arXiv subjects

Eliot Fried

Publications and source records attributed to Eliot Fried.

At least 19 recordsLinked to original sources

arXiv2026

Compressible fluids with distinct mass and linear-momentum transport

We formulate a thermodynamically consistent continuum theory for compressible, viscous, heat-conducting fluids in which the velocity entering the balance of mass is distinguished from the specific linear momentum entering the balances of linear momentum and energy. Starting from balances of mass, linear momentum, angular momentum, and internal energy, together with a power identity and the Clausius--Duhem inequality, we derive the mechanical and thermodynamic consequences of allowing these fields to differ. From local angular-momentum balance, we show that the Cauchy stress need not be symmetric and we determine its skew part. From the dissipation inequality, we obtain an admissible internal-energy flux and a closure in which the relative transport between mass and linear momentum is proportional to the pressure gradient rather than to the mass-density gradient. We also derive a free-enthalpy imbalance across shocks and a reduced wall dissipation inequality for rigid, impermeable walls undergoing prescribed rigid motion, together with simple admissible wall laws for temperature-controlled and heat-flow-controlled settings. For ideal gases, we write the governing equations in conservative dimensionless form, recover the classical compressible Navier--Stokes--Fourier theory when relative transport vanishes, and identify a distinguished low-Mach regime in which mass transport and linear-momentum transport remain distinct at leading order.

physics.flu-dyn↗

arXiv2026

Direct laser writing of high aspect ratio nanochannels for nanofluidics

Nanochannels with high width-to-height aspect ratios are desirable for many applications, particularly those requiring optical access, but remain challenging to fabricate. In this work, the direct laser writing of such channels between diamond films and glass substrates is introduced. As previously reported, laser light can transform a portion of diamond film into a nanostrip. The strip induces delamination of the surrounding film, causing the formation of two nanochannels with triangular cross-sections. Here, it is demonstrated that nanochannels with rectangular cross-sections and width-to-height aspect ratios exceeding fifty can form between pairs of nanostrips. With atomic force microscopy, the maximum strip spacing that produces these nanochannels is investigated, and it is demonstrated that the reflectance of the channels can be measured by microspectrophotometry. The microstructure of the nanochannels, including nanostrips, and processes that occur during laser writing are inferred from transmission electron microscopy and electron energy loss spectroscopy. By fabricating a nanofluidic device and using microspectrophotometry, it is found that the nanochannels fill with water through capillary action, are resistant to clogging, and are mechanically stable against water filling. A versatile platform for producing high-aspect-ratio nanochannels that are optically accessible and fluidically functional is presented, thereby expanding opportunities for advanced applications.

physics.optics↗

arXiv2025

Construction of an isometric immersion of a bounded, planar region from a framed curve

We develop a framework for characterizing isometric immersions of simply connected, bounded, planar regions with piecewise smooth boundaries into three-dimensional space. Each immersion is associated with a framed curve along the boundary of the image surface, comprised by a parametrized curve and a unit normal vector. We identify a set of compatibility and regularity conditions on this framed curve that ensure the existence of a $C^1$ isometric immersion that is $C^2$ almost everywhere and possesses finite bending energy. Under these conditions, we derive an exact dimensional reduction of the bending energy to a line integral over the boundary curve, without relying on asymptotic assumptions or approximations. By analyzing the behavior of the unit normal vector along the framed boundary, we distinguish between planar and curved regions of the immersed surface. We identify the geometric conditions under which global $C^2$ regularity is potentially lost, in which case the associated immersion belongs to $W^{2,2}$ -- a Sobolev space that arises naturally in variational models of unstretchable elastic surfaces.

math.DG↗

arXiv2025

Probing growth precursor diffusion lengths by inter-surface diffusion

Understanding and optimizing thin-film synthesis requires measuring the diffusion length $d_\alpha$ of adsorbed growth precursors. Despite technological advances, in-situ measurements of $d_\alpha$ are often unachievable due to harsh deposition conditions, such as high temperatures or reactive environments. In this paper, we propose a fitting approach to determine $d_\alpha$ from experimental data by leveraging inter-surface diffusion between a substrate and a strip obtained by, for example, processing a film. The substrate serves as a source or sink of precursors, influencing the growth dynamics and shaping the profile of the strip. By fitting simulated profiles to given profiles, we demonstrate that $d_\alpha$ can be determined. To achieve this, we develop a theoretical growth model, a simulation strategy, and a fitting procedure. The growth model incorporates inter-surface diffusion, adsorption, and desorption of growth precursors, with growth being proportional to the concentration of adsorbed precursors. In our simulations, a chain of nodes represents a profile, and growth is captured by the displacement of those nodes, while keeping the node density approximately constant. For strips significantly wider than $d_\alpha$, a scaled precursor concentration and $d_\alpha$ are the fitting parameters that are determined by minimizing a suitably defined measure of the distance between simulated and given profiles. We evaluate the robustness of our procedure by analyzing the effect of profile resolution and noise on the fitted parameters. Our approach can offer valuable insights into thin-film growth processes, such as those occurring during plasma-enhanced chemical vapor deposition.

cond-mat.mtrl-sci↗

arXiv2024

Derivation, characterization, and application of complete orthonormal sequences for representing general three-dimensional states of residual stress

Residual stresses are self-equilibrated stresses on unloaded bodies. Owing to their complex origins, it is useful to develop functions that can be linearly combined to represent any sufficiently regular residual stress field. In this work, we develop orthonormal sequences that span the set of all square-integrable residual stress fields on a given three-dimensional region. These sequences are obtained by extremizing the most general quadratic, positive-definite functional of the stress gradient on the set of all sufficiently regular residual stress fields subject to a prescribed normalization condition; each such functional yields a sequence. For the special case where the sixth-order coefficient tensor in the functional is homogeneous and isotropic and the fourth-order coefficient tensor in the normalization condition is proportional to the identity tensor, we obtain a three-parameter subfamily of sequences. Upon a suitable parameter normalization, we find that the viable parameter space corresponds to a semi-infinite strip. For a further specialized spherically symmetric case, we obtain analytical expressions for the sequences and the associated Lagrange multipliers. Remarkably, these sequences change little across the entire parameter strip. To illustrate the applicability of our theoretical findings, we employ three such spherically symmetric sequences to accurately approximate two standard residual stress fields. Our work opens avenues for future exploration into the implications of different sequences, achieved by altering both the spatial distribution and the material symmetry class of the coefficient tensors, toward specific objectives.

math-ph↗

arXiv2024

Sedimentation dynamics of triply-twisted Möbius bands: Geometry versus topology

Chiral objects have intrigued scientists across several disciplines, including mathematics, crystallography, chemistry, and biology. A Möbius band, an emblematic chiral structure, can be made by connecting the ends of a strip after applying an odd number of twists. Traditionally, the direction of the twist governs its rotational behaviour during sedimentation in a fluid. Here, we present experimental and computational investigations of triply-twisted Möbius bands boasting threefold rotational symmetry that challenge this prevailing understanding. We explore three types of bands with different curvatures, each defined by its construction method. Experimental observations reveal that all three types of bands align axially and exhibit rotational motion during sedimentation. Surprisingly, for only one type of band the spinning direction (chiral hydrodynamic response) departs from expectations; it is not solely determined by the twist direction but changes with the aspect ratio of the band. Numerical simulations corroborate this observation, and an in-depth analysis of the resistance tensors of each type of band sheds light on the possible causes of this transition. We propose that modifications in fluid-induced drag, combined with inertial effects, underpin this phenomenon. Our study challenges existing knowledge of chiral object hydrodynamics, enriching our understanding of complex fluid dynamics. Moreover, it offers transformative potential across diverse fields, promising advancements in mixing, separation processes, and innovative passive swimmers.

physics.flu-dyn↗

arXiv2023

Marangoni spreading on liquid substrates in new media art

With the advent of new media art, artists have harnessed fluid dynamics to create captivating visual narratives. A striking technique known as dendritic painting employs mixtures of ink and isopropanol atop paint, yielding intricate tree-like patterns. To unravel the intricacies of that technique, we examine the spread of ink/alcohol droplets over liquid substrates with diverse rheological properties. On Newtonian substrates, the droplet size evolution exhibits two power laws, suggesting an underlying interplay between viscous and Marangoni forces. The leading edge of the droplet spreads as a precursor film with an exponent of 3/8, while its main body spreads with an exponent of 1/4. For a weakly shear-thinning acrylic resin substrate, the same power laws persist, but dendritic structures emerge, and the texture of the precursor film roughens. The observed roughness and growth exponents (3/4 and 3/5) suggest a connection to the quenched Kardar--Parisi--Zhang universality class, hinting at the existence of quenched disorder in the liquid substrate. Mixing the resin with acrylic paint renders it more viscous and shear-thinning, refining the dendrite edges and further roughening the precursor film. At larger paint concentrations, the substrate becomes a power-law fluid. The roughness and growth exponents then approach 1/2 and 3/4, respectively, deviating from known universality classes. The ensuing structures have a fractal dimension of 1.68, characteristic of diffusion-limited aggregation. These findings underscore how the non-linear rheological properties of the liquid substrate, coupled with the Laplacian nature of Marangoni spreading, can overshadow the local kinetic roughening of the droplet interface.

physics.flu-dyn↗

arXiv2022

Early stages of polycrystalline diamond deposition: Laser reflectance at substrates with growing nanodiamonds

The chemical vapor deposition of polycrystalline diamond (PCD) films is typically done on substrates seeded with diamond nanoparticles. Specular laser reflectance and a continuous film model have been used to monitor the thickness of these films during their deposition. However, most seeds are isolated during the early stages of the deposition, which questions the utility of applying such a continuous film model for monitoring deposition before film formation. In this work, we present a model based on the Rayleigh theory of scattering for laser reflectance at substrates with growing nanodiamonds to capture the early stages of PCD deposition. The reflectance behavior predicted by our model differs from that of a continuous film, which is well-described by the continuous film model. This difference enlarges as the seed density used in our model decreases. We verify this trend experimentally by depositing diamond under identical conditions on substrates with various seed densities. A relation derived from our model is used to fit reflectance data from which seed densities are obtained that are proportional to those found with electron microscopy. We also show that relying on the continuous film model for describing the early stages of deposition can result in falsely deducing the existence of incubation, and that the continuous film model can be used safely beyond the early stages of deposition. Based on these findings, we delineate a robust method for obtaining growth rates and incubation periods from reflectance measurements. This work may also advance the general understanding of nanoparticle growth and formation.

cond-mat.mtrl-sci↗

arXiv2022

Formation and morphology of closed and porous films grown from grains seeded on substrates: Two-dimensional simulations

Two-dimensional simulations are used to explore topological transitions that occur during the formation of films grown from grains that are seeded on substrates. This is done for a relatively large range of the initial value $Φ_s$ of the grain surface fraction $Φ$. The morphology of porous films is captured at the transition when grains connect to form a one-component network using newly developed raster-free algorithms that combine computational geometry and network theory. Further insight on the morphology of porous films and their suspended counterparts is obtained by studying the pore surface fraction $Φ_p$, the pore over grain ratio, the pore area distribution, and the contribution of pores of certain chosen areas to $Φ_p$. Pinhole survival is evaluated at the transition when film closure occurs using survival function estimates. The morphology of closed films ($Φ= 1$) is also characterized and is quantified by measuring grain areas and perimeters. The majority of investigated quantities are found to depend sensitively on $Φ_s$ and the long-time persistence of pinholes exhibits critical behavior as a function of $Φ_s$. In addition to providing guidelines for designing effective processes for manufacturing thin films and suspended porous films with tailored properties, this work may advance the understanding of continuum percolation theory.

cond-mat.mtrl-sci↗

arXiv2020

Boundary Curvature Effect on the Wrinkling of Thin Suspended Films

In this letter, we demonstrate a relation between the boundary curvature $κ$ and the wrinkle wavelength $λ$ of a thin suspended film under boundary confinement. Experiments are done with nanocrystalline diamond films of thickness $t \approx 184$~nm grown on glass substrates. By removing portions of the substrate after growth, suspended films with circular boundaries of radius $R$ ranging from approximately 30 to 811 $μ$m are made. Due to residual stresses, the portions of film attached to the substrate are of compressive prestrain $ε_0 \approx 11 \times 10^{-4}$ and the suspended portions of film are azimuthally wrinkled at their boundary. We find that $λ$ monotonically decreases with $κ$ and present a model predicting that $λ\propto t^{1/2}(ε_0 + ΔR κ)^{-1/4}$, where $ΔR$ denotes a penetration depth over which strain relaxes at a boundary. This relation is in agreement with our experiments and may be adapted to other systems such as plant leaves. Also, we establish a novel method for measuring residual compressive strain in thin films.

cond-mat.soft↗

arXiv2019

Nanocrystalline diamond-glass platform for the development of three-dimensional micro- and nanodevices

Low-cost and robust platforms are key for the development of next-generation 3D micro- and nanodevices. To fabricate such platforms, nanocrystalline diamond (NCD) is a highly appealing material due to its biocompatibility, robustness, and mechanical, electrical, electrochemical, and optical properties, while glass substrates with through vias are ideal interposers for 3D integration due to the excellent properties of glass. However, developing devices that are comprised of NCD films and through glass vias (TGVs) has rarely been attempted due to a lack of effective process strategies. In this work, a low-cost process - free of photolithography and transfer-printing - for fabricating arrays of TGVs that are sealed with suspended portions of an ultra-thin NCD film on one side is presented. These highly transparent structures may serve as a platform for the development of microwells for single-cell culture and analysis, 3D integrated devices such as microelectrodes, and quantum technologies. The process is demonstrated by fabricating TGVs that are sealed with an NCD film of thickness 175 nm and diameter 60 $μ$m. The technology described can be extended by replacing NCD with silicon nitride or silicon carbide, allowing for the development of complex heterogenous structures on the small scale.

physics.app-ph↗

arXiv2018

Spatial averaging of a dissipative particle dynamics model for active suspensions

Starting from a fine-scale dissipative particle dynamics (DPD) model of self-motile point particles, we derive meso-scale continuum equations by applying a spatial averaging version of the Irving--Kirkwood--Noll procedure. Since the method does not rely on kinetic theory, the derivation is valid for highly concentrated particle systems. Spatial averaging yields a stochastic continuum equations similar to those of Toner and Tu. However, our theory also involves a constitutive equation for the average fluctuation force. According to this equation, both the strength and the probability distribution vary with time and position through the effective mass density. The statistics of the fluctuation force also depend on the fine scale dissipative force equation, the physical temperature, and two additional parameters which characterize fluctuation strengths. Although the self-propulsion force entering our DPD model contains no explicit mechanism for aligning the velocities of neighboring particles, our averaged coarse-scale equations include the commonly encountered cubically nonlinear (internal) body force density.

nlin.AO↗

arXiv2017

Importance and effectiveness of representing the shapes of Cosserat rods and framed curves as paths in the special Euclidean algebra

We discuss how the shape of a special Cosserat rod can be represented as a path in the special Euclidean algebra. By shape we mean all those geometric features that are invariant under isometries of the three-dimensional ambient space. The representation of the shape as a path in the special Euclidean algebra is intrinsic to the description of the mechanical properties of a rod, since it is given directly in terms of the strain fields that stimulate the elastic response of special Cosserat rods. Moreover, such a representation leads naturally to discretization schemes that avoid the need for the expensive reconstruction of the strains from the discretized placement and for interpolation procedures which introduce some arbitrariness in popular numerical schemes. Given the shape of a rod and the positioning of one of its cross sections, the full placement in the ambient space can be uniquely reconstructed and described by means of a base curve endowed with a material frame. By viewing a geometric curve as a rod with degenerate point-like cross sections, we highlight the essential difference between rods and framed curves, and clarify why the family of relatively parallel adapted frames is not suitable for describing the mechanics of rods but is the appropriate tool for dealing with the geometry of curves.

math-ph↗

arXiv2017

Influence of surface tension in the surfactant-driven fracture of closely-packed particulate monolayers

A phase-field model is used to capture the surfactant-driven formation of fracture patterns in particulate monolayers. The model is intended for the regime of closely-packed systems in which the mechanical response of the monolayer can be approximated as a linearly elastic solid. The model approximates the loss in tensile strength of the monolayer as the surfactant concentration increases through the evolution of a damage field. Initial-boundary value problems are constructed and spatially discretized with finite element approximations to the displacement and surfactant damage fields. A comparison between model-based simulations and existing experimental observations indicates a qualitative match in both the fracture patterns and temporal scaling of the fracture process. The importance of surface tension differences is quantified by means of a dimensionless parameter, revealing thresholds that separate different regimes of fracture. These findings are supported by newly performed experiments that validate the model and demonstrate the strong sensitivity of the fracture pattern to differences in surface tension.

cond-mat.soft↗

arXiv2017

Effect of a surface tension imbalance on a partly submerged cylinder

We perform a static analysis of a circular cylinder that forms a barrier between surfactant-laden and surfactant-free portions of a liquid$-$gas interface. In addition to determining the general implications of the balances for forces and torques, we quantify how the imbalance $Δγ=γ_a-γ_b$ between the uniform surface tension $γ_a$ of the surfactant-free portion of the interface and the uniform surface tension $γ_b$ of the surfactant-laden portion of the interface influences the load-bearing capacity of a hydrophobic cylinder. Moreover, we demonstrate that the difference between surface tensions on either side of a cylinder with a cross-section of arbitrary shape induces a horizontal force component $f^h$ equal to $Δγ$ in magnitude, when measured per unit length of the cylinder. With an energetic argument, we show that this relation also applies to rod-like barriers with cross-sections of variable shape. In addition, we apply our analysis to amphiphilic Janus cylinders and we discuss practical implications of our findings for Marangoni propulsion and surface pressure measurements.

physics.flu-dyn↗

arXiv2017

Continuum balances from extended Hamiltonian dynamics

The classical procedure devised by Irving and Kirkwood in 1950 and completed slightly later by Noll produces counterparts of the basic balance laws of standard continuum mechanics starting from an ordinary Hamiltonian description of the dynamics of a system of material points. Post-1980 molecular dynamics simulations of the time evolution of such systems use extended Hamiltonians such as those introduced by Andersen, Nosé, and Parrinello and Rahman. The additional terms present in these extensions affect the statistical properties of the system so as to capture certain target phenomenologies that would otherwise be beyond reach. We here propose a physically consistent application of the Irving-Kirkwood-Noll procedure to extended Hamiltonian systems of material points. Our procedure produces balance equations at the continuum level featuring non-standard terms, because the presence of auxiliary degrees of freedom gives rise to additional fluxes and sources that influence the thermodynamic and transport properties of the continuum model. Being aware of the additional contributions may prove crucial when designing multiscale computational schemes in which information is exchanged between the atomistic and continuum levels.

math-ph↗

arXiv2017

Behavior of self-propelled acetone droplets in a Leidenfrost state on liquid substrates

It is demonstrated that non-coalescent droplets of acetone can be formed on liquid substrates. The fluid flows around and in an acetone droplet hovering on water are recorded to shed light on the mechanisms which might lead to non-coalescence. For sufficiently low impact velocities, droplets undergo a damped oscillation on the surface of the liquid substrate but at higher velocities clean bounce-off occurs. Comparisons of experimentally observed static configurations of floating droplets to predictions from a theoretical model for a small non-wetting rigid sphere resting on a liquid substrate are made and a tentative strategy for determining the thickness of the vapor layer under a small droplet on a liquid is proposed. This strategy is based on the notion of effective surface tension. The droplets show self-propulsion in straight line trajectories in a manner which can be ascribed to a Marangoni effect. Surprisingly, self-propelled droplets can become immersed beneath the undisturbed water surface. This phenomenon is reasoned to be drag-inducing and might provide a basis for refining observations in previous work.

physics.flu-dyn↗

arXiv2017

Solution of the Kirchhoff-Plateau problem

The Kirchhoff-Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a liquid film, with the filament being modeled as a Kirchhoff rod and the action of the spanning surface being solely due to surface tension. We establish the existence of an equilibrium shape that minimizes the total energy of the system under the physical constraint of non-interpenetration of matter, but allowing for points on the surface of the bounding loop to come into contact. In our treatment, the bounding loop retains a finite cross-sectional thickness and a nonvanishing volume, while the liquid film is represented by a set with finite two-dimensional Hausdorff measure. Moreover, the region where the liquid film touches the surface of the bounding loop is not prescribed a priori. Our mathematical results substantiate the physical relevance of the chosen model. Indeed, no matter how strong is the competition between surface tension and the elastic response of the filament, the system is always able to adjust to achieve a configuration that complies with the physical constraints encountered in experiments.

math-ph↗