arXiv subjects

Donald L. Koch

Publications and source records attributed to Donald L. Koch.

18 recordsLinked to original sources

arXiv2026

Probing the many-body energy landscape of a soft glass with graph neural networks

Many-body interactions govern the complex behavior of many amorphous materials, from metallic glasses to biological tissues, yet are often replaced by pairwise additive frameworks for computational efficiency. Here, we use classical density functional theory (DFT) to study a model soft glass of solvent-free polymer-grafted nanoparticles (PGNs), where the absence of solvent forces grafted chains to uniformly fill the interstitial space, generating strong angular-dependent many-body interactions between the cores. We show that NequIP, an equivariant message-passing graph neural network (GNN), predicts the equilibrium states with DFT-level accuracy, despite being trained only on high-energy, out-of-equilibrium configurations. Systematic analysis of GNN hyperparameters offers physical insights into the range, anisotropy, and effective body order of interactions. GNN-driven Monte Carlo simulations recover equilibrium structures in agreement with experiments and reveal locally favored icosahedral-like structures. Our results position machine-learned potentials as a tool for probing many-body glass physics beyond atomistic settings.

cond-mat.dis-nn↗

arXiv2026

Collision efficiency of rapidly settling particle pairs in a turbulent flow

We investigate the collision dynamics of hydrodynamically interacting inertialess spherical particle pairs sedimenting in a homogeneous isotropic turbulent flow. The analysis focuses on the rapid-settling limit, in which the particle settling time across a Kolmogorov eddy is much shorter than the Kolmogorov time scale. We also consider continuum breakdown during lubrication interactions, which is important when the separation the particles is comparable to the $O(100)$ nm mean-free path of a gaseous media. Owing to the sub-Kolmogorov particle sizes considered here, we approximate the local flow field in the vicinity of a particle pair as a stochastic linear flow induced by the background turbulence. In the rapid-settling regime, the cumulative effect of turbulent strain fluctuations is weak, and the relative particle motion may therefore be described as a diffusive process. In addition, hydrodynamic interactions generate a net relative drift between the particle pairs. We obtain the hydrodynamic diffusivity and relative drift velocity from the Lagrangian autocorrelation function of the fluid velocity gradient evaluated along the settling trajectory. The rapid-settling assumption further enables us to relate the autocorrelation function to the turbulence energy spectrum. Using these results, we solve the advection-diffusion equation for the pair probability density function to determine the collision rate. We show that the ideal collision rate increases monotonically with increasing relative strength of gravity to turbulence, whereas the collision efficiency decreases monotonically over the same range.

physics.flu-dyn↗

arXiv2026

An inertial slender-body theory

We present a fully inertial slender-body theory (SBT) that incorporates the effect of fluid inertia on the scale of the length (the "outer" region) as well as the characteristic diameter (the "inner" region) of a steadily translating slender particle. This is achieved by matching the solution of the quasi-two-dimensional full Navier-Stokes equations in the inner region to an outer solution that consists of a superposition of a solution of the linearized Navier-Stokes equations driven by a line of forces and a potential flow solution driven by a line distribution of sources and source dipoles. The drag and lift forces result from the distribution of Oseen force singularities. These Oseenlets also predominantly govern the torque at small Reynolds numbers and large aspect ratios. However, the potential flow singularities play a crucial role in yielding a torque that grows with increasing Reynolds number at large Reynolds numbers and finite aspect ratios. By comparing the forces and torque on the steadily translating particle with those obtained from a finite difference Navier-Stokes solution, we demonstrate the accuracy of the resulting inertial SBT for $\mathrm{Re}_D$ up to 10, where $\mathrm{Re}_D$ is the Reynolds number based on the smallest dimension, i.e., the characteristic cross-sectional diameter of the slender particle.

physics.flu-dyn↗

arXiv2026

Simulating the swimming motion of a flagellated bacterium in a microstructured bio-fluid

We develop a numerical framework to simulate the locomotion of a flagellated bacterium with a spheroidal head (such as Escherichia coli) in biological fluids like mucus, which are entangled polymer solutions exhibiting elasto-viscoplastic (EVP) rheology and porous microstructure. To account for the scale disparity between the large bacterial head and the slender flagellar bundle, whose thickness is comparable to the pore size, we employ a two-fluid model in which the bundle directly drives the solvent and exchanges momentum with the polymer phase via drag proportional to their relative velocity. The numerical implementation combines a finite-difference discretization of the two-fluid equations with a slender-body theory (SBT) to model flagellar forcing. A key observation is that the coupled mass and momentum equations for these inertialess flows, together with SBT, are linear in the pressure and velocity fields and in the force distribution along the flagellar bundle. By treating the polymer stress as a body force, we decompose the flow field and hydrodynamic moments into three additive contributions: kinematic (motion), flagellar forcing, and polymer stress. This decomposition allows several components of the flow to be precomputed and enables the determination of swimming velocity via a resistivity formulation driven by polymer-induced forces, which greatly improves computational efficiency during transient calculations of the polymer stress and the resulting flow. We validate the method and use it to analyze how polymer microstructure and its interactions with the bacterial head and tail affect motility in complex biofluids.

physics.flu-dyn↗

arXiv2025

Stress analysis of dilute particle suspensions in non-Newtonian fluids with efficient evaluation in the weakly non-Newtonian limit

We present a semi-analytical framework to compute the suspension stress in dilute particle-laden non-Newtonian fluids, separating Newtonian and non-Newtonian contributions. The ensemble-averaged stress includes both the particle-induced non-Newtonian stress (PINNS) and an interaction stresslet arising from surface tractions due to the non-Newtonian stress and its induced Newtonian flow. Using a generalized reciprocal theorem, we express this interaction stresslet entirely in terms of the non-Newtonian stress, for a general constitutive model. For weakly non-Newtonian fluids, a regular perturbation expansion combined with the method of characteristics yields all leading-order stress contributions from the Newtonian velocity field alone, avoiding the need to solve coupled partial differential equations. This generalizes the method of Koch et al. (Phys. Rev. Fluids 1, 013301 (2016)) beyond polymeric fluids to any weakly non-Newtonian medium driven by velocity and its gradients. We apply the method to two systems: (i) spheres suspended in a fluid of smaller spheroids, where the interaction stress becomes negative for sufficiently anisotropic shapes due to orientation misalignment of the spheroids; and (ii) suspensions in weakly anisotropic nematic liquid crystals. In the latter, assuming a uniform director field fixed by an external field, PINNS vanishes while interaction stresslets remain, either opposing or enhancing background anisotropic stress. These results demonstrate the utility of our framework in capturing first-order particle-microstructure interactions across a broad class of non-Newtonian fluids.

cond-mat.soft↗

arXiv2025

Extensional rheology of dilute suspensions of spheres in polymeric liquids

The extensional rheology of dilute suspensions of spheres in viscoelastic or polymeric liquids is studied computationally. At low polymer concentration (c) and Deborah number (De), a wake of highly stretched polymers forms downstream of the particles due to larger local velocity gradients than the imposed flow, indicated by a positive deviation in local De. This increases the suspension's extensional viscosity with time and De for De less than 0.5. When De exceeds 0.5 (the coil-stretch transition), the fully stretched polymers from the far field collapse in regions with lower local velocity gradients around the particle's stagnation points, reducing suspension viscosity relative to the polymer-only liquid. The interaction between local flow and polymers intensifies with increasing c. Highly stretched polymers impede local flow, reducing local De, while it increases in regions with collapsed polymers. Initially, increasing c aligns local De and polymer stretch with far-field values, diminishing particle-polymer interaction effects. However, beyond a certain c, a new mechanism emerges. At low c, fluid three particle radii upstream exhibits increased local De, stretching polymers beyond their undisturbed state. As c increases, this deviation becomes negative, collapsing polymers and resulting in increasingly negative stress from particle-polymer interactions at large De and time. At high c, this negative interaction stress scales as c squared, surpassing the linear increase in polymer stress, making dilute sphere suspensions more effective at reducing the viscosity of viscoelastic liquids at larger De and c.

physics.flu-dyn↗

arXiv2025

Sedimentation and shear-induced dynamics of spheroids in fluids with spatial viscosity variations

A generalized reciprocal theorem is used to relate the force and torque induced on a particle in an inertia-less fluid with small variation in viscosity to integrals involving Stokes flow fields and the spatial dependence of viscosity. These resistivity expressions are analytically evaluated using spheroidal harmonics and then used to obtain the mobility of the spheroid during sedimentation, and in linear flows, of a fluid with linear viscosity stratification. The coupling between the rotational and translational motion induced by stratification rotates the spheroid's centerline, creating a variety of rotational and translational dynamics dependent upon the particle's aspect ratio, $κ$, and the component of the stratification unit vector in the gravity direction, $d_g$. Spheroids with $0.55\lessapproxκ\lessapprox2.0$ exhibit the largest variety of settling behaviors. Interestingly, this range covers most microplastics and typical microorganisms. One of the modes include a stable orientation dependent only on $κ$ and $d_g$, but independent of initial orientation, thus allowing for the potential control of settling angles and sedimentation rates. In a simple shear flow, cross-streamline migration occurs due to the stratification-induced force generated on the particle. Similarly, a particle no longer stays at the stagnation point of a uniaxial extensional flow. While fully analytical results are obtained for spheroids, numerical simulations provide a source of validation. These simulations also provide additional insights into the stratification-induced force- and torque-producing mechanisms through the stratification-induced stress, which is not accessed in the reciprocal theorem-based analytical calculations.

physics.flu-dyn↗

arXiv2024

A swimming bacterium in a two-fluid model of a polymer solution

We analyse the motion of a flagellated bacterium in a two-fluid medium using slender body theory. The two-fluid model is useful for describing a body moving through a complex fluid with a microstructure whose length scale is comparable to the characteristic scale of the body. This is true for bacterial motion in biological fluids (entangled polymer solutions), where the entanglement results in a porous microstructure with typical pore diameters comparable to or larger than the flagellar bundle diameter but smaller than the diameter of the bacterial head. Thus the polymer and solvent satisfy different boundary conditions on the flagellar bundle and move with different velocities close to it. This gives rise to a screening length $L_B$ within which the fluids exchange momentum and the relative velocity between the two fluids decays. In this work, both the solvent and polymer of the two-fluid medium are modeled as Newtonian fluids with different viscosities $μ_s$ and $μ_p$ (viscosity ratio $λ= μ_p/μ_s$), thereby capturing the effects solely introduced by the microstructure of the complex fluid. From our calculations, we observe an increased drag anisotropy for a rigid, slender flagellar bundle moving through this two-fluid medium, resulting in an enhanced swimming velocity of the organism. The results are sensitive to the interaction between the bundle and the polymer and we discuss two physical scenarios corresponding to two types of interaction. Our model provides an explanation for the experimentally observed enhancement of swimming velocity of bacteria in entangled polymer solutions and motivates further experimental investigations.

physics.flu-dyn↗

arXiv2023

Finite difference method in prolate spheroidal coordinates for freely suspended spheroidal particles in linear flows of viscous and viscoelastic fluids

A finite difference scheme is used to develop a numerical method to solve the flow of an unbounded viscoelastic fluid with zero to moderate inertia around a prolate spheroidal particle. The equations are written in prolate spheroidal coordinates, and the shape of the particle is exactly resolved as one of the coordinate surfaces representing the inner boundary of the computational domain. As the prolate spheroidal grid is naturally clustered near the particle surface, good resolution is obtained in the regions where the gradients of relevant flow variables are most significant. This coordinate system also allows large domain sizes with a reasonable number of mesh points to simulate unbounded fluid around a particle. Changing the aspect ratio of the inner computational boundary enables simulations of different particle shapes ranging from a sphere to a slender fiber. Numerical studies of the latter particle shape allow testing of slender body theories. The mass and momentum equations are solved with a Schur complement approach allowing us to solve the zero inertia case necessary to isolate the viscoelastic effects. The singularities associated with the coordinate system are overcome using L'Hopital's rule. A straightforward imposition of conditions representing a time-varying combination of linear flows on the outer boundary allows us to study various flows with the same computational domain geometry. {For the special but important case of zero fluid and particle inertia we obtain a novel formulation that satisfies the force- and torque-free constraint in an iteration-free manner.} The numerical method is demonstrated for various flows of Newtonian and viscoelastic fluids around spheres and spheroids (including those with large aspect ratio). Good agreement is demonstrated with existing theoretical and numerical results.

physics.flu-dyn↗

arXiv2023

Rotation of a fiber in simple shear flow of a dilute polymer solution

The motion of a freely rotating prolate spheroid in a simple shear flow of a dilute polymeric solution is examined in the limit of large particle aspect ratio, $κ$. A regular perturbation expansion in the polymer concentration, $c$, a generalized reciprocal theorem, and slender body theory to represent the velocity field of a Newtonian fluid around the spheroid are used to obtain the $\mathcal{O}(c)$ correction to the particle's orientational dynamics. The resulting dynamical system predicts a range of orientational behaviors qualitatively dependent upon $c\cdot De$ ($De$ is the imposed shear rate times the polymer relaxation time) and $κ$ and quantitatively on $c$. At a small but finite $c\cdot De$, the particle spirals towards a limit cycle near the vorticity axis for all initial conditions. Upon increasing $κ$, the limit cycle becomes smaller. Thus, ultimately the particle undergoes a periodic motion around and at a small angle from the vorticity axis. At moderate $c\cdot De$, a particle starting near the flow-gradient plane departs it monotonically instead of spirally, as this plane (a limit cycle at smaller $c\cdot De$) obtains a saddle and an unstable node. The former is close to the flow direction. Upon further increasing $c\cdot De$, the saddle-node changes to a stable node. Therefore, depending upon the initial condition, a particle may either approach a periodic orbit near the vorticity axis or obtain a stable orientation near the flow direction. Upon further increasing $c\cdot De$, the limit cycle near the vorticity axis vanishes, and the particle aligns with the flow direction for all starting orientations.

physics.flu-dyn↗

arXiv2023

Orientation of Finite Reynolds Number Anisotropic Particles Settling in Turbulence

We present experimental and computational results for the orientation distributions of slender fibers and ramified particles settling in an isotropic turbulent flow. The rotational dynamics of the particles is modeled using a slender-body theory that includes the inertial torque due to sedimentation that tends to rotate the particles toward a broadside orientation. The particles are assumed to rotate due to viscous forces associated with the turbulent velocity gradients occurring on the particle length scale. In the simulations, the turbulence is obtained from a stochastic model of the velocity gradient in a Lagrangian reference frame. In the experiments, the turbulence is generated by active jets in a vertical water tunnel. It is well known that axisymmetric particles rotate according to Jeffery's solution for the rotation of a spheroidal particle if one adopts an appropriate effective aspect ratio. We show that the same result applies to a ramified particle consisting of three coplanar fibers connected with equal angles at a central point which rotates like a thin oblate spheroid. The orientation statistics can be quantified with a single non-dimensional parameter, the settling factor $S_F$, defined as the ratio of rotations due to sedimentation and turbulent shear. For low values of $S_F$, we observe nearly isotropically oriented particles, whereas particles become strongly aligned near the horizontal plane for high values of $S_F$. The variance of the angle away from horizontal scales as $S_F^{-2}$ for $S_F \gg 1$, but the orientation distribution is non-Gaussian due to turbulent intermittency in this limit.

physics.flu-dyn↗

arXiv2022

Electroconvective flow in presence of polyethylene glycol oligomer additives

Metal electrodeposition in batteries is fundamentally unstable and affected by different instabilities depending on operating conditions and chemical composition. Particularly at high charging rates, a hydrodynamic instability called electroconvection sets in that aggravates the situation by creating non-uniform ion flux and preferential deposition at the electrode. Here, we experimentally investigate how oligomer additives interact with the hydrodynamic instability at a cation selective interface. From electrochemical measurements and direct visualization experiments, we find that electroconvection is delayed and suppressed at all voltage in the presence of oligomers. Our results also reveal that it is important to consider the role of polymers at the interface, in addition to their bulk effects, to understand the stabilization effect and its mechanism.

physics.flu-dyn↗

arXiv2022

Suppression of electroconvection due to van der Waals attraction of polymer additives towards the metal electrode

Electroconvection in rechargeable batteries enhances the growth of dendrites at the electrode surface. The addition of low molecular weight polymers to the electrolyte in batteries results in the formation of a thin layer of higher polymer concentration near the electrode. This is due to van der Waals forces of attraction between the metal electrode and the polymers dissolved in the electrolyte. The van der Waals forces act as a restoring body force on the electrolyte and oppose the growth of perturbations. Using linear stability analysis, we show that this force opposes electroconvective flow. This increases the critical voltage required for the onset of electroconvection.

physics.flu-dyn↗

arXiv2022

Steady state extensional rheology of a dilute suspension of spheres in a dilute polymer solution

We investigate the steady-state extensional rheology of a dilute suspension of spherical particles in a dilute polymer solution. For a particle-free polymeric fluid, in addition to the solvent viscosity, the extensional viscosity due to the polymers, $μ^\text{poly}$, contributes to the total non-dimensionalized extensional viscosity $1+μ^\text{poly}$. When a small volume fraction, $ϕ$, of spheres is added to a polymeric fluid, the stress is altered by the Einstein viscosity of 2.5$ϕ$ and two additional stress contributions: the interaction stresslet and the particle-induced polymer stress (PIPS). The net interaction stress is positive at lower Deborah numbers (product of extension rate and polymer relaxation time), $De\lesssim0.5$, and negative at large $De$. Relative to undisturbed flow, the presence of spheres in uniaxial extensional flow creates larger and smaller local stretching regions. Below the coil-stretch transition ($De<0.5$), the polymers far from the particles are in a coiled state, and a wake of stretched polymers forms downstream of the particle as they are stretched by the large stretching regions around the particle. This leads to a positive interaction stresslet (surface) and the PIPS (stretched wake). Beyond the coil-stretch transition, polymers far from the particle are highly stretched, but they collapse closer to the coiled state as they arrive at the low-stretching regions near the particle surface. Therefore, a negative PIPS results from the regions of collapsed polymers. When $De\gtrsim0.6$, the changes in extensional viscosity from the interaction stresslet and the PIPS are $ϕμ^\text{poly}$ and approximately -1.85$ϕμ^\text{poly}$, respectively. At large $De$, the polymer extensional viscosity, $μ^\text{poly}$, is large. Therefore, adding particles reduces the extensional viscosity of the suspension ($(2.5-0.85μ^\text{poly})ϕ<0$).

cond-mat.soft↗

arXiv2020

Suppression of Electroconvective and Morphological Instabilities by an Imposed Cross Flow of the Electrolyte

Electroconvection and its coupling with a morphological instability are important in many applications, including electrodialysis, batteries and fuel cells. In this work, we study the effects of a two-dimensional channel flow on the electroconvective and morphological instabilities using two approaches. In the bulk analysis, we consider the instability of the electroneutral bulk region driven by a second kind electroosmosis slip velocity boundary condition and derive the asymptotic solutions for small and large wavenumbers. In the full analysis, we consider the entire region of the liquid electrolyte and use the ultraspherical spectral method to numerically solve the eigenvalue problems. Both studies show that the imposed flow significantly affects the electroconvective instability. The imposed flow generates a shielding effect by deforming the perturbed ion concentration field and hinders the ion transfer from low- to high- concentration regions which causes the instability. It fully suppresses the electroconvective instability at small wavenumbers and reduces the growth rate of the perturbations at large wavenumbers. The direct effect of the flow on the morphological instability is minor, while the suppression of the electroconvective instability may change the wavenumber of the most unstable mode of the coupled instabilities. For the electroconvective instability, the bulk analysis is qualitatively different from the full analysis at high wavenumbers. For the morphological instability, good agreement is found between the two studies at both small and large wavenumbers.

physics.flu-dyn↗

arXiv2019

Slender body theory for particles with non-circular cross-sections

This paper presents a theory to obtain the force per unit length acting on a slender filament with a non-circular cross-section moving in a fluid at low Reynolds number. Using a regular perturbation of the inner solution, we show that the force per unit length has $O(1/ln(2A))$ + $O(α/ln^2(2A))$ contributions driven by the relative motion of the particle and the local fluid velocity and an $O(α/(ln(2A)A))$ contribution driven by the gradient in the imposed fluid velocity. Here, the aspect ratio ($A=l/a_0$) is defined as the ratio of the size of the particle ($l$) and the cross-sectional dimension ($a_0$); and $α$ is the amplitude of the non-circular perturbation. Using thought experiments, we show that two-lobed and three-lobed cross-sections affect the response to relative motion and velocity gradients, respectively. A two-dimensional Stokes flow calculation is used to extend the perturbation analysis to cross-sections that deviate significantly from a circle (i.e., $α\sim O(1)$). We demonstrate the ability of our method to accurately compute the resistance to translation and rotation of a slender triaxial ellipsoid. Furthermore, we illustrate novel dynamics of straight rods in a simple shear flow that translate and rotate quasi-periodically if they have two-lobed cross-section; and rotate chaotically and translate diffusively if they have a combination of two- and three-lobed cross-sections. Finally, we show the remarkable ability of our theory to accurately predict the motion of rings, retaining great accuracy for moderate aspect ratios ($\sim 10$) and cross-sections that deviate significantly from a circle, thereby making our theory a computationally inexpensive alternative to other Stokes flow solvers.

physics.flu-dyn↗

arXiv2018

Clustering of Rapidly Settling, Low-Inertia Particle Pairs in Isotropic Turbulence. I. Drift and Diffusion Flux Closures

In this two--part study, we present the development and analysis of a stochastic theory for characterizing the relative positions of monodisperse, low-inertia particle pairs that are settling rapidly in homogeneous isotropic turbulence. In the limits of small Stokes number and Froude number such that $Fr \ll St_η\ll 1$, closures are developed for the drift and diffusion fluxes in the probability density function (PDF) equation for the pair relative positions. The theory focuses on the relative motion of particle pairs in the dissipation regime of turbulence, i.e., for pair separations smaller than the Kolmogorov length scale. In this regime, the theory approximates the fluid velocity field in a reference frame following the primary particle as locally linear.

physics.flu-dyn↗

arXiv2018

Clustering of Rapidly Settling, Low-Inertia Particle Pairs in Isotropic Turbulence. II. Comparison of Theory and DNS

Part I of this study presented a stochastic theory for the clustering of monodisperse, rapidly settling, low-Stokes-number particle pairs in homogeneous isotropic turbulence. The theory involved the development of closure approximations for the drift and diffusion fluxes in the probability density function (PDF) equation for pair relative positions. In this Part II paper, the theory is quantitatively analyzed by comparing its predictions of particle clustering with data from direct numerical simulations (DNS) of isotropic turbulence containing particles settling under gravity. DNS were performed at a Taylor micro-scale Reynolds number $Re_λ= 77.76$ for three Froude numbers $Fr = \infty,~ 0.052,~ 0.006$. The Froude number $Fr$ is defined as the ratio of the Kolmogorov scale of acceleration and the magnitude of gravitational acceleration. Thus, $Fr = \infty$ corresponds to zero gravity, and $Fr = 0.006$ to the highest magnitude of gravity among the three DNS cases. For each $Fr$, particles of six Stokes numbers in the range $ 0.01 \le St_η\le 0.2$ were tracked in the DNS, and particle clustering quantified both as a function of separation and the spherical polar angle. %Here $St_η$~is the ratio of %the particle viscous relaxation time to the Kolmogorov time scale. We compared the DNS and theory values for the power-law exponent $β$ characterizing the dependence of clustering on separation. Reasonable agreement is seen between the DNS $β$'s for the $Fr = 0.006$ case and the theoretical predictions obtained using the second drift closure (referred to as DF2). Further, in conformity with the DNS, theory shows that the clustering of $St_η\ll 1$ particles is only weakly anisotropic.

physics.flu-dyn↗