. Here, we show that immotile microbial colonies confined in a model transparent yield-stress matrix can achieve long-range dispersal by harnessing their own metabolism. Using yeast as a model organism, we find that fermentation drives dissolved CO$_2$ to supersaturation, nucleating biogenic bubbles that grow, yield the matrix, and rise, hydrodynamically entraining cells vertically in their wake. Sequential bubble nucleation sculpts persistent columnar colonies extending far beyond what growth alone permits. Multiple colonies interact via their fermentation byproducts, merging and mixing genetically as they collectively sculpt self-sustaining conduit networks. Our findings reveal a third mode of microbial dispersal, distinct from the canonical mechanisms of motility and growth, with implications for ecology, environmental science, and biotechnology. More broadly, they exemplify a previously unrecognized class of active behavior -- Metabolically Driven Active Matter -- in which metabolic byproducts reshape the physical landscape of confinement to drive population-scale motion.

physics.bio-ph↗

arXiv2025

Rheology of Two-Dimensional Dilute Emulsions

The single droplet under shear is a foundational problem in fluid mechanics. In computational fluid dynamics, the two-dimensional (2D) formulation offers advantages in both computational efficiency and relevance, yet its theoretical treatment remains relatively underdeveloped. In this brief note, we present an analytical treatment of this problem, beginning with a derivation of the Lamb solution for 2D Stokes flows, which in turn is used to obtain the flow fields around a droplet in a purely extensional flow. Using these flow fields, expressions are obtained for the apparent viscosity, $\mu^*$, of a dilute emulsion as well as a small deformation theory. We show that $\mu^* = \mu( 1 + f(\lambda) \phi) + \mathcal{O}(\phi^2)$ with $f(\lambda) = (2\lambda + 1)/(\lambda + 1)$ where $\lambda$ is the ratio of the droplet viscosity to the matrix viscosity and $\phi$ is the area fraction covered by the suspended phase. Also the steady state value of the Taylor deformation parameter $D_T^\infty$, in the capillarity-dominated regime, obeys $D_T^\infty = g(\lambda)\,\text{Ca}$, where Ca is the capillary number and $g(\lambda) = 1$. This contrasts with the 3D case, where $g(\lambda)$ depends on $\lambda$. These results are then validated through direct numerical simulations across a wide range of viscosity ratios ($0.01 < \lambda < 100$). Our results provide a basic theoretical framework for interpreting 2D droplet simulations and provide clear benchmarks for computational fluid dynamics.

physics.flu-dyn↗