arXiv subjects

Jason R. Picardo

Publications and source records attributed to Jason R. Picardo.

At least 19 recordsLinked to original sources

arXiv2026

Localizing polymers promotes the centre-mode elastic instability

The centre-mode elastic instability, prevalent in rectilinear flows of dilute polymer solutions, allows dynamic states to emerge even in the absence of inertia. Here, we show that this instability can be significantly enhanced when the base flow has a nonuniform spatial-distribution of polymers. In such a flow, the polymeric stress not only depends on the conformation tensor (determined here by the Oldroyd-B equation) but also varies proportionally with the polymer concentration field, which satisfies a scalar transport equation. Focusing on the inertialess Stokes limit, we first consider the simple setting of periodic Kolmogorov flow. A linear stability analysis shows that a nonuniform polymer concentration either promotes or suppresses the centre-mode instability, depending on whether the polymers are localised near or away from the maximum of the base-velocity profile. We then focus on a base flow with a distinct polymer-laden stream overlying the base-velocity maximum, and sandwiched between polymer-free streams. We find that the critical Weissenberg number (product of the elastic relaxation time and the typical strain-rate) at the onset of instability undergoes a sudden decrease as the total polymer loading is increased. An energy analysis attributes this destabilisation to elastic feedback forces that arise from concentration gradients near the interfaces between the polymer-laden and polymer-free streams. The insights from Kolmogorov flow are shown to carry over to channel flow, where localising polymers about the centreline strongly promotes the centre-mode instability.

cond-mat.soft↗

arXiv2026

Resolving the inverse problem in pulse response analysis of TAP reactors

Pulse experiments in the temporal analysis of products (TAP) reactor are one of the most important methods for studying transient kinetics of gas-solid catalytic reactions. The Y-procedure (Yablonsky et al., Chem. Eng. Sci. 62, 6754, 2007) is a model-free analysis framework for inferring the relationship between the reaction-rate $R$ and the reactant concentration $C$ from measurements of the outlet flux of gas. While elegant in conception, its application is hindered by the amplification of measurement noise that results from having to backtrack diffusive transport from the outlet to the reaction zone. Here, we explicitly recognize the inverse problem inherent in the Y-procedure and treat it using well-developed tools from the field of inverse problems. While previous implementations of the Y-procedure used Fourier-based filtering, we do not pre-process the measurements with an ad hoc noise-filter. Instead, we use a basis of localized square pulses to formulate a discrete inverse problem, whose regularized solution is obtained via the truncated singular value decomposition (TSVD) method. This method requires one to select a cutoff mode number; while we show how the choice of this regularization parameter can be guided by a Picard plot, we also develop an objective selection strategy for state defining experiments, for which $R(C)$ is a single-valued function. We apply our proposed inverse-problem approach to synthetic data corresponding to linear and nonlinear reactions and compare the results with the Fourier-filtration method. The former produces better reconstructions of the $R$ vs $C$ relationship, especially for nonlinear reactions. Our work facilitates the automation of pulse response analyses and enables the application of other discrete inverse-problem techniques, such as Tikhonov regularization or machine-learning methods.

physics.chem-ph↗

arXiv2025

Stretching and breaking of particles in compressible random flows

A key feature of turbulent suspensions that involve floating particles on the surface or inertial particles in the bulk is the compressibility of the effective particle-phase velocity field. Little, however, is known about the effects of small-scale flow compressibility on the stretching and breaking of particles. Here, we gain insight into the nature of these effects by studying the deformation of tiny particles in model fluctuating flows. We consider a generic particle with extensional dynamics that are governed by a vector model, which accounts for elasticity, internal viscosity, and non-affine deformation. Applying the dynamical systems approach of Balkovsky, Fouxon & Lebedev (2000), we first obtain general results for the stationary statistics of particle extension in compressible chaotic flows. We then specialize to a time-decorrelated Gaussian random flow and derive an exact solution for the Batchelor regime of the compressible Kraichnan model. We also perform numerical simulations for a time-correlated renewing flow. While straining is suppressed on the average in compressible flows, our results show that large deviations of the strain rate strongly stretch particles and give rise to a power-law distribution of extensions. Extreme straining events are particularly important for stiff particles and, in the examples considered here, give rise to a counter-intuitive effect: stiff particles stretch more and break faster in flows of increasing compressibility. Highly-elastic particles, whose deformation is dictated by the mean straining, stretch less and break slower. Though based on specific random flows, our work shows how compressibility can affect the extensional dynamics of particles by altering the fluctuations of the strain rate, including its large deviations.

physics.flu-dyn↗

arXiv2025

Morphology of mucus films in lung airways: secretion and ciliary evacuation

Lung airways are lined by a film of mucus which protects the epithelium from inhaled particles. To maintain a uniform coating, the mucus that is secreted into airways must be distributed into a film by wall-attached cilia, which constantly convey mucus along the airway. However, the film's natural tendency is to accumulate into humps and plugs, due to the Rayleigh-Plateau instability. To understand the behaviour of the film amidst these competing factors, we perform simulations of an idealized tubular airway using a reduced-order thin-film model. The axial boundaries are nonperiodic, allowing for cilia-driven inflow and outflow; a tangential velocity along the tubular wall models ciliary transport, while a localized source at the wall accounts for secretion. On increasing the mucus input rate, we find three distinct film morphologies: (i) uniform flat films; (ii) nonuniform films that are composed of travelling unduloid-shaped humps, separated by mucus-depleted zones; and (iii) films that form an occluding plug. The flat-film regime, absent in closed periodic domains, emerges as a consequence of the convective nature of the Rayleigh-Plateau instability in the presence of ciliary transport. Higher secretion rates increase the mean film-thickness and induce a convective-to-absolute transition, which manifests in the appearance of travelling humps. In the plug-forming regime, capillary forces dominate and drive the incoming mucus into a single hump, which resists ciliary translation and remains near the mucus source. Our results show how low-level baseline secretion sustains a protective, uniform mucus film, and how hypersecretion -- stimulated, for example, by inhaled allergens -- produces mucus plugs.

physics.flu-dyn↗

arXiv2025

Bioluminescence in turbulence: intermittent straining lights up dinoflagellates

Dinoflagellates are marine phytoplankton that emit flashes of light in response to flow-induced deformation; they are responsible for illuminating breaking-waves, wakes of ships, and other intensely turbulent spots of the upper ocean. Here, we ask how bioluminescence is affected by the fluctuating nature of turbulence -- a question motivated by the dependence of emitted flashes on both the extent and rate of deformation. Introducing a light-emitting dumbbell as a minimal model, we study the Lagrangian dynamics of flashing in a homogeneous isotropic turbulent flow, and contrast it with that in an extensional flow and a Gaussian random flow. We show that turbulent fluctuations strongly enhance bioluminescence, while introducing a Poisson-like stochasticity in the flashing dynamics. Furthermore, the intermittent fluctuations of the velocity-gradient subjects the dinoflagellate to bursts of extreme straining and produces bright flashes -- more intense, though less frequent, than what would result from Gaussian fluctuations. Our results suggest that radiant displays of marine bioluminescence are strongly promoted by turbulence and its dissipation-scale intermittency.

physics.flu-dyn↗

arXiv2025

How hydrodynamic interactions alter polymer stretching in turbulence

Hydrodynamic interactions (HI) between segments of a polymer have long been known to strongly affect polymer stretching in laminar viscometric flows. Yet the role of HI in fluctuating turbulent flows remains unclear. Using Brownian dynamics simulations, we examine the stretching dynamics of bead-spring chains with inter-bead HI, as they are transported in a homogeneous isotropic turbulent flow (within the ultra-dilute, one-way coupling regime). We find that HI-endowed chains exhibit a steeper coil-stretch transition as the elastic relaxation time is increased, i.e., HI cause less stretching of stiff polymers and more stretching of moderately to highly elastic polymers. The probability distribution function of the end-to-end extension is also modified, with HI significantly limiting the range of extensions over which a power-law range appears. On quantifying the repeated stretching and recoiling of chains by computing persistence time distributions, we find that HI delays migration between stretched and coiled states. These effects of HI, which are consistent with chains experiencing an effective conformation-dependent drag, are sensitive to the level of coarse-graining in the bead-spring model. Specifically, an HI-endowed dumbbell, which cannot form a physical coil, is unable to experience the hydrodynamic shielding effect of HI. Our results highlight the importance of incorporating an extension-dependent drag force in dumbbell-based simulations of turbulent polymer solutions. To develop and test such an augmented dumbbell model, we propose the use of a time-correlated Gaussian random flow, in which the turbulent stretching statistics are shown to be well-approximated.

cond-mat.soft↗

arXiv2025

Aerosol deposition in mucus-lined ciliated airways

We study the transport and deposition of inhaled aerosols in a mid-generation, mucus-lined lung airway, with the aim of understanding if and how airborne particles can avoid the mucus and deposit on the airway wall -- an outcome that is harmful in case of allergens and pathogens but beneficial in case of aerosolized drugs. We adopt the weighted-residual integral boundary-layer model of Dietze and Ruyer-Quil (J. Fluid Mech., vol. 762, 2015, pp. 68-109) to describe the dynamics of the mucus-air interface, as well as the flow in both phases. The transport of mucus induced by wall-attached cilia is also considered, via a coarse-grained boundary condition at the base of the mucus. We show that the capillary-driven Rayleigh-Plateau instability plays an important role in particle deposition by drawing the mucus into large annular humps and leaving substantial areas of the wall exposed to particles. We find, counter-intuitively, that these mucus-depleted zones enlarge on increasing the mucus volume fraction. Particles spanning a range of sizes (0.1 to 50 microns) are modelled using the Maxey-Riley equation, augmented with Brownian forces. We find a non-monotonic dependence of deposition on size. Small particles diffuse across streamlines due to Brownian motion, while large particles are thrown off streamlines by inertial forces -- particularly when air flows past mucus humps. Intermediate-sized particles are tracer-like and deposit the least. Remarkably, increasing the mucus volume need not increase entrapment: the effect depends on particle-size, because more mucus produces not only deeper humps that intercept inertial particles, but also larger depleted-zones that enable diffusive particles to deposit on the wall.

physics.flu-dyn↗

arXiv2025

Deriving thin-film averaged equations using computer algebra

We demonstrate the use of computer algebra for facilitating the derivation of thin film reduced-order models. We focus on the weighted residual integral boundary layer (WRIBL) method, which has proven to be a very effective technique for developing reduced-order models by averaging the Navier-Stokes equations over the thin-gap direction. In particular, we use SymPy (the symbolic computing library in Python) to derive the core-annular WRIBL model of Dietze and Ruyer-Quil (J. Fluid Mech. 762, 60, 2015); the derivation is especially involved due to the inclusion of second-order terms, the presence of two hydrodynamically active phases, the enforcement of interfacial boundary conditions, and the cylindrical geometry. We show, using excerpts of code, how each step of the derivation can be broken down into substeps that are amenable to symbolic computation. To illustrate the application of the derived model, we solve it numerically using scientific computing libraries in Python, and briefly explore the dynamics of the Rayleigh-Plateau instability. The use of open-source computer algebra, in the manner described here, greatly eases the derivation of averaged models, thereby facilitating their use for the study of multiscale flows, as well as for computationally-efficient prediction and optimization.

physics.flu-dyn↗

arXiv2025

Turbulent stretching of dumbbells with hydrodynamic interactions: an analytical study

We study the stretching of an elastic dumbbell in a turbulent flow, with the aim of understanding and quantifying the effect of hydrodynamic interactions (HI) between the beads of the dumbbell. Adopting the Batchelor-Kraichnan model for the flow, we derive a Fokker-Planck equation and solve it analytically to obtain the probability distribution of the dumbbell's extension. Using different formulations of the HI tensor, we find that HI preferentially enhances the stretching of stiff dumbbells, i.e., those with a small Weissenberg number. We also evaluate the averaging approximations commonly used to simplify the description of HI effects; the consistently-averaged approximation shows that HI result in a less-pronounced coil-stretch transition in chaotic flows. Finally, we confirm the relevance of our analytical results by a comparison with Brownian dynamics simulations of dumbbells transported in a direct numerical simulation of homogeneous isotropic turbulence.

physics.flu-dyn↗

arXiv2025

Active waves from non-reciprocity and cytoplasmic exchange

Pattern formation in active biological matter typically arises from the feedback between chemical concentration fields and mechanical stresses. The actomyosin cortex of cells is an archetypal example of an active thin film that displays such patterns. Here, we show how pulsatory patterns emerge in a minimal model of the actomyosin cortex with a single stress-regulating chemical species that exchanges material with the cytoplasm via a linear turnover reaction. Deriving a low-dimensional amplitude-phase model, valid for a one-dimensional periodic domain and a spherical surface, we show that nonlinear waves arise from a secondary parity-breaking bifurcation that originates from the nonreciprocal interaction between spatial modes of the concentration field. Numerical analysis confirms these analytical predictions, and also reveals analogous pulsatory patterns on impermeable domains. Our study provides a generic route to the emergence of nonreciprocity-driven pulsatory patterns that can be controlled by both the strength of activity and the turnover rate.

physics.bio-ph↗

arXiv2025

Probabilistic plugging of airways by sliding mucus films

When do mucus films plug lung airways? Using reduced-order simulations of a large ensemble of randomly perturbed films, we show that the answer is not determined by just the film's volume. While very thin films always stay open and very thick films always plug, we find a range of intermediate films for which plugging is uncertain. The fastest-growing linear mode of the Rayleigh-Plateau instability ensures that the film's volume is divided among multiple humps. However, the nonlinear growth of these humps can occur unevenly, due to spontaneous axial sliding -- a lucky hump can sweep up a disproportionate share of the film's volume and so form a plug. This sliding-induced plugging is robust and prevails with or without gravitational and ciliary transport.

physics.flu-dyn↗

arXiv2023

Preserving large-scale features in simulations of elastic turbulence

Simulations of elastic turbulence, the chaotic flow of highly elastic and inertialess polymer solutions, are plagued by numerical difficulties: The chaotically advected polymer conformation tensor develops extremely large gradients and can loose its positive definiteness, which triggers numerical instabilities. While efforts to tackle these issues have produced a plethora of specialized techniques -- tensor decompositions, artificial diffusion, and shock-capturing advection schemes -- we still lack an unambiguous route to accurate and efficient simulations. In this work, we show that even when a simulation is numerically stable, maintaining positive-definiteness and displaying the expected chaotic fluctuations, it can still suffer from errors significant enough to distort the large-scale dynamics and flow-structures. Focusing on two-dimensional simulations of the Oldroyd-B and FENE-P equations, we first compare two decompositions of the conformation tensor: symmetric square root (SSR) and Cholesky with a logarithmic transformation (Cholesky-log). While both simulations yield chaotic flows, only the Cholesky-log preserves the pattern of the forcing, i.e., its vortical cells remain ordered in a lattice as opposed to the vortices of the SSR simulations which shrink, expand and reorient constantly. To identify the accurate simulation, we appeal to a hitherto overlooked mathematical bound on the determinant of the conformation tensor, which unequivocally rejects the SSR simulation. Importantly, the accuracy of the Cholesky-log simulation is shown to arise from the logarithmic transformation. We then consider local artificial diffusion, a potential low-cost alternative to high-order advection schemes, and find unfortunately that it significantly modifies the dynamics. We end with an example, showing how the spurious large-scale motions identified here contaminate predictions of scalar mixing.

physics.flu-dyn↗

arXiv2023

Polymers in turbulence: stretching statistics and the role of extreme strain-rate fluctuations

Polymers in a turbulent flow are stretched out by the fluctuating velocity gradient; the stationary probability distribution function (p.d.f.) of extensions $R$ has a power-law tail with an exponent that increases with the Weissenberg number $Wi$, a nondimensional measure of polymer elasticity. This study addresses the following questions: (i) What is the role of the non-Gaussian statistics of the turbulent velocity gradient on polymer stretching? (ii) How does the p.d.f. of $R$ evolve to its asymptotic stationary form? Our analysis is based on simulations of the dynamics of finitely-extensible bead-spring dumbbells and chains, in the extremely dilute limit, that are transported in a homogeneous and isotropic turbulent flow, as well as in a Gaussian random flow. First, we recall the large deviations theory of polymer stretching, and illustrate its application. Then, we compare polymer stretching in turbulent and Gaussian random flows and show that while extreme-valued strain rates aid in stretching small-$Wi$ stiff polymers, they are unimportant for high-$Wi$ polymers, which instead are stretched by the cumulative action of moderate strain-rates. This result is supported by an analysis of the persistence time of polymers in stretched states. Next, beginning from a distribution of coiled polymers, we find that the p.d.f. of $R$ has the form of an evolving power-law, for low to moderate $Wi$, though this is not the case at high $Wi$. In either case, the p.d.f. relaxes to its stationary form exponentially. The corresponding time scales of equilibration, measured as a function of $Wi$, point to a critical slowing down at the coil-stretch transition. Importantly, these results show no qualitative change when chains in a turbulent flow are replaced by dumbbells in a Gaussian flow, thereby supporting the use of the latter for reduced-order modelling.

physics.flu-dyn↗

arXiv2022

Thin-gap averaging of variable-viscosity flows: application to thermoviscous fingering

A consistent averaging technique, using the weighted residual integral boundary layer (WRIBL) method, is presented for flow through a thin-gap geometry wherein the fluid's viscosity varies across the gap. In such situations, the flow has a non-parabolic cross-gap velocity profile -- an effect that is ignored by Darcy models conventionally used for such Hele-Shaw flows. The WRIBL technique systematically accounts for the cross-gap variation of viscosity and yields reduced-order equations for the gap-averaged fluid flow rate. As a test case, we consider a fluid with a temperature-dependent viscosity and analyse the previously-studied problem of thermoviscous fingering: a hot fluid flowing through a Hele-Shaw geometry with cold walls spontaneously forms channels of low-viscosity, hot fluid, separated by regions of high-viscosity, cold fluid. The temperature of the cold walls is assumed either to be constant, a scenario that mimics the upward flow of magma through fissures in the Earth's crust, or to vary linearly along the direction of flow. In both cases, the predictions of the WRIBL model, regarding the multiplicity of uniform steady flow states and their linear stability, are compared with that of the hitherto used, ad hoc, Darcy model (Helfrich, J. Fluid Mech., vol. 305, 1995, pp. 219-238), as well as with calculations of the full three-dimensional governing equations (Wylie and Lister, J. Fluid Mech., vol. 305, 1995, pp. 239-261). Though the results are qualitatively similar, the WRIBL model is found to be much more accurate than the Darcy model. The averaging method is presented in a general manner to facilitate its application to other physical situations where, for example, the viscosity depends on solute/particle concentration in a solution/suspension.

physics.flu-dyn↗

arXiv2021

Fluid dynamics in clouds: The sum of its parts

This entry is aimed at describing cloud physics with an emphasis on fluid dynamics. As is inevitable for a review of an enormously complicated problem, it is highly selective and reflects of the authors' focus. The range of scales involved, and the relevant physics at each scale is described. Particular attention is given to droplet dynamics and growth, and turbulence with and without thermodynamics.

physics.flu-dyn↗

arXiv2021

Sedimenting Elastic Filaments in Turbulent Flows

We investigate the gravitational settling of a long, model elastic filament in homogeneous isotropic turbulence. We show that the flow produces a strongly fluctuating settling velocity, whose mean is moderately enhanced over the still-fluid terminal velocity, and whose variance has a power-law dependence on the filament's weight but is surprisingly unaffected by its elasticity. In contrast, the tumbling of the filament is shown to be closely coupled to its stretching, and manifests as a Poisson process with a tumbling time that increases with the elastic relaxation time of the filament.

physics.flu-dyn↗

arXiv2020

Dynamics of a long chain in turbulent flows: Impact of vortices

We show and explain how a long bead-spring chain, immersed in a homogeneous, isotropic turbulent flow, preferentially samples vortical flow structures. We begin with an elastic, extensible chain which is stretched out by the flow, up to inertial-range scales. This filamentary object, which is known to preferentially sample the circular coherent vortices of two-dimensional (2D) turbulence, is shown here to also preferentially sample the intense, tubular, vortex filaments of 3D turbulence. In the 2D case, the chain collapses into a tracer inside vortices. In 3D, on the contrary, the chain is extended even in vortical regions, which suggests that it follows axially-stretched tubular vortices by aligning with their axes. This physical picture is confirmed by examining the relative sampling behaviour of the individual beads, and by additional studies on an inextensible chain with adjustable bending-stiffness. A highly-flexible, inextensible chain also shows preferential sampling in 3D, provided it is longer than the dissipation scale, but not much longer than the vortex tubes. This is true also for 2D turbulence, where a long inextensible chain can occupy vortices by coiling into them. When the chain is made inflexible, however, coiling is prevented and the extent of preferential sampling in 2D is considerably reduced. In 3D, on the contrary, bending stiffness has no effect, because the chain does not need to coil in order to thread a vortex tube and align with its axis.

physics.flu-dyn↗

arXiv2020

Polymer scission in turbulent flows

Polymers in a turbulent flow are subject to intense strain, which can cause their scission and thereby limit the experimental study and application of phenomena such as turbulent drag reduction and elastic turbulence. In this paper, we study polymer scission in homogeneous isotropic turbulence, through a combination of stochastic modelling, based on a Gaussian time-decorrelated random flow, and direct numerical simulations (DNSs) with both one-way (passive) and two-way (active) coupling of the polymers and the flow. For the first scission of passive polymers, the stochastic model yields analytical predictions which are found to be in good agreement with results from the DNSs, for the temporal evolution of the fraction of unbroken polymers and the statistics of the survival of polymers. The impact of scission on the dynamics of a turbulent polymer solution is investigated through DNSs with two-way coupling (active polymers). Our results indicate that the reduction of kinetic energy dissipation due to feedback from stretched polymers is an inherently transient effect, which is lost as the polymers breakup. Thus, the overall dissipation-reduction is maximised by an intermediate polymer relaxation time, for which polymers stretch significantly but without breaking too quickly. We also study the dynamics of the polymer fragments which form after scission; these daughter polymers can themselves undergo subsequent, repeated, breakups to produce a hierarchical population of polymers with a range of relaxation times and scission rates.

physics.flu-dyn↗