arXiv subjects

Simon J. Haward

Publications and source records attributed to Simon J. Haward.

At least 19 recordsLinked to original sources

arXiv2026

Coexisting chaos and order in micro-textured elastic flows

Viscoelastic fluid flows over micro-textured surfaces - densely covered by slender protrusions like cilia lining the body airways or villi covering the intestinal epithelium - underpin essential biological processes including transport, mixing, and absorption. Despite their ubiquity, the dynamics generated by the interplay between fluid elasticity and these complex geometries remain largely unexplored. Here we combine fully resolved numerical simulations with microfluidic experiments to reveal the flow dynamics established above dense arrays of microscopic pillars (canopies) immersed in the low-Reynolds-number flow of a viscoelastic liquid. We observe that the flow above the canopy tips spontaneously develops elastic turbulence. Remarkably, the chaotic state coexists with elastic waves emerging from the coupling between fluid elasticity and the heterogeneous shear induced by the canopy geometry. These ordered fluid motions persist across a broad range of flow conditions and canopy configurations. Our results demonstrate that coherent wave propagation and elastic turbulence are complementary manifestations of viscoelastic fluid flow. Beyond their fundamental significance, these mechanisms have broad implications for transport in biological and engineered environments, and reveal how structured geometries can harness the spontaneous dynamics of viscoelastic liquids to manipulate complex flows.

physics.flu-dyn↗

arXiv2026

Elastic wakes mediate collective viscoelastic fluid-structure interactions in side-by-side cantilever arrays

Fluid-structure interaction (FSI) in viscoelastic flows past deformable structures at low Reynolds numbers remains poorly understood, despite its relevance to biological systems such as cilia and flagella, and to engineered microsystems. We investigate viscoelastic FSI in side-by-side flexible cantilever arrays using a bottom-up approach that systematically varies the number of cantilevers and the rheology of the test fluid, comparing weakly shear-thinning (WS) and highly shear-thinning (HS) polyethylene oxide solutions. For both fluids, with increasing Weissenberg number (Wi), an elongated elastic wake develops behind a single isolated cantilever. For multiple cantilevers, the WS fluid undergoes a transition at a critical Weissenberg number (Wi*) from separated to merged elastic wakes, accompanied by the emergence of a divergent flow field and coordinated inward spanwise cantilever deflection. The critical Wi* increases as the number of cantilevers in the array is increased from two to three, demonstrating a strong dependence of the onset on the array configuration. For the HS fluid, wake merger, flow divergence, and inward cantilever deflection are suppressed across the full range of Wi investigated, despite comparable elasticity and the formation of elastic wakes. This contrast shows that elasticity alone promotes wake formation but is insufficient to produce the collective instability, which instead requires both shear-thinning and interactions between neighboring cantilevers. These findings demonstrate that viscoelastic FSI in flexible arrays is governed by the combined effects of fluid elasticity, shear-thinning, and geometric configuration, with elastic wake interactions mediating the collective instability and linking local elastic wakes to array-scale structural response.

physics.flu-dyn↗

arXiv2026

Numerical analysis of capillarity-driven thinning rheometry for polydisperse polymer solutions

Liquid bridges of polymer solutions that are self-thinning due to the action of capillarity undergo a transition from Newtonian-like linear thinning to exponential elastocapillary (EC) thinning when the polymer chains are stretched by the elongational flow and the resulting elastic contribution to the stress exceeds the viscous stress. As the Oldroyd-B model predicts that the EC thinning rate is set by the relaxation time ($τ$) of the polymer, the characteristic thinning timescale extracted from the exponential decay ($τ_{EC}$) is commonly interpreted as a direct measure of $τ$. Here we show that for real polydisperse polymer solutions, $τ_{EC}$ reflects only a subset of the molecular weight (MW) distribution -- those chains actively stretched by the flow. We demonstrate this using a multi-mode FENE-PM model that explicitly incorporates the molecular weight distribution, validated against the filament thinning experiments of Calabrese et al. [Phys. Rev. X 15, 021025 (2025)] on bidisperse blends of narrowly-distributed low-MW and high-MW polystyrene solutions. The model predicts that only chains with effective Weissenberg number $Wi = \dot{\varepsilon} τ> 1/2 $ are extended by the flow and contribute elastic stress; this threshold naturally favors high molecular weight species, whose longer relaxation times allow them to remain stretched throughout the elastocapillary regime. The measured $τ_{EC}$ is therefore set by this stress-contributing sub-ensemble rather than the full distribution. Further, our model predicts that $τ_{EC}$ depends on both the molecular weight distribution and total polymer concentration, as well as experimental parameters including pre-stretch and initial filament diameter, confirming that it is best understood as an experiment-specific quantity rather than an intrinsic fluid property.

cond-mat.soft↗

arXiv2026

Polymer extension at stagnation points governs flow thickening of polymer solutions in ordered porous media

Polymer solutions exhibit anomalous flow thickening -- marked by an abrupt increase in the macroscopic flow resistance -- above a threshold flow rate in a porous medium, but not in bulk solution. This phenomenon has evaded a mechanistic description for over half a century. Here, we develop a model that quantitatively links pore-scale flow fields and fluid rheology to macroscopic flow thickening, and validate it in experiments in two- and three-dimensional (2D and 3D) porous media. We find that flow thickening in ordered media is governed by polymer extension at stagnation points -- in contrast to disordered media, where viscous dissipation by unsteady flow fluctuations also contributes substantially. Our results provide a foundation to predict and control such flows in energy, environmental, industrial, and microfluidic applications.

physics.flu-dyn↗

arXiv2026

Flow-history-dependent orientational relaxation in dilute polydisperse colloidal rod suspensions

Orientation and relaxation dynamics of rod-like colloids under flow govern the optical and mechanical properties of many emerging soft materials. In polydisperse suspensions, particles of different lengths exhibit distinct rotational diffusion timescales, yet how this polydispersity influences relaxation following flow cessation remains unclear. In particular, it is not well understood how the pre-shear rate determines the subsequent orientation relaxation dynamics. To address this question, we performed simple shear on dilute cellulose nanocrystal (CNC) suspensions in a narrow-gap Taylor-Couette cell and measured birefringence relaxation after flow cessation using high-speed polarization imaging. To interpret the experiments, we formulated a polydisperse Fokker-Planck model parameterized by the measured length distribution. As a result, the average orientation relaxation time systematically decreases with increasing pre-shear rate. Moreover, when organized by the Péclet number based on the rotational diffusion coefficient of the weighted average rod length, the data agree well with the theory over a wide range of shear rates. This trend arises because the rod sub-population contributing most strongly to the orientation shifts from longer rods to shorter rods as the pre-shear rate increases, showing that the flow history governs the orientation relaxation dynamics. In polydisperse systems, the orientation relaxation time is no longer a material-specific constant but is determined by both the flow conditions and the polydispersity. This study provides a quantitative framework for understanding orientation dynamics in polydisperse rod suspensions and for interpreting rheo-optical measurements.

cond-mat.soft↗

arXiv2025

Transport of spherical microparticles in a 3D vortex flow

Particles are common in biological and environmental flows and are widely used in industrial and pharmaceutical applications. Their motion and flow dynamics are strongly affected by interactions with the surrounding flow structure. While particle-flow interactions have been extensively studied in low Reynolds number (Re) flows as well as in fully developed turbulence, the transport mechanisms of these particles in intermediate flow regimes remain less explored. Here, we investigate the response of neutrally buoyant spherical particles to a single vortex flow field. Using a microfluidic cross-slot geometry, we generate a well-characterized, stationary, three-dimensional streamwise vortex at moderate $\text{Re}$ ($\sim 50$). Our experimental results, supported by numerical simulations, show that with increasing particle diameter, they are progressively excluded from the vortex core. Initially, small particles follow a Burgers vortex-like self-similar motion, but for larger particle diameters, deviations from this trend emerge due to fluid inertia and finite-size effects. These findings enhance our understanding of particle dynamics in vortical flows and have implications for microfluidic applications involving particle sorting and separation.

physics.flu-dyn↗

arXiv2025

Colloidal rod dynamics under large amplitude oscillatory extensional flow

We perform a combined experimental and theoretical investigation of the orientational dynamics of rod-like colloidal particles in dilute suspension as they are subjected to a time-dependent homogeneous planar elongational flow. Our experimental approach involves the flow of dilute suspensions of cellulose nanocrystals (CNC) within a cross-slot-type stagnation point microfluidic device through which the extension rate is modulated sinusoidally over a wide range of Péclet number amplitudes ($Pe_0$) and Deborah numbers ($De$). The time-dependent orientation of the CNC is assessed via quantitative flow-induced birefringence measurements. For small $Pe_0 \lesssim 1$ and small $De \lesssim 0.03$, the birefringence response is sinusoidal and in phase with the strain rate, i.e., the response is linear. With increasing $Pe_0$, the response becomes non-sinusoidal (i.e., nonlinear) as the birefringence saturates due to the high degree of particle alignment at higher strain rates during the cycle. With increasing $De$, the CNC rods have insufficient time to respond to the rapidly changing strain rate, leading to asymmetry in the birefringence response around the minima and a residual effect as the strain rate passes through zero. These varied dynamical responses of the rod-like CNC are captured in a detailed series of Lissajous plots of the birefringence versus the strain rate. Experimental measurements are compared with simulations performed on both monodisperse and polydisperse systems, with rotational diffusion coefficients $D_r$ matched to the CNC. A semiquantitative agreement is found for simulations of a polydisperse system with $D_r$ heavily weighted to the longest rods in the measured CNC distribution. The results will be valuable for understanding, predicting, and optimizing the orientation of rod-like colloids during transient processing flows such as fiber spinning and film casting.

cond-mat.soft↗

arXiv2025

Capillary-driven thinning of DNA solutions

Capillary thinning of polymeric fluids is central to biological and industrial processes, yet the mechanisms governing thinning dynamics remain unresolved, especially for semi-flexible polymers. Using ideal solutions of semi-flexible DNA, we validate a predictive model for exponential capillary thinning that accounts for each polymer in the molecular weight distribution. For semi-flexible polymers, self-selection of the exponential time constant occurs by a fundamentally different mechanism than for highly flexible systems, and is not simply governed by the longest polymer relaxation time.

cond-mat.soft↗

arXiv2025

Large Amplitude Oscillatory Extension (LAOE) of dilute polymer solutions

This study presents an experimental framework for large amplitude oscillatory extension (LAOE) to investigate nonlinear material properties of complex fluids. Using a microfluidic optimized shape cross-slot extensional rheometer, we generate approximately homogeneous planar extensional flows driven by programmable syringe pumps operating in oscillatory or pulsatile sinusoidal modes. Micro-particle image velocimetry and simultaneous pressure drop measurements are employed to analyze the time-dependent flow field and elastic stress response. For Newtonian fluids, a linear relationship between the applied strain rate and pressure drop is observed across a wide range of oscillation amplitudes and frequencies. In contrast, dilute polymer solutions exhibit significant deviations, with excess pressure drops and divergence between average strain rates along extension and compression axes during the LAOE cycle. By spanning a broad range of Weissenberg and Deborah numbers, we identify unique Lissajous curves and critical conditions for the onset of nonlinearities under oscillatory extension. Numerical simulations, assuming homogeneous flow, underpin the experimental findings, validating the robustness of our microfluidic approach. This study demonstrates the utility of oscillatory extensional flows for probing the nonlinear rheological behavior of soft materials, offering quantitative insights into their extensional properties under nonlinear flow conditions.

physics.flu-dyn↗

arXiv2024

Stagnation points at grain contacts generate an elastic flow instability in 3D porous media

Many environmental, energy, and industrial processes involve the flow of polymer solutions in three-dimensional (3D) porous media where fluid is confined to navigate through complex pore space geometries. As polymers are transported through the tortuous pore space, elastic stresses accumulate, leading to the onset of unsteady flow fluctuations above a threshold flow rate. How does pore space geometry influence the development and features of this elastic instability? Here, we address this question by directly imaging polymer solution flow in microfabricated 3D ordered porous media with precisely controlled geometries consisting of simple-cubic (SC) or body-centered cuboid (BC) arrays of spherical grains. In both cases, we find that the flow instability is generated at stagnation points arising at the contacts between grains rather than at the polar upstream/downstream grain surfaces, as is the case for flow around a single grain. The characteristics of the flow instability are strongly dependent on the unit cell geometry: in SC packings, the instability manifests through the formation of time-dependent, fluctuating 3D eddies, whereas in BC packings, it manifests as continual fluctuating 'wobbles' and crossing in the flow pathlines. Despite this difference, we find that characteristics of the transition from steady to unsteady flow with increasing flow rate have commonalities across geometries. Moreover, for both packing geometries, our data indicate that extensional flow-induced polymeric stresses generated by contact-associated stagnation points are the primary contributor to the macroscopic resistance to flow across the entire medium. Altogether, our work highlights the pivotal role of inter-grain contacts -- which are typically idealized as discrete points and therefore overlooked, but are inherent in most natural and engineered media -- in shaping elastic instabilities in porous media.

physics.flu-dyn↗

arXiv2024

The interplay of plasticity and elasticity in elastoviscoplastic flows in wavy channels

Elastoviscoplastic (EVP) fluids, which exhibit both solid-like and liquid-like behavior depending on the applied stress, are critical in industrial processes involving complex geometries such as porous media and wavy channels. In this study, we investigate how flow characteristics and channel design affect EVP fluid flow through a wavy channel, using numerical simulations supported by microfluidic experiments. Our results reveal that elasticity significantly influences flow dynamics, reducing pressure drops and expanding unyielded regions. Notably, we find that even minimal elasticity can shift the flow from steady to time-dependent regimes, a transition less pronounced in viscoelastic fluids. Additionally, we show that the development of stagnation regions can be prevented when using a modified EVP fluid with enhanced elasticity, thus providing a full global yielding of the material. This study elucidates the role of elasticity in modifying flow patterns and stress distribution within EVP fluids, offering insights into the optimization of industrial applications, such as the displacement of yield stress fluids in enhanced oil recovery, gas extraction, cementing, and other processes where flow efficiency is critical.

physics.flu-dyn↗

arXiv2024

Effects of polydispersity and concentration on elastocapillary thinning of dilute polymer solutions

The thinning of liquid bridges under capillary stress occurs in widespread processes like jetting, dripping, and spraying, and creates a strong extensional flow capable of stretching dissolved polymers. If the elastic stress exceeds the viscous stress, an exponential `elastocapillary' (EC) thinning regime arises, yielding a timescale $τ_{EC}$ commonly considered to be the longest relaxation time of the polymer $λ$. A longstanding question is why $τ_{EC}$ depends on the polymer concentration, even at high dilutions where $λ$ should be constant in theory. To date this is understood in terms of intermolecular interactions that arise as polymers stretch. However, we show how the concentration dependence of $τ_{EC}$ can be explained by considering the molecular weight distribution (MWD) inherent in real polymer samples. We demonstrate this by blending low-$M$ and high-$M$ polymer samples with narrow MWDs at dilute concentrations and in different proportions, and by measuring $τ_{EC}$ for each blend in capillary thinning experiments. A simple model qualitatively reproduces the experimental results, showing how elastic stresses generated by the polymer build up prior to the EC regime due to sequential stretching of decreasing molecular weight species in the MWD. Since the elastic stress generated by each species depends on its concentration, the fraction of the MWD that is required to stretch in order to induce the EC regime depends on the total polymer concentration $c$. For higher $c$ the EC regime is induced by stretching of a higher-$M$ (longer $λ$) fraction of the MWD, and results in a longer measurement of $τ_{EC}$. Our results have significant implications for the application of capillary thinning measurements to extensional rheometry, for the interpretation of such measurements, and for the understanding of elastocapillary thinning dynamics in general.

cond-mat.soft↗

arXiv2024

From yield stress to elastic instabilities: Tuning the extensional behavior of elastoviscoplastic fluid

In this study, we delve into the intricacies of elastoviscoplastic (EVP) fluids, particularly focusing on how polymer additives influence their extensional behavior. Our findings reveal that polymer additives significantly alter the extensional properties of the EVP fluids, such as relaxation time and extensional stresses, while having negligible impact on the shear rheology. Interestingly, the modified fluids exhibit a transition from yield stress-like behavior to viscoelastic-like behavior under high extensional rates, ultimately leading to destabilization under extreme deformation. This research enhances the fundamental understanding of EVP fluids and highlights potential advancements in applications, especially in precision-demanding fields like 3D printing.

physics.flu-dyn↗

arXiv2024

How do polymers stretch in capillary-driven extensional flows?

Measurements of the capillary-driven thinning and breakup of fluid filaments are widely used to extract extensional rheological properties of complex materials. For viscoelastic (e.g., polymeric) fluids, the determination of the longest relaxation time depends on several assumptions concerning the polymeric response to the flow that are derived from constitutive models. Our capillary thinning experiments using polymeric fluids with a wide range of extensibility, suggest that these assumptions are likely only valid for highly extensible polymers but do not hold in general. For polymers with relatively low extensibility, such as polyectrolytes in salt-free media, conventional extrapolation of the longest relaxation time from capillary thinning techniques leads to a significant underestimation.

cond-mat.soft↗

arXiv2023

Extensibility governs the flow-induced alignment of polymers and rod-like colloids

Polymers and rod-like colloids (PaRC) adopt a favorable orientation under sufficiently strong flows. However, how the flow kinematics affect the alignment of such nanostructures according to their extensibility remains unclear. By analysing the shear- and extension-induced alignment of chemically and structurally different PaRC, we show that extensibility is a key determinant of the structural response to the imposed kinematics. We propose a unified description of the effectiveness of extensional flow, compared to shearing flow, at aligning PaRC of different extensibility.

cond-mat.soft↗

arXiv2023

Extensional rheometry of mobile fluids. Part II: Comparison between the uniaxial, planar and biaxial extensional rheology of dilute polymer solutions using numerically-optimized stagnation point microfluidic devices

In Part I of this paper [Haward et al. submitted (2023)], we presented a new three-dimensional microfluidic device (the optimized uniaxial and biaxial extensional rheometer, OUBER) for generating near-homogeneous uniaxial and biaxial elongational flows. In this Part II of the paper, we employ the OUBER device to examine the uniaxial and biaxial extensional rheology of some model dilute polymer solutions. We also compare the results with measurements made under planar extension in the optimized-shape cross-slot extensional rheometer [or OSCER, Haward et al. Phys. Rev. Lett. (2012)]. In each case (uniaxial, planar and biaxial extension), we use micro-particle image velocimetry to measure the extension rate as a function of the imposed flow rate, and we measure the excess pressure drop across each device in order to estimate the tensile stress difference generated in the fluid. We present a new analysis, based on solving the macroscopic power balance for flow through each device, to refine the estimate of the tensile stress difference obtained from the measured pressure drop. Based on this analysis, we find that for our most dilute polymer sample, which is "ultradilute", the extensional viscosity is well described by the finitely extensible non-linear elastic dumbbell model. In this limit, the biaxial extensional viscosity at high Weissenberg numbers (Wi) is half that of the uniaxial and planar extensional viscosities. At higher polymer concentrations, the experimental measurements deviate from the model predictions, which is attributed to the onset of intermolecular interactions as polymers unravel in the extensional flows. Of practical significance (and fundamental interest), elastic instability occurs at a significantly lower Wi in uniaxial extensional flow than in either biaxial or planar extensional flow, limiting the utility of this flow type for extensional viscosity measurement.

physics.flu-dyn↗

arXiv2023

Extensional rheometry of mobile fluids. Part I: OUBER, an optimized uniaxial and biaxial extensional rheometer

We present a numerical optimization of a "6-arm cross-slot" device, yielding several three-dimensional shapes of fluidic channels designed to impose close approximations to ideal uniaxial (or biaxial) stagnation point extensional flow under the constraints of having four inlets and two outlets (or two inlets and four outlets) and Newtonian creeping flow conditions. Of the various numerically-generated geometries, one is selected as being most suitable for fabrication at the microscale, and numerical simulations with the Oldroyd-B and Phan-Thien and Tanner models confirm that the optimal flow fields in the chosen geometry are observed for both constant viscosity and shear thinning viscoelastic fluids. Fabrication of the geometry, which we name the optimized uniaxial and biaxial extensional rheometer (OUBER), is achieved with high precision at the microscale by selective laser-induced etching of a fused-silica substrate. Employing a viscous Newtonian fluid with a refractive index matched to that of the optically transparent microfluidic device, we conduct microtomographic-particle image velocimetry in order to resolve the flow field at low Reynolds number (< 0.1) in a substantial volume around the stagnation point. The flow velocimetry confirms the accurate imposition of the desired and predicted flows, with pure extensional flow at an essentially uniform deformation rate being applied over a wide region around the stagnation point. In Part II of this paper [Haward et al., J. Rheol. submitted (2023)], pressure drop measurements in the OUBER geometry will be used to assess the uniaxial and biaxial extensional rheometry of dilute polymeric solutions, in comparison to measurements made in planar extension using an optimized-shape cross-slot extensional rheometer (OSCER, Haward et al, Phys. Rev. Lett., 2012).

physics.flu-dyn↗

arXiv2022

Canopy elastic turbulence: spontaneous formation of waves in beds of slender microposts

In a viscoelastic flow over a microfluidic canopy of polymeric pillars, we report the spontaneous emergence of waves in the form of propagating regions of low flow velocity compared to the surrounding flow. The occurrence of the wave is chaotic and shows characteristics of elastic turbulence. We systematically study the coupling between the low velocity wave and the microfluidic canopy by combining flow velocimetry experiments and high speed tracking of the pillars. The waves form an angle $β$ with the primary flow direction that depends on the geometry of the pillar array. If the canopy is composed of flexible structures, the passage of a wave deflects the structures locally in a manner reminiscent of the emergence of the Monami waves observed in inertial turbulence over canopies of vegetation. Due to the analogies with classical (inertial) canopy turbulence, we name our newly-observed phenomenon as canopy elastic turbulence.

physics.flu-dyn↗