arXiv subjects

Howard A. Stone

Publications and source records attributed to Howard A. Stone.

At least 19 recordsLinked to original sources

arXiv2026

The effects of surfactant solubility on inertial Marangoni flow: theory and numerics

Surface active agents (surfactants) are common contaminants found on most air-liquid interfaces. Surfactants lower the surface tension, and hence surfactant concentration gradients generate surface tension gradients, which leads to flow. A canonical surfactant-induced flow is the outward spreading due to the localised deposition of surfactants onto an otherwise clean liquid interface. Eshima et al. (Phys. Rev. Lett., accepted, 2026) demonstrated experimentally and theoretically, through a late-time similarity solution, that surfactant solubility enhances surfactant-induced flows of air-liquid-air sheets and that soluble surfactant solutions can be mapped onto equivalent insoluble surfactant solutions. Here we extend the work theoretically and numerically, developing a systematic framework for the derivation and analysis of such solutions. The relevant nondimensional parameters are quantitatively defined, and the physically accessible parameter space is wide, which our theory and numerical simulations are able to span. We link the solutions for finitely soluble surfactants to the solutions for the limiting regimes of insoluble and infinitely soluble surfactants, where the latter link only holds transiently: the solution of the infinitely soluble limit appears as an intermediate solution that persists ever longer as solubility increases, before the ultimate late-time solution, which maps onto insoluble surfactants, is obtained.

physics.flu-dyn↗

arXiv2026

Translation of a spherical viscous drop driven by localized forcing in Stokes flow

Localized forcing in the fluid inside or outside a viscous drop can drive drop translation. Using the Lorentz reciprocal theorem, we derive an integral expression for the translational velocity of a spherical Newtonian drop subject to localized force and source distributions in either fluid and to interfacial traction. For a clean drop, we obtain explicit responses to Stokeslets, force dipoles, rotlets, general second force moments, and source dipoles as functions of position, orientation, and viscosity ratio. Interior forcing obeys a finite selection rule: only force moments through second order and the first source moment contribute directly to translation. Exterior forcing can couple to multipoles of all orders and produces distance-dependent responses. Although different enclosed singularities can produce the same drop velocity, resolving their exterior flows in drop-centered spherical Stokes modes provides additional constraints on the underlying forcing. We also distinguish regularized force distributions, governed by prescribed kernel moments, from resolved rigid particles, governed by low-order surface-traction moments and prescribed slip. The framework unifies these representations and shows how exterior-flow measurements provide information beyond drop translation, laying the foundation for constructing squirmer-like viscous drop solutions with controllable far-field behaviors.

physics.flu-dyn↗

arXiv2026

Expansion of a hole in a viscoelastic liquid sheet

Experiments on highly viscous polymeric films show that punctured holes expand exponentially in time, without sustained accumulation of liquid near the rim. This response departs from the Taylor--Culick description, in which displaced liquid accumulates in a growing rim that moves at constant speed. Although these differences were initially attributed to viscoelasticity, they were later rationalized using a purely viscous theory, leaving the role of viscoelastic stresses unresolved. We analyze the expansion of an axisymmetric hole in a freely suspended viscoelastic liquid sheet described by the Oldroyd-B model. Exploiting the separation of length scales between hole radius and film thickness, we derive extensional thin-film equations on the scale of the hole and an effective boundary condition from an asymptotic force balance in the tip region. Analytical solutions are obtained for weak viscoelasticity, $Wi\ll 1$, and the ultra-dilute limit, $\mu_p\ll\mu_s$, where $Wi$ is the Weissenberg number, while $\mu_s$ and $\mu_p$ are solvent and polymeric viscosities, respectively. For weak viscoelasticity, the dimensionless hole radius grows approximately as $e^{(0.5+\alpha Wi \beta_p)T}$, where $\alpha=(12 - 6\log 2-\pi)/21\approx 0.224$ and $\beta_p=\mu_p/(\mu_s+\mu_p)$. In the ultra-dilute limit, the radius grows approximately as $e^{(0.5+\alpha^{*}\beta_p )T}$, where $\alpha^{*}(Wi)>0$ is evaluated numerically. In both regimes, viscoelastic stresses increase the exponential growth rate relative to the Newtonian limit and induce film-thickness variations, with thickening near the retracting edge. This acceleration arises from azimuthal stretching and radial compression of the polymers, which redistribute stresses in the film and modify the stress balance at the tip, leading to a stronger outward radial extensional flow.

physics.flu-dyn↗

arXiv2026

Understanding the Theory--Experiment Discrepancy in Pressure Drop of Dilute Polymer Solutions in Channel Flows

For decades researchers have experimentally observed that the flow of dilute viscoelastic polymer solutions through contraction or contraction--expansion channels yields results at odds with theory and simulations. In particular, the experimentally reported pressure drops are larger than those of generalized Newtonian reference fluids with the same shear viscosity, while constitutive models, such as Oldroyd-B and FENE-P, predict smaller pressure drops under conditions of low Reynolds numbers and stable flow at small Weissenberg ($Wi$) or Deborah ($De$) numbers. This apparent contradiction between experiments and theory has been a long-standing puzzle in the field. Here, we characterize the properties of dilute viscoelastic polymer solutions and employ two distinct types of pressure-sensing systems, conventional recessed pressure taps and flush-mounted diaphragm sensors, to systematically measure pressure drops across channels of different geometrical configurations. These measurements yield qualitative agreement with theoretical predictions across all geometries if the largest relaxation time is adopted for the analysis of the flow. Our results indicate that the apparent discrepancies mentioned above can be attributed to improper interpretation of the measurements and to mismatches between experimental conditions and assumptions made in the theoretical and numerical studies, which include hole pressure effects, the choice of relaxation time of the fluid, and the presence of experimental flow instabilities. For quantitative improvements, our results suggest the use of continuum-level constitutive models containing more realistic microscopic features of polymer solutions.

physics.flu-dyn↗

arXiv2026

Nonlinear diffusion and compressive rims in source-driven biopolymer condensates

Many subcellular condensates continuously produce biopolymers. Coupling Flory-Huggins thermodynamics to two-fluid viscoelasticity, we probe the diffusion of such source-driven polymeric droplets, and identify a universal structural compressive rim at their diffusion front. Integrating analytical scaling laws, numerical simulations, and experimental data, we show that this framework captures key structural and dynamic characteristics of the nucleolus, demonstrating the role of polymer diffusion in non-equilibrium biological transport.

cond-mat.soft↗

arXiv2026

Polymer-polymer interdiffusion: effects of entanglements and a polymeric source

Many industrial applications and biological scenarios involve the interdiffusion of two polymeric species. Motivated by biological subcellular source-driven processes, we study polymer-polymer interdiffusion problems in the absence or the presence of a polymeric source, for both unentangled and entangled scenarios. Utilizing a two-fluid formalism, we arrive at scaling relations, self-similar reductions, and analytical solutions, which are confirmed with one- and two-dimensional numerical simulations. The introduction of a source term breaks the self-similar structure, modifying the boundary conditions and the domain of integration. Nevertheless, we show that the front characteristics of the diffusing droplet exhibit similar spatial structures as in the absence of a source. Our results allow deeper understanding of polymer-polymer interdiffusion and nonlinear transport, especially in the presence of a source.

cond-mat.soft↗

arXiv2026

Enucleated incompressible red blood cells in shear flow: theoretical analysis of shape instabilities

Red blood cells (RBCs) are essential for oxygen transport, and their remarkable ability to undergo significant deformations during flow is a crucial feature for their physiological function. At intermediate shear rates typical of the microcirculation, RBCs can adopt complex, multi-lobed shapes, signifying a dynamic instability. Here we adopt a perturbative theoretical framework of a quasi-spherical RBC under external shear flow to study such shape instabilities. To better capture RBC maturation and enucleation, we first extend the framework to explicitly account for different excess areas between the stress-free and current membrane shapes. We revisit the reduced equations of motion obtained for an ellipsoidally-shaped RBC, and demonstrate the effect of different excess areas and initial orientation on the dynamical trajectories. Then, we introduce additional spatial modes and show that an emerging instability critically depends on the RBC's shear and bending moduli, the internal to external viscosity ratio, and the excess area, mainly through the RBC's membrane tension. We also study the instability-induced saturation of the membrane tension, and the resulting excess area redistribution at long times. The theoretical framework and the emerging picture of the different instabilities provide insights into the emergence of stomatocyte and trilobe shapes exhibited by RBCs under external flow.

cond-mat.soft↗

arXiv2026

Solubility enhanced surfactant-induced flow in air-liquid-air sheets

Liquid interfaces appear throughout nature and engineering and are typically contaminated by surface active agents (surfactants), which are characterized by a wide range of solubility. We demonstrate that solubility enhances by an order of magnitude surfactant-induced flow in air-liquid-air films, in contrast to previously studied geometries where solubility dampens the flow. The enhancement is described by a single parameter comparing the depletion length to the film thickness. Our experiments are well described by an asymptotic theory of the Navier-Stokes equations with surfactant kinetics.

physics.flu-dyn↗

arXiv2026

Upper bounds on the colloid separation efficiency of diffusiophoresis

The separation of colloidal particles from fluids is essential to ensure a safe global supply of drinking water, yet in the case of microscopic particles, it remains a highly energy-intensive process when using traditional filtration methods. Water cleaning through diffusiophoresis, spontaneous colloid migration in chemical gradients, effectively circumvents the need for physical filters, representing a promising alternative. This separation process is typically realized in internal flows, where a cross-channel electrolyte gradient drives particle accumulation at walls, with colloid separation slowly increasing in the streamwise direction. However, the maximum separation efficiency, achieved sufficiently downstream as diffusiophoretic migration (driving particle accumulation) is balanced by Brownian motion (inducing diffusive spreading), has not yet been characterized. In this work, we develop an asymptotic theory to predict colloid separation in this limit, deriving expressions for the water recovery, defined as the fraction of clean water that can be obtained from the suspension. We find that the mechanism by which the chemical permeates in the channel and the reaction kinetics governing its dissociation into ions play key roles in the process. Moreover, we identify four distinct regimes in which separation is controlled by different scaling laws involving Damköhler and Péclet numbers, which measure the ratios of reaction kinetics to ion diffusion and diffusiophoresis to Brownian motion, respectively. We also confirm the scaling of one of these regimes using microfluidic experiments where separation is driven by CO2 gradients. Our results shed light on pathways toward new, more efficient separations and are also applicable to quantify colloidal accumulation in the presence of chemical gradients in more general situations.

cond-mat.soft↗

arXiv2026

Similarity Solutions of Shock Formation for First-order Strictly Hyperbolic Systems

Shocks due to hyperbolic partial differential equations (PDEs) appear throughout mathematics and science. The canonical example is shock formation in the inviscid Burgers' equation $\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}=0$. Previous studies have shown that when shocks form for the inviscid Burgers' equation, for positions and times close to the shock singularity, the dynamics are locally self-similar and universal, i.e., dynamics are equivalent regardless of the initial conditions. In this paper, we show that, in fact, shock formation is self-similar and universal for general first-order strictly hyperbolic PDEs in one spatial dimension, and the self-similarity is like that of the inviscid Burgers' equation. An analytical formula is derived for the self-similar universal solution.

math.AP↗

arXiv2026

Polydisperse polymer fractionation between phases

Polymer mixtures fractionate between phases depending on their molecular weight. Consequently, by varying solvent conditions, a polydisperse polymer sample can be separated between phases so as to achieve a particular molecular weight distribution in each phase. In principle, predictive physics-based theories can help guide separation design and interpret experimental phase-diagram and fractionation measurements. Even so, applying the standard Flory-Huggins model can require numerical computations that hamper the predictions considering the full molecular weight distribution. Here, we apply a recently-derived exact analytical solution of multi-component Flory-Huggins theory for polydisperse homopolymers to understand the principles of polymer fractionation for common molecular weight distributions. Consistent with previous studies, the method highlights the sensitivity of polymer fractionation to the shape, and in particular the tails, of this distribution. Our results provide a systematic approach to evaluate the full molecular weight distribution in phase coexistence calculations over the possible composition space.

cond-mat.soft↗

arXiv2026

A vertically integrated model with phase change for aquifers in cold firn

Surface meltwater from glaciers and ice sheets contributes significantly to sea-level rise, yet the processes governing its transport and retention within cold firn remain poorly constrained, particularly in multiple dimensions. Here we present a multidimensional, vertically integrated modeling framework for aquifers in cold firn that incorporates phase change and residual trapping of liquid water. This mathematical framework, together with its numerical implementation, extends terrestrial groundwater models to describe aquifers expanding within otherwise cold firn, highlighting the analogous physics governing both systems. We derive semi-analytical solutions for finite-volume aquifers and validate them against numerical simulations and higher-fidelity model results. These solutions elucidate key features of meltwater dynamics and provide benchmarks for firn hydrologic models. We further demonstrate the three-dimensional expansion of an aquifer in cold, heterogeneous firn. Both the semi-analytical and numerical results show that lateral aquifer propagation slows at lower initial firn temperatures due to porosity reduction and associated loss of liquid water from freezing. Overall, this framework provides new insights into the formation and expansion of firn aquifers in percolation zones and helps clarify how subsurface meltwater storage modulates meltwater fluxes, surface mass loss, and contributes to global sea-level rise.

physics.flu-dyn↗

arXiv2026

Design of model Boger fluids with systematically controlled viscoelastic properties

The subject of viscoelastic flow phenomena is crucial to many areas of engineering and the physical sciences. Although much of our understanding of viscoelastic flow features stems from carefully designed experiments, preparation of model viscoelastic fluids remains a challenge; for example, fabricating a series of fluids with different fluid shear moduli $G_0$, but with an identical relaxation time $τ$, is nontrivial. In this work, we harness the non-ideality of nearly constant-viscosity elastic fluids, commonly known as `Boger fluids', made with polyisobutylene, to develop an experimental methodology that produces a set of fluids with desired viscoelastic properties, specifically, $G_0$, $τ$, and the first normal stress difference coefficient $ψ_1$. Through a linear algebraic relation between the rheological properties of interest ($G_0$, $τ$, $ψ_1$) and the fluid compositions in terms of polymer concentration $c$, molecular weight $M_w$, and solvent viscosity $η_s$, we developed a `design equation' that takes $G_0$, $τ$, $ψ_1$ as inputs and calculates values for $c$, $M_w$, $η_s$ as outputs. Using this method, fabrication of dilute viscoelastic fluids whose rheological properties are \textit{a priori} known can be achieved.

cond-mat.soft↗

arXiv2026

Polymer-Residue Accessibility Shapes Sequence Dependence of Critical Temperatures for Phase Separation

Biological polymers, such as intrinsically disordered proteins, play a central role in cellular biology, including mediating phase separation and controlling activity of biological condensates. The physical properties and functions of biopolymers are determined by their residue sequence. Recently, significant computational and theoretical efforts have been devoted to characterizing the combinatorially complex sequence dependence of biopolymer phase diagrams. Here, we quantitatively show that monomer accessibility is central to determining the strength of pair interactions. We formulate an analytical perturbative approach, phenomenologically precluding two polymers' centers of mass from overlapping within a correlation hole. This theory yields the correction to the strength of mean-field interactions in terms of a residue-accessibility parameter (RAP), which accounts for the limited availability of inner monomers to interactions. Despite the simplicity of the approach, RAP rationalizes the variations in critical temperatures found in extensive Monte-Carlo simulations for thousands of two-letter polymer solutions of varying length and sequence. RAP may thus be effective for deciphering the polymer-sequence dependence of phase diagrams given any polymer length, set of monomer types, and polymer mixtures.

cond-mat.soft↗

arXiv2026

Autophoresis of a Janus particle near a planar wall: a lubrication limit

We study the self-diffusiophoresis of a spherical chemically active particle near a planar, impermeable wall, with a focus on the influence of particle orientation on propulsion. We analyze a Janus particle with asymmetric surface chemical activity, consisting of a small inert region within a catalytically active cap. While numerical simulations have been used to study such particles, they encounter difficulties resolving the flow and transport in the near-wall regime due to geometric confinement and steep solute concentration gradients. We address this limitation through an asymptotic analysis in the lubrication limit, where the gap between the particle and the wall is narrow. In particular, we consider the distinguished limit in which the inert region is asymptotically comparable in size to the lubrication region. We analyze an axisymmetric configuration in which the inert face is oriented parallel to the wall and extend the analysis to slightly tilted orientations. We find that the cap size determines whether a tilted particle rotates back toward the axisymmetric state or continues to reorient, thereby characterizing its rotational stability in the near-contact regime.

cond-mat.soft↗

arXiv2026

Retraction Dynamics of a Highly Viscous Liquid Sheet

We study the one-dimensional capillary-driven retraction of a finite, planar liquid sheet in the asymptotic regime where both the Ohnesorge number $\mathrm{Oh}$ and the initial length-to-thickness ratio $l_0/h_0$ are large. In this regime, the fluid domain decomposes into two regions: a thin-film region governed by one-dimensional mass and momentum equations, and a small tip region near the free edge described by a self-similar Stokes flow. Asymptotic matching between these regions yields an effective boundary condition for the thin-film region, representing a balance between viscous and capillary forces at the free edge. Surface tension drives the thin-film flow only through this boundary condition, while the local momentum balance is dominated by viscous and inertial stresses. We show that the thin-film flow possesses a conserved quantity, reducing the equation of thickness to heat equation with time-dependent boundary conditions. The reduced problem depends on a single dimensionless parameter $\mathcal{L} = l_0 / (4 h_0 \mathrm{Oh})$. Numerical solutions of the reduced model agree well with previous studies and reveal that the sheet undergoes distinct retraction regimes depending on $\mathcal{L}$ and a dimensionless time after rupture $T$. We derive asymptotic approximations for the thickness profile, velocity profile, and retraction speed during the early and late stages of retraction. At early times, the retraction speed grows as $T^{1/2}$, while at late times it decays as $1/T^2$. An intermediate regime arises for very long sheets ($\mathcal{L} \gg 1$). During this phase, the retraction speed approaches the Taylor-Culick value. When $T \approx \mathcal{L}$, the speed undergoes fast deceleration from the Taylor-Culick speed to late-time asymptotics.

physics.flu-dyn↗

arXiv2026

Flash Freeze--Thaw Phenomenon in Sprayed Evaporating Micrometer Droplets

Two-fluid spray nozzles are widely used in combustion, chemical processing, pharmaceutical coating, environmental control, and spray drying to atomize liquids with pressurized gas. However, the adiabatic cooling and resulting flash freeze--thaw exposure of atomized droplets remain underexplored. Using high-fidelity computational fluid dynamics coupled with droplet-scale nucleation modeling, we show that the atomizing gas temperature at the nozzle exit can fall from $22\,^{\circ}\mathrm{C}$ to below $-130\,^{\circ}\mathrm{C}$, initiating rapid ice nucleation and freezing in micro-scale droplets. For atomizing gas at $5\,\mathrm{bar}$ (gauge) and $22\,^{\circ}\mathrm{C}$, all droplets smaller than $1.5\,μ\mathrm{m}$ freeze, whereas droplets larger than $3\,μ\mathrm{m}$ remain liquid. These frozen droplets thaw within $O(10)\,μ\mathrm{s}$ upon leaving the cold zone, subjecting sensitive actives to intense freeze--thaw thermomechanical stresses near the nozzle even when the bulk drying gas is warm. Parametric studies show that ice formation is eliminated at atomizing gas temperatures above $110\,^{\circ}\mathrm{C}$ for all gas-to-liquid mass ratios (GLRs) between 8 and 25, or at $\mathrm{GLR}<12$ for all atomizing gas temperatures; the chamber drying gas does not influence near-nozzle freezing. Additionally, we demonstrate that swirling flow intensifies flash freeze--thaw by deepening gas cooling, whereas non-swirling flow extends cold-zone residence time, yet both designs produce similar iced-droplet fractions. We construct an operating map delineating conditions that avoid flash freeze--thaw and show that the no-ice boundary provides a conservative criterion for both swirl and non-swirl nozzles. These findings identify a previously unrecognized freeze--thaw stress mechanism that can compromise spray-dried pharmaceutical product stability.

physics.flu-dyn↗

arXiv2026

Coalescence of viscoelastic sessile drops: the small and large contact angle limits

The coalescence and breakup of drops are classic examples of flows that feature singularities. The behavior of viscoelastic fluids near these singularities is particularly intriguing - not only because of their added complexity, but also due to the unexpected responses they often exhibit. In particular, experiments have shown that the coalescence of viscoelastic sessile drops can differ significantly from their Newtonian counterparts, sometimes resulting in a sharply defined interface. However, the mechanisms driving these differences in dynamics, as well as the potential influence of the contact angle are not fully known. Here, we study two different flow regimes effectively induced by varying the contact angle and demonstrate how that leads to markedly different coalescence behaviors. We show that the coalescence dynamics is effectively unaltered by viscoelasticity at small contact angles. The Deborah number, which is the ratio of the relaxation time of the polymer to the timescale of the background flow, scales as $θ^3$ for $θ\ll 1$, thus rationalizing the near-Newtonian response. On the other hand, it has been shown previously that viscoelasticity dramatically alters the shape of the interface during coalescence at large contact angles. We study this large contact angle limit using experiments and 2D numerical simulations of the equation of motion. We show that the departure of the coalescence dynamics from the Newtonian case is a function of the Deborah number and the elastocapillary number, which is the ratio between the shear modulus of the polymer solution and the characteristic stress in the fluid.

physics.flu-dyn↗