Publications

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Models and experiments are developed to investigate how a small amount of gas can cause large rectified motion of a piston in a vibrated liquid-filled housing when piston drag depends on piston position so that damping is nonlinear even for viscous flow. Two bellows serve as surrogates for the upper and lower gas regions maintained by Bjerknes forces. Without the bellows, piston motion is highly damped. With the bellows, the piston, the liquid, and the two bellows move together so that almost no liquid is forced through the gaps between the piston and the housing. This Couette mode has low damping and a strong resonance: the piston and the liquid vibrate against the spring formed by the two bellows (like the pneumatic spring formed by the gas regions). Near this resonance, the piston motion becomes large, and the nonlinear damping produces a large rectified force that pushes the piston downward against its spring suspension. A recently developed model based on quasi-steady Stokes flow is applied to this system. A drift model is developed from the full model and used to determine the equilibrium piston position as a function of vibration amplitude and frequency. Corresponding experiments are performed for two different systems. In the two-spring system, the piston is suspended against gravity between upper and lower springs. In the spring-stop system, the piston is pushed up against a stop by a lower spring. Model and experimental results agree closely for both systems and for different bellows properties.

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The Direct Simulation Monte Carlo (DSMC) method has been used for more than 50 years to simulate rarefied gases. The advent of modern supercomputers has brought higher-density near-continuum flows within range. This in turn has revived the debate as to whether the Boltzmann equation, which assumes molecular chaos, can be used to simulate continuum flows when they become turbulent. In an effort to settle this debate, two canonical turbulent flows are examined, and the results are compared to available continuum theoretical and numerical results for the Navier-Stokes equations.

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We provide a demonstration that gas-kinetic methods incorporating molecular chaos can simulate the sustained turbulence that occurs in wall-bounded turbulent shear flows. The direct simulation Monte Carlo method, a gas-kinetic molecular method that enforces molecular chaos for gas-molecule collisions, is used to simulate the minimal Couette flow at Re=500. The resulting law of the wall, the average wall shear stress, the average kinetic energy, and the continually regenerating coherent structures all agree closely with corresponding results from direct numerical simulation of the Navier-Stokes equations. These results indicate that molecular chaos for collisions in gas-kinetic methods does not prevent development of molecular-scale long-range correlations required to form hydrodynamic-scale turbulent coherent structures.

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We provide the first demonstration that molecular-level methods based on gas kinetic theory and molecular chaos can simulate turbulence and its decay. The direct simulation Monte Carlo (DSMC) method, a molecular-level technique for simulating gas flows that resolves phenomena from molecular to hydrodynamic (continuum) length scales, is applied to simulate the Taylor-Green vortex flow. The DSMC simulations reproduce the Kolmogorov -5/3 law and agree well with the turbulent kinetic energy and energy dissipation rate obtained from direct numerical simulation of the Navier-Stokes equations using a spectral method. This agreement provides strong evidence that molecular-level methods for gases can be used to investigate turbulent flows quantitatively.

We develop an idealized experimental system for studying how a small amount of gas can cause large net (rectified) motion of an object in a vibrated liquid-filled housing when the drag on the object depends strongly on its position. Its components include a cylindrical housing, a cylindrical piston fitting closely within this housing, a spring suspension that supports the piston, a post penetrating partway through a hole through the piston (which produces the position-dependent drag), and compressible bellows at both ends of the housing (which are well characterized surrogates for gas regions). In this system, liquid can flow from the bottom to the top of the piston and vice versa through the thin annular gaps between the hole and the post (the inner gap) and between the housing and the piston (the outer gap). When the bellows are absent, the piston motion is highly damped because small piston velocities produce large liquid velocities and large pressure drops in the Poiseuille flows within these narrow gaps. However, when the bellows are present, the piston, the liquid, and the bellows execute a collective motion called the Couette mode in which almost no liquid is forced through the gaps. Since its damping is low, the Couette mode has a strong resonance. Near this frequency, the piston motion becomes large, and the nonlinearity associated with the position-dependent drag of the inner gap produces a net (rectified) force on the piston that can cause it to move downward against its spring suspension. Experiments are performed using two variants of this system. In the single-spring setup, the piston is pushed up against a stop by its lower supporting spring. In the two-spring setup, the piston is suspended between upper and lower springs. The equilibrium piston position is measured as a function of the vibration frequency and acceleration, and these results are compared to corresponding analytical results (Torczynski et al., 2017). A quantitative understanding of the nonlinear behavior of this system may enable the development of novel tunable dampers for sensing vibrations of specified amplitudes and frequencies.

Models and simulations are employed to analyze the motion of a spring-supported piston in a vibrated liquid-filled cylinder. The piston motion is damped by forcing liquid through a narrow gap between a hole through the piston and a post fixed to the housing. As the piston moves, the length of this gap changes, so the piston damping coefficient depends on the piston position. This produces a nonlinear damper, even for highly viscous flow. When gas is absent, the vibration response is overdamped. However, adding a little gas changes the response of this springmass-damper system to vibration. During vibration, Bjerknes forces cause some of the gas to migrate below the piston. The resulting pneumatic spring enables the liquid to move with the piston so as to force very little liquid through the gap. Thus, this "Couette mode" has low damping and a strong resonance near the frequency given by the pneumatic spring constant and the total mass of the piston and the liquid. Near this frequency, the amplitude of the piston motion is large, so the nonlinear damper produces a large net force on the piston. To analyze the effect of this nonlinear damper in detail, a surrogate system is developed by modifying the original system in two ways. First, the gas regions are replaced by upper and lower bellows with similar compressibility to give a well-defined "pneumatic" spring. Second, the upper stop against which the piston is pushed by its lower supporting spring is replaced with an upper spring, thereby removing the nonlinearity from the stop. An ordinary-differential-equation (ODE) drift model based on quasi-steady Stokes flow is used to produce a regime map of the vibration amplitudes and frequencies for which the piston is up or down for conditions of experimental interest. These results agree fairly well with Arbitrary Lagrangian Eulerian (ALE) simulations of the incompressible Navier-Stokes (NS) equations for the liquid and Newton's 2nd Law for the piston and bellows. A quantitative understanding of this nonlinear behavior may enable the development of novel tunable dampers for sensing vibrations of specified amplitudes and frequencies.

The Rayleigh-Taylor instability (RTI) is investigated using the Direct Simulation Monte Carlo (DSMC) method of molecular gas dynamics. Here, two-dimensional and three-dimensional DSMC RTI simulations are performed to quantify the growth of flat and single-mode-perturbed interfaces between two atmospheric-pressure monatomic gases. The DSMC simulations reproduce all qualitative features of the RTI and are in reasonable quantitative agreement with existing theoretical and empirical models in the linear, nonlinear, and self-similar regimes. At late times, the instability is seen to exhibit a self-similar behavior, in agreement with experimental observations. For the conditions simulated diffusion can influence the initial instability growth significantly.

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In this paper, the Rayleigh-Taylor instability (RTI) is investigated using the direct simulation Monte Carlo (DSMC) method of molecular gas dynamics. Here, fully resolved two-dimensional DSMC RTI simulations are performed to quantify the growth of flat and single-mode perturbed interfaces between two atmospheric-pressure monatomic gases as a function of the Atwood number and the gravitational acceleration. The DSMC simulations reproduce many qualitative features of the growth of the mixing layer and are in reasonable quantitative agreement with theoretical and empirical models in the linear, nonlinear, and self-similar regimes. In some of the simulations at late times, the instability enters the self-similar regime, in agreement with experimental observations. Finally, for the conditions simulated, diffusion can influence the initial instability growth significantly.

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This report presents the test cases used to verify, validate and demonstrate the features and capabilities of the first release of the 3D Direct Simulation Monte Carlo (DSMC) code SPARTA (Stochastic Real Time Particle Analyzer). The test cases included in this report exercise the most critical capabilities of the code like the accurate representation of physical phenomena (molecular advection and collisions, energy conservation, etc.) and implementation of numerical methods (grid adaptation, load balancing, etc.). Several test cases of simple flow examples are shown to demonstrate that the code can reproduce phenomena predicted by analytical solutions and theory. A number of additional test cases are presented to illustrate the ability of SPARTA to model flow around complicated shapes. In these cases, the results are compared to other well-established codes or theoretical predictions. This compilation of test cases is not exhaustive, and it is anticipated that more cases will be added in the future.

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We have developed a mature laboratory at Sandia to measure interfacial rheology, using a combination of home-built, commercially available, and customized commercial tools. An Interfacial Shear Rheometer (KSV ISR-400) was modified and the software improved to increase sensitivity and reliability. Another shear rheometer, a TA Instruments AR-G2, was equipped with a du Nouey ring, bicone geometry, and a double wall ring. These interfacial attachments were compared to each other and to the ISR. The best results with the AR-G2 were obtained with the du Nouey ring. A Micro-Interfacial Rheometer (MIR) was developed in house to obtain the much higher sensitivity given by a smaller probe. However, it was found to be difficult to apply this technique for highly elastic surfaces. Interfaces also exhibit dilatational rheology when the interface changes area, such as occurs when bubbles grow or shrink. To measure this rheological response we developed a Surface Dilatational Rheometer (SDR), in which changes in surface tension with surface area are measured during the oscillation of the volume of a pendant drop or bubble. All instruments were tested with various surfactant solutions to determine the limitations of each. In addition, foaming capability and foam stability were tested and compared with the rheology data. It was found that there was no clear correlation of surface rheology with foaming/defoaming with different types of surfactants, but, within a family of surfactants, rheology could predict the foam stability. Diffusion of surfactants to the interface and the behavior of polyelectrolytes were two subjects studied with the new equipment. Finally, surface rheological terms were added to a finite element Navier-Stokes solver and preliminary testing of the code completed. Recommendations for improved implementation were given. When completed we plan to use the computations to better interpret the experimental data and account for the effects of the underlying bulk fluid.

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The rheology at gas-liquid interfaces strongly influences the stability and dynamics of foams and emulsions. Several experimental techniques are employed to characterize the rheology at liquid-gas interfaces with an emphasis on the non-Newtonian behavior of surfactant-laden interfaces. The focus is to relate the interfacial rheology to the foamability and foam stability of various aqueous systems. An interfacial stress rheometer (ISR) is used to measure the steady and dynamic rheology by applying an external magnetic field to actuate a magnetic needle suspended at the interface. Results are compared with those from a double wall ring attachment to a rotational rheometer (TA Instruments AR-G2). Micro-interfacial rheology (MIR) is also performed using optical tweezers to manipulate suspended microparticle probes at the interface to investigate the steady and dynamic rheology. Additionally, a surface dilatational rheometer (SDR) is used to periodically oscillate the volume of a pendant drop or buoyant bubble. Applying the Young-Laplace equation to the drop shape, a time-dependent surface tension can be calculated and used to determine the effective dilatational viscosity of an interface. Using the ISR, double wall ring, SDR, and MIR, a wide range of sensitivity in surface forces (fN to nN) can be explored as each experimental method has different sensitivities. Measurements will be compared to foam stability.

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Lack of robust manufacturing capabilities have limited our ability to make tailored materials with useful optical and thermal properties. For example, traditional methods such as spontaneous self-assembly of spheres cannot generate the complex structures required to produce a full bandgap photonic crystals. The goal of this work was to develop and demonstrate novel methods of directed self-assembly of nanomaterials using optical and electric fields. To achieve this aim, our work employed laser tweezers, a technology that enables non-invasive optical manipulation of particles, from glass microspheres to gold nanoparticles. Laser tweezers were used to create ordered materials with either complex crystal structures or using aspherical building blocks.

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Optical tweezers has become a powerful and common tool for sensitive determination of electrostatic interactions between colloidal particles. Recently, two techniques, 'blinking' tweezers and direct force measurements, have become increasingly prevalent in investigations of inter-particle potentials. The 'blinking' tweezers method acquires physical statistics of particle trajectories to determine drift velocities, diffusion coefficients, and ultimately colloidal forces as a function of the center-center separation of two particles. Direct force measurements monitor the position of a particle relative to the center of an optical trap as the separation distance between two continuously trapped particles is gradually decreased. As the particles near each other, the displacement from the trap center for each particle increases proportional to the inter-particle force. Although commonly employed in the investigation of interactions of colloidal particles, there exists no direct comparison of these experimental methods in the literature. In this study, an experimental apparatus was developed capable of performing both methods and is used to quantify electrostatic potentials between particles in several particle/solvent systems. Comparisons are drawn between the experiments conducted using the two measurement techniques, theory, and existing literature. Forces are quantified on the femto-Newton scale and results agree well with literature values.

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