arXiv subjects

Howard A. Stone

Publications and source records attributed to Howard A. Stone.

At least 55 records · Page 3Linked to original sources

arXiv2024

High-throughput measurement of elastic moduli of microfibers by rope coiling

There are many fields where it is of interest to measure the elastic moduli of tiny fragile fibers, such as filamentous bacteria, actin filaments, DNA, carbon nanotubes, and functional microfibers. The elastic modulus is typically deduced from a sophisticated tensile test under a microscope, but the throughput is low and limited by the time-consuming and skill-intensive sample loading/unloading. Here, we demonstrate a simple microfluidic method enabling the high-throughput measurement of the elastic moduli of microfibers by rope coiling using a localized compression, where sample loading/unloading are not needed between consecutive measurements. The rope coiling phenomenon occurs spontaneously when a microfiber flows from a small channel into a wide channel. The elastic modulus is determined by measuring either the buckling length or the coiling radius. The throughput of this method, currently 3,300 fibers per hour, is a thousand times higher than that of a tensile tester. We demonstrate the feasibility of the method by testing a nonuniform fiber with axially varying elastic modulus. We also demonstrate its capability for in situ inline measurement in a microfluidic production line. We envisage that high-throughput measurements may facilitate potential applications such as screening or sorting by mechanical properties and real-time control during production of microfibers.

cond-mat.soft↗

arXiv2023

Stochastic Theory of the Size Distribution of Raindrops

For over a century, raindrop size distributions have been a subject of extensive scientific study, typically described by models including the Marshall-Palmer exponential equation, gamma, Weibull, lognormal, and other mathematical functions. In this work, we present a theory that integrates deterministic principles from thermodynamics and fluid dynamics with stochastic elements to predict expected raindrop diameters and describe ground-level drop-size distributions. Importantly, our approach avoids assuming specific drop-size dispersion processes or relying on multi-variable empirical data fitting. We derive analytical equations for key raindrop parameters (e.g., median diameter, expected minimum and maximum diameters) and drop-size distributions as functions of rainfall intensity. Our theoretical predictions align well with extensive published experimental data, covering rainfall intensities from 0.4 to 40 mm/h across diverse global locations. Additionally, consistent with observations of super-large raindrops, our theory suggests a maximum ground-level raindrop diameter limit of around 10 mm. We establish analytical expressions for meteorological parameters like the Marshall-Palmer constant and total raindrop concentration, validated against empirical data. The theoretical approach presented here can find broad applications in climate modeling, sprays and aerosol dynamics, bubbles and particles, extraterrestrial rainfall, and paleoclimatology.

physics.flu-dyn↗

arXiv2023

Soft matter physics of the ground beneath our feet

Inspired by presentations by the authors during a workshop organized at the Princeton Center for Theoretical Science (PCTS) in January 2022, we present a perspective on some of the outstanding questions related to the "physics of the ground beneath our feet." These identified challenges are intrinsically shared with the field of Soft Matter but also have unique aspects when the natural environment is studied.

cond-mat.soft↗

arXiv2023

Anomalous crystalline ordering of particles in a viscoelastic fluid under high shear

Addition of particles to a viscoelastic suspension dramatically alters the properties of the mixture, particularly when it is sheared or otherwise processed. Shear-induced stretching of the polymers results in elastic stress that causes a substantial increase in measured viscosity with increasing shear, and an attractive interaction between particles, leading to their chaining. At even higher shear rates, the flow becomes unstable, even in the absence of particles. This instability makes it very difficult to determine the properties of a particle suspension. Here we use a fully immersed parallel plate geometry to measure the high-shear-rate behavior of a suspension of particles in a viscoelastic fluid. We find an unexpected separation of the particles within the suspension resulting in the formation of a layer of particles in the center of the cell. Remarkably, monodisperse particles form a crystalline layer which dramatically alters the shear instability. By combining measurements of the velocity field and torque fluctuations, we show that this solid layer disrupts the flow instability and introduces a new, single-frequency component to the torque fluctuations that reflects a dominant velocity pattern in the flow. These results highlight the interplay between particles and a suspending viscoelastic fluid at very high shear rates.

cond-mat.soft↗

arXiv2023

A note about convected time derivatives for flows of complex fluids

We present a direct derivation of the typical time derivatives used in a continuum description of complex fluid flows, harnessing the principles of the kinematics of line elements. The evolution of the microstructural conformation tensor in a flow and the physical interpretation of different derivatives then follow naturally.

physics.flu-dyn↗

arXiv2023

Non-Fickian macroscopic model of axial diffusion of granular materials in a long cylindrical tumbler

We provide new concepts for understanding transport phenomena in flows of granular materials by using a non-Fickian macroscopic model of axial diffusion of a granular material in a finite cylindrical tumbler. The model accounts for diffusion induced by particle collisions only in a thin surface flowing layer due to localization of shear within the cross-section of the drum. All model parameters are related to measurable quantities in a granular flow. It is shown that the proposed model is a member of the general class of linear constitutive relations with memory. An exact solution for the spreading of a finite-width pulse initial condition under the proposed non-Fickian model is derived and compared to the solution of a Fickian model (i.e., the ``classical'' diffusion equation).

cond-mat.soft↗

arXiv2023

Viscosity measurements of glycerol in a parallel-plate rheometer exposed to atmosphere

Glycerol is a hygroscopic fluid that spontaneously absorbs water vapor from the atmosphere. For applications involving glycerol, care must be taken to avoid exposure to humidity, since its viscosity decreases quickly as water is absorbed. We report experimental measurements of the viscosity of glycerol in a parallel-plate rheometer where the outer interface is exposed to atmosphere. The measurements decrease with time as water is absorbed from the atmosphere and transported throughout the glycerol via diffusion and advection. Measured viscosities drop faster at higher relative humidities, confirming the role of hygroscopicity on the transient viscosities. The rate of viscosity decrease shows a non-monotonic relationship with the rheometer gap height. This behavior is explained by considering the transition from diffusion-dominated transport in the narrow gap regime to the large gap regime where transport is dominated by inertia-driven secondary flows. Numerical simulations of the water absorption and transport confirm this non-monotonic behavior. The experimental viscosity measurements show unexpectedly fast decreases at very small gap heights, violating the parallel-plate, axisymmetric model. We propose that this drop-off may be due to misalignment in the rheometer that becomes non-negligible for small gaps. Theoretical considerations show that secondary flows in a misaligned rheometer dominate the typical secondary inertial flows in parallel-plate rheometers at small gaps. Finally, simulations in a misaligned parallel-plate system demonstrate the same sharp drop-off in viscosity measurements at small gap heights. This modeling can be used to estimate the gap height where misalignment effects dominate the transient glycerol viscosity measurements.

physics.flu-dyn↗

arXiv2022

Transport of a passive scalar in wide channels with surface topography

We generalize classical dispersion theory for a passive scalar to derive an asymptotic long-time convection-diffusion equation for a solute suspended in a wide, structured channel and subject to a steady low-Reynolds-number shear flow. Our theory, valid for small roughness amplitudes of the channel, holds for general surface shapes expandable as a Fourier series. We determine an anisotropic dispersion tensor, which depends on the characteristic wavelengths and amplitude of the surface structure. For surfaces whose corrugations are tilted with respect to the applied flow direction, we find that dispersion along the principal direction (i.e., the principal eigenvector of the dispersion tensor) is at an angle to the main flow direction and becomes enhanced relative to classical Taylor dispersion. In contrast, dispersion perpendicular to it can decrease compared to the short-time diffusivity of the particles. Furthermore, for an arbitrary surface shape represented in terms of a Fourier decomposition, we find that each Fourier mode contributes at leading order a linearly-independent correction to the classical Taylor dispersion tensor.

physics.flu-dyn↗

arXiv2022

Diffusiophoresis in the presence of a pH gradient

Diffusiophoresis is the spontaneous motion of particles under gradients of solutes. In electrolyte-driven diffusiophoresis, the zeta potential of the particles is an important surface property that characterizes diffusiophoretic mobility. However, the zeta potential is not a fixed material property and colloidal surfaces often show varying potentials depending on the physical chemistry of the surrounding fluid, e.g., solute type, ionic strength, and pH. In this article, we study experimentally and theoretically pH-dependent diffusiophoresis of polystyrene particles using a dead-end pore geometry. In particular, the influence of the isoelectric point (pI) on diffusiophoresis is demonstrated in the absence and presence of wall diffusioosmosis. Throughout the paper, we show with experiments and model calculations how the pH-dependent diffusiophoresis and diffusioosmosis influence the particle motion in dead-end pore configurations, including changes that occur when there is a sign change in the zeta potential near the pI.

cond-mat.soft↗

arXiv2022

Flow rate-pressure drop relation for deformable channels via fluidic and elastic reciprocal theorems

Viscous flows through configurations manufactured from soft materials apply both pressure and shear stress at the solid-liquid interface, leading to deformation of the cross-section, which affects the flow rate-pressure drop relation. Conventionally, calculating this flow rate-pressure drop relation requires solving the complete elastohydrodynamic problem, which couples the fluid flow and elastic deformation. In this work, we use the reciprocal theorems for Stokes flow and linear elasticity to derive a closed-form expression for the flow rate-pressure drop relation in deformable channels, bypassing the detailed calculation of the solution to the fluid-structure-interaction problem. For small deformations (under a domain perturbation scheme), our theory provides the leading-order effect, of the interplay between the fluid stresses and the compliance of the channel, on the flow rate-pressure drop relation. Our approach uses solely the fluid flow solution and the elastic deformation due to the fluid stress distribution in an undeformed channel, eliminating the need to solve the coupled elastohydrodynamic problem. Unlike previous theoretical studies that neglected the presence of lateral sidewalls and considered shallow geometries of effectively infinite width, our approach allows to determine the influence of confining sidewalls on the flow rate-pressure drop relation. For the flow-rate-controlled situation and the plate-bending theory for the elastic deformation, we show a trade-off between the effect of compliance of the deforming top wall and the drag due to sidewalls on the pressure drop. While increased compliance decreases the pressure drop, the effect of the sidewalls increases it. Our theoretical framework may provide insight into existing experimental data and pave the way for the design of novel optimized soft microfluidic configurations of different cross-sectional shapes.

physics.flu-dyn↗

arXiv2022

Microswimmers near corrugated, periodic surfaces

We explore hydrodynamic interactions between microswimmers and corrugated, or rough, surfaces, as found often in biological systems and microfluidic devices. Using the Lorentz reciprocal theorem for viscous flows we derive exact expressions for the roughness-induced velocities up to first order in the surface-height fluctuations and provide solutions for the translational and angular velocities valid for arbitrary surface shapes. We apply our theoretical predictions to elucidate the impact of a periodic, wavy surface on the velocities of microswimmers modeled in terms of a superposition of Stokes singularities. Our findings, valid in the framework of a far-field analysis, show that the roughness-induced velocities vary non-monotonically with the wavelength of the surface. For wavelengths comparable to the swimmer-surface distance a pusher can experience a repulsive contribution due to the reflection of flow fields at the edge of a surface cavity, which decreases the overall attraction to the wall.

cond-mat.soft↗

arXiv2022

Possible, Impossible, and Expected Diameters and Production Rates of Droplets in Aerosols and Sprays

Liquid atomization processes generating sprays and aerosols of droplets are used in many delivery and coating systems involving pure solvents, solutions, and suspensions. In our recent experimental work, we introduced a novel liquid atomization process generating micro-sprays and aerosols of submicron-diameter droplets for pure solvents, solutions, and suspensions: gas jets disintegrate thin liquid films that are formed as bubbles approach a liquid surface. Here we develop a theoretical description of droplet sizes and flow rates, using the first principles of conservation of mass and energy, and accounting for the ratios of specific energies and the ratios of specific energy rates provided by the atomizing gas and dissipated by the atomized liquid. We introduce atomization diagrams as a graphical tool to determine possible, impossible, and expected droplet diameters and specific flow rates in aerosols and sprays produced under various conditions. We find a reasonable agreement between the theory and experiments for five different liquids converted into aerosols of submicron-diameter droplets by an atomization process where gas jets disintegrate thin liquid films that are formed as bubbles approach a liquid surface, and also for five traditional pressure nozzles that produce sprays of droplets of hundreds of microns in diameter. Our study explored the overall range of Ohnesorge number between 0.01-100, and the analysis and atomization diagrams contribute to understanding of liquid atomization and can serve as a theoretical framework for comparing different liquid atomization techniques.

physics.flu-dyn↗

arXiv2021

Pressure-driven flow of the viscoelastic Oldroyd-B fluid in narrow non-uniform geometries: analytical results and comparison with simulations

We analyze the pressure-driven flow of a viscoelastic fluid in arbitrarily shaped, narrow channels and present a theoretical framework for calculating the relationship between the flow rate $q$ and pressure drop $Δp$. We utilize the Oldroyd-B model and first identify the characteristic scales and dimensionless parameters governing the flow in the lubrication limit. Employing a perturbation expansion in powers of the Deborah number ($De$), we provide analytical expressions for the velocity, stress, and the $q-Δp$ relation in the weakly viscoelastic limit up to $O(De^2)$. Furthermore, we exploit the reciprocal theorem derived by Boyko $\&$ Stone (Phys. Rev. Fluids, vol. 6, 2021, pp. L081301) to obtain the $q-Δp$ relation at the next order, $O(De^3)$, using only the velocity and stress fields at the previous orders. We validate our analytical results with two-dimensional numerical simulations of the Oldroyd-B fluid in a hyperbolic, symmetric contracting channel and find excellent agreement. For the flow-rate-controlled situation, both our theory and simulations reveal weak dependence of the velocity field on the Deborah number, so that the velocity can be approximated as Newtonian. In contrast to the velocity, the pressure drop strongly depends on the viscoelastic effects and decreases with $De$. Elucidating the relative importance of different terms in the momentum equation contributing to the pressure drop, we identify that a pressure drop reduction for narrow contracting geometries is primarily due to gradients in the viscoelastic shear stresses, while viscoelastic axial stresses have a minor effect on the pressure drop along the symmetry line.

physics.flu-dyn↗

arXiv2021

Perspectives on viscoelastic flow instabilities and elastic turbulence

Viscoelastic fluids are a common subclass of rheologically complex materials that are encountered in diverse fields from biology to polymer processing. Often the flows of viscoelastic fluids are unstable in situations where ordinary Newtonian fluids are stable, owing to the nonlinear coupling of the elastic and viscous stresses. Perhaps more surprisingly, the instabilities produce flows with the hallmarks of turbulence -- even though the effective Reynolds numbers may be $O(1)$ or smaller. We provide perspectives on viscoelastic flow instabilities by integrating the input from speakers at a recent international workshop: historical remarks, characterization of fluids and flows, discussion of experimental and simulation tools, and modern questions and puzzles that motivate further studies of this fascinating subject. The materials here will be useful for researchers and educators alike, especially as the subject continues to evolve in both fundamental understanding and applications in engineering and the sciences.

physics.flu-dyn↗

arXiv2021

A Geometric Criterion for the Optimal Spreading of Active Polymers in Porous Media

We perform Brownian dynamics simulations of active stiff polymers undergoing run-reverse dynamics, and so mimic bacterial swimming, in porous media. In accord with recent experiments of \emph{Escherichia coli}, the polymer dynamics are characterized by trapping phases interrupted by directed hopping motion through the pores. We find that the effective translational diffusivities of run-reverse agents can be enhanced up to two orders in magnitude, compared to their non-reversing counterparts, and exhibit a non-monotonic behavior as a function of the reversal rate, which we rationalize using a coarse-grained model. Furthermore, we discover a geometric criterion for the optimal spreading, which emerges when their run lengths are comparable to the longest straight path available in the porous medium. More significantly, our criterion unifies results for porous media with disparate pore sizes and shapes and thus provides a fundamental principle for optimal transport of microorganisms and cargo-carriers in densely-packed biological and environmental settings.

cond-mat.soft↗

arXiv2021

CO2-driven diffusiophoresis and water cleaning: Similarity solutions for predicting the exclusion zone in a channel flow

We investigate experimentally and theoretically diffusiophoretic separation of negatively charged particles in a rectangular channel flow, driven by CO2 dissolution from one side-wall. Since the negatively charged particles create an exclusion zone near the boundary where CO2 is introduced, we model the problem by applying a shear flow approximation in a two-dimensional configuration. From the form of the equations we define a similarity variable to transform the reaction-diffusion equations for CO2 and ions and the advection-diffusion equation for the particle distribution to ordinary differential equations. The definition of the similarity variable suggests a characteristic length scale for the particle exclusion zone. We consider height-averaged flow behaviors in rectangular channels to rationalize and connect our experimental observations with the model, by calculating the wall shear rate as functions of channel dimensions. Our observations and the theoretical model provide the design parameters such as flow speed, channel dimensions and CO2 pressure for the in-flow water cleaning systems.

physics.flu-dyn↗

arXiv2021

Low-Reynolds-number, bi-flagellated Quincke swimmers with multiple forms of motion

In the limit of zero Reynolds number (Re), swimmers propel themselves exploiting a series of non-reciprocal body motions. For an artificial swimmer, a proper selection of the power source is required to drive its motion, in cooperation with its geometric and mechanical properties. Although various external fields (magnetic, acoustic, optical, etc.) have been introduced, electric fields are rarely utilized to actuate such swimmers experimentally in unbounded space. Here we use uniform and static electric fields to demonstrate locomotion of a bi-flagellated sphere at low Re via Quincke rotation. These Quincke swimmers exhibit three different forms of motion, including a self-oscillatory state due to elasto-electro-hydrodynamic interactions. Each form of motion follows a distinct trajectory in space. Our experiments and numerical results demonstrate a new method to generate, and potentially control, the locomotion of artificial flagellated swimmers.

cond-mat.soft↗

arXiv2021

Perturbing ordinary differential equations to generate resonant and repeated root solutions

In the study of ordinary differential equations (ODEs) of the form $\hat{L}[y(x)]=f(x)$, where $\hat{L}$ is a linear differential operator, two related phenomena can arise: resonance, where $f(x)\propto u(x)$ and $\hat{L}[u(x)]=0$, and repeated roots, where $f(x)=0$ and $\hat{L}=\hat{D}^n$ for $n\geq 2$. We illustrate a method to generate exact solutions to these problems by taking a known homogeneous solution $u(x)$, introducing a parameter $ε$ such that $u(x)\rightarrow u(x;ε)$, and Taylor expanding $u(x;ε)$ about $ε= 0$. The coefficients of this expansion $\frac{\partial^k u}{\partialε^k}\big{|}_{ε=0}$ yield the desired resonant or repeated root solutions to the ODE. This approach, whenever it can be applied, is more insightful and less tedious than standard methods such as reduction of order or variation of parameters. While the ideas can be introduced at the undergraduate level, we could not find any elementary or advanced text that illustrates these ideas with appropriate generality.

math.CA↗