arXiv subjects

Daniel Lester

Publications and source records attributed to Daniel Lester.

11 recordsLinked to original sources

arXiv2025

Fluid Deformation in Random Unsteady Flow

Fluid deformation controls myriad processes in random flows including mixing and dispersion, stress development in complex fluids, colloid transport and deposition, droplet breakup and emulsification, fluid-structure interaction, chemical reactions and biological activity. Despite this, fundamental aspects are not well understood, including the link between the Lagrangian velocity gradient tensor $\boldsymbol\epsilon$ and deformation measures such as Lyapunov exponents ($\lambda_{\infty,i}$), their finite-time counterparts (FTLEs) and the right Cauchy-Green tensor $\mathbf{C}$. We address these knowledge gaps by developing an \emph{ab initio} stochastic model of fluid deformation in ergodic and stationary random unsteady flows. We show that although the Lagrangian velocity process is non-Markovian and non-Fickian, temporal decorrelation in unsteady random flows results in Fickian evolution of $\boldsymbol\epsilon$. Application of an objective coordinate transform renders $\boldsymbol\epsilon^\prime$ upper triangular, the basis vectors of which exponentially converge to Lyapunov vectors. As such, the diagonal components of $\boldsymbol\epsilon^\prime$ correspond to increments of the Lyapunov spectra, while the off-diagonal components objectively quantify shear and vorticity. This leads to a stochastic model of Lagrangian fluid deformation as a simple Brownian process that provides a direct link between $\boldsymbol\epsilon^\prime$ and fluid deformation. We develop closed-form expressions for the evolution of $\mathbf{C}$ and the FTLEs, and apply the stochastic model to numerical results for a model 2D unsteady flow and 3D forced homogeneous isotropic turbulence, returning excellent agreement with direct calculations of deformation measures.

physics.flu-dyn↗

arXiv2025

Mixing of Gaussian Solute Plumes

We consider the general problem of mixing of Gaussian solute plumes arising across a range of different flows ranging from two-dimensional (2D) to three-dimensional (3D), steady to unsteady, regular to chaotic, Stokes to turbulent. We consider a a range of infinitesimal injection protocols (point or line sources, continuous or pulsed) which generate solute points, lines and sheets and their finite-sized counterparts (blobs, tubes and slabs). We show that evolution of this broad family of Gaussian plumes is solely governed by the initial solute distribution, the dispersion tensor and the Lagrangian history of the deformation gradient tensor. Significant simplifications arise when the deformation tensor is placed in the Protean (Lester et al, JFM, 2018) coordinate frame (which aligns with the maximum and minimum fluid stretching directions and renders the deformation tensor upper triangular), allowing evolution of the Gaussian covariance matrix to be expressed in physically relevant terms such as Lyapunov exponents, longitudinal and transverse shear rates. We couch these results in terms of evolution of the maximum concentration and scalar entropy of Gaussian plume for a range of flows and injection protocols. These results provide significant insights into the processes that govern mixing in a broad range of flows and provide the building blocks of efficient numerical methods using e.g. radial basis functions for solute transport and mixing in arbitrary flows.

physics.flu-dyn↗

arXiv2025

Sedimentation of particulate suspensions under stagnant conditions in horizontal pipes

Sedimentation of particulate suspensions in horizontal pipes can lead to formation, growth and consolidation of a solid-like bed which can severely retard pipeline performance. As stagnant flow conditions frequently arise during industrial processes, critical operational questions are: (i) at what rate and extent does sedimentation proceed, and (ii) can the sedimentation dynamics be predicted from conventional suspension characterisation methods? We address these questions by characterising the sedimentation properties of an aqueous Kaolin suspension via batch settling tests and comparing predictions from 1D sedimentation theory with experiments in a horizontally oriented cylindrical pipe. We show that particulate sedimentation can be accurately predicted, indicating that the estimated sedimentation properties are representative material properties, and that transient effects such as gravity currents are not significant. Conversely, we find that the consolidation of the sediment is not well predicted by 1D theory, suggesting that the stress state is not 1D and likely involves contributions from the pipe walls. These stagnant cylindrical pipe results provide a basis for the development of methods to predict pipeline sedimentation under more general (laminar and turbulent) flow conditions.

physics.flu-dyn↗

arXiv2025

Line Stretching in Random Flows

How finite-sized material lines stretch in chaotic (mono-scale) and turbulent (multi-scale) flows remains a central but unresolved problem that governs mixing, transport and reaction. We show elongation is controlled by a finite-sampling process balancing ensemble and temporal averaging that is mediated by particle dispersion. These results expose the rich dynamics of line stretching and compel reassessment of experimental data and models of fluid-borne phenomena.

physics.flu-dyn↗

arXiv2025

Turbulent Pipe Flow of Thixotropic Fluids

Complex materials with internal microstructure such as suspensions and emulsions exhibit time-dependent rheology characterized by viscoelasticity and thixotropy. In many large-scale applications such as turbulent pipe flow, the elastic response occurs on a much shorter timescale than the thixotropy, hence these flows are purely thixotropic. The fundamental dynamics of thixotropic turbulence is poorly understood, particularly the interplay between microstructural state, rheology, and turbulence structure. To address this gap, we conduct direct numerical simulations (DNS) of fully developed turbulent pipe flow of a model thixotropic (Moore) fluid over a range of thixoviscous numbers $\Lambda$ from slow ($\Lambda\ll 1$) to fast ($\Lambda\gg 1$) thixotropic kinetics relative to the eddy turnover time. Analysis of DNS results in the Lagrangian frame shows that, as expected, in the limits of slow and fast kinetics, these time-dependent flows behave as time-independent purely viscous (generalized Newtonian) analogues. For intermediate kinetics ($\Lambda\sim 1$), the rheology is governed by a \emph{path integral} of the thixotropic fading memory kernel over the distribution of Lagrangian shear history, the latter of which is modelled via a simple stochastic model for the radially non-stationary pipe flow. DNS computations based on this effective viscosity closure exhibit excellent agreement (within 2.4\% error) with the fully thixotropic model for $\Lambda=1$, indicating that the purely viscous (generalized Newtonian) analogue persists for arbitrary values of $\Lambda\in[0,\infty^+)$ and across nonlinear rheology models. These results uncover the feedback mechanisms between microstructure, rheology, and turbulence and offer fundamental insights into the structure of thixotropic turbulence.

physics.flu-dyn↗

arXiv2024

A Unified Theory for Chaotic Mixing in Porous Media: from Pore Networks to Granular Systems

Recent studies have revealed the central role of chaotic stretching and folding at the pore scale in controlling mixing within porous media, whether the solid phase is discrete (as in granular and packed media) or continuous (as in vascular networks and open porous structures). Despite its widespread occurrence, a unified theory of chaotic mixing across these diverse systems remains to be developed. Furthermore, previous studies have focused on fluid stretching mechanisms but the folding mechanisms are largely unknown. We address these shortcomings by presenting a unified theory of mixing in porous media. We thus show that fluid stretching and folding (SF) arise through the same fundamental kinematics driven by the topological complexity of the medium. We find that mixing in continuous porous media manifests as discontinuous mixing through a combination of SF and cutting and shuffling (CS) actions, but the rate of mixing is governed by SF only. Conversely, discrete porous media involves SF motions only. We unify these diverse systems and mechanisms by showing that continuous media represents an analog of discrete media with finite-sized grain contacts. This unified theory provides insights into the generation of pore-scale chaotic mixing and points to design of novel porous architectures with tuneable mixing and transport properties.

physics.flu-dyn↗

arXiv2022

A Primer on the Dynamical Systems Approach to Transport in Porous Media

Historically, the dominant conceptual paradigm of porous media flow, solute mixing and transport was based on steady two-dimensional flows in heterogeneous porous media. Although it is now well recognised that novel transport phenomena can arise in unsteady and/or three-dimensional flows at both the pore- or Darcy-scales, appropriate methods for analysis and understanding of these more complex flows have not been widely employed. In this primer we advocate for methods borrowed from dynamical systems (chaos) theory, which aim to uncover the \emph{Lagrangian kinematics} of these flows: namely how fluid particle trajectories (which form a dynamical system) are organized and interact and the associated impacts on solute transport and mixing. This dynamical systems approach to transport is inherently Lagrangian, and the Lagrangian kinematics form Lagrangian coherent structures (LCSs), special sets of trajectories that divide the Lagrangian frame into chaotic mixing regions, poorly mixing hold-up regions (and in some cases non-mixing ``islands'') and the transport barriers that organise these regions. Hence the dynamical systems approach provides insights into flows that may exhibit chaotic, regular (non-chaotic) or mixed Lagrangian kinematics, and also into how LCSs organize solute transport and mixing. Novel experimental methods are only recently permitting visualization of LCSs are in porous media flows. In this primer we review the dynamical systems approach to porous media flow and transport and connect the associated tools and techniques with the latest research findings from pore to Darcy scales. This primer provides an introduction to the methods and tools of dynamical systems theory. Once familiar with these approaches, porous media researchers will be better positioned to know when to expect complex Lagrangian kinematics, how to uncover and understand LCSs and their impacts ...

physics.flu-dyn↗

arXiv2020

Lagrangian complexity persists with multimodal flow forcing in poroelastic systems

We extend previous analyses of the origins of complex transport dynamics in poroelastic media to the case where the input transient signal at a boundary is generated by a multimodal spectrum. By adding harmonic and anharmonic modal frequencies as perturbations to a fundamental mode we examine how such multimodal signals affect the Lagrangian complexity of poroelastic flow. While the results apply to all poroelastic media (industrial, biological and geophysical), for concreteness we couch the discussion in terms of unpumped coastal groundwater systems having a discharge boundary forced by tides. Particular local regions of the conductivity field generate saddles that hold up and braid (mix) trajectories, resulting in unexpected behaviours of groundwater residence time distributions and topological mixing manifolds near the tidal boundary. While increasing spectral complexity can reduce the occurrence of periodic points, especially for anharmonic spectra with long characteristic periods, other signatures of Lagrangian complexity persist. The action of natural multimodal tidal signals on confined groundwater flow in heterogeneous aquifers can induce exotic flow topologies and mixing effects that are profoundly different to conventional concepts of groundwater discharge processes. Taken together, our results imply that increasing spectral complexity results in more complex Lagrangian structure in flows through poroelastic media.

physics.flu-dyn↗

arXiv2020

Hierarchical Jamming in Frictional Particle Assemblies

The postulate of the existence of a jamming phase diagram (Liu and Nagel, Nature 396, 21 EP (1998aa)) provides a theoretical basis for the classification of a wide range of amorphous solids (colloidal, molecular and emulsion glasses, colloidal and polymer gels, foams and granular matter) on the basis of whether these materials are in the jammed or unjammed state. Whilst such simple classification is appealing, it fails to capture that the criterion of rigidity of such amorphous solids may be defined with respect to a particular deformation orientation or mode (i.e. shear, extrusion, consolidation). We consider this problem via the consolidation of strong colloidal gels, and find that the critical transitions during the consolidation of a strong colloidal gel (as indicated by maxima and minima in the relative normal stress difference) correspond directly to directed, frictional and non-frictional rigidity percolation. These results indicate a hierarchy of directed, jammed states during consolidation of such amorphous solids, and a direct link between particle-scale interactions and macroscopic collective behaviour of these systems driven far from equilibrium

cond-mat.soft↗

arXiv2018

Natural Groundwater Systems Can Display Chaotic Mixing at the Darcy Scale

Although steady, isotropic Darcy flows are inherently laminar and non-mixing, it is well understood that transient forcing via engineered pumping schemes can induce rapid, chaotic mixing in groundwater. In this study we explore the propensity for such mixing to arise in natural groundwater systems subject to cyclical forcings, e.g. tidal or seasonal influences. Using a conventional linear groundwater flow model subject to tidal forcing, we show that under certain conditions these flows generate Lagrangian transport and mixing phenomena (chaotic advection) near the tidal boundary. We show that aquifer heterogeneity, storativity, and forcing magnitude cause reversals in flow direction over the forcing cycle which, in turn, generate coherent Lagrangian structures and chaos. These features significantly augment fluid mixing and transport, leading to anomalous residence time distributions, flow segregation, and the potential for profoundly altered reaction kinetics. We define the dimensionless parameter groups which govern this phenomenon and explore these groups in connection with a set of well-characterised coastal systems. The potential for Lagrangian chaos to be present near discharge boundaries must be recognized and assessed in field studies.

physics.flu-dyn↗

arXiv2016

Hydrodynamic drift ratchet scalability

The rectilinear "drift" of particles in a hydrodynamic drift ratchet arises from a combination of diffusive motion and particle-wall hydrodynamic interactions, and is therefore dependent on particle diffusivity, particle size, the amplitude and frequency of fluid oscillation and pore geometry. Using numerical simulations, we demonstrate that the drift velocity relative to the pore size is constant across different sized drift ratchet pores, if all the relevant non-dimensional groups (Peclet number, Strouhal number and ratio of particle to pore size) remain constant. These results clearly indicate for the first time the scaling parameters under which the drift ratchet achieves dynamic similarity, and so facilitates design, fabrication and testing of drift ratchets for experiments and eventually as commercial micro/nano fluidic separation devices.

physics.flu-dyn↗