(2+δ)-dimensional theory of the electromechanics of lipid membranes. III. Constitutive models
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We present variational and Hamiltonian formulations of incompressible fluid dynamics with a free surface and nonvanishing odd viscosity. We show that within the variational principle the odd viscosity contribution corresponds to geometric boundary terms. These boundary terms modify Zakharov’s Poisson brackets and lead to a new type of boundary dynamics. The modified boundary conditions have a natural geometric interpretation describing an additional pressure at the free surface proportional to the angular velocity of the surface itself. These boundary conditions are believed to be universal since the proposed hydrodynamic action is fully determined by the symmetries of the system.
Instantaneous thickness of a frozen layer is a function of specific heat, heat of fusion, temperatures, the frozen layer thickness at equilibrium, the thermal conductivity, and heat transfer coefficient. The equation can be evaluated on a desk calculator.
Applications of bubble and drop technologies are discussed and include: low gravity manufacturing, containerless melts, microballoon fabrication, ink printers, laser fusion targets, generation of organic glass and metal shells, and space processing. The fluid dynamics of bubbles and drops were examined. Thermomigration, capillary flow, and interfacial tension are discussed. Techniques for drop control are presented and include drop size control and drop shape control.
A detailed evaluation of the influence of growth conditions on the radial and axial compositional variations in directionally solidified Hg(1-x)Cd(x)Se alloys was performed. The measured axial compositional profiles were fitted to theoretical profiles to determine the effective solute (CdSe) diffusion coefficient (D) for the Hg(1-x)Cd(x)Se system. The value for D was estimated to be 3.0 + or - 0.5 x 10 to the -5th sq cm/s and did not appear to be significantly affected by the rate of crystal growth. The axial crystal uniformity was shown to be highly growth-rate dependent, with the faster growth rates producing crystals of more uniform composition in the axial direction. The magnitude of the radial variations was also shown to be highly growth-rate dependent, with the slower growth rates producing crystals of greater radial uniformity. This translation rate dependence of the radial uniformity is discussed in terms of lateral solute diffusion and convective interfacial fluid flows.
This paper is the first in a series of symposia presenting research activity in microgravity fluid mechanics. General topics addressed include two-phase flow and transport phenomena, thermo-capillary flow, and interfacial stability. Papers present mathmatical models of fluid dynamics in the microgravity environment. Applications suggested include space manufacturing and storage of liquids in low gravity.
Will discuss the recent activities on the international space station, including the adiabatic two phase flow, capillary flow and interfacial phenomena, and boiling and condensation. Will also give a historic introduction to Microgravity Studies at Glenn Research Center. Talk will be given to students and faculty at University of Louisville.
Bell-Plesset (BP) effects account for the influence of global convergence or divergence of the fluid flow on the evolution of the interfacial perturbations embedded in the flow. The development of the Rayleigh-Taylor instability in radiation-driven spherical capsules and magnetically-driven cylindrical liners necessarily includes a significant contribution from BP effects due to the time dependence of the radius, velocity, and acceleration of the unstable surfaces or interfaces. An analytical model is presented that, for an ideal incompressible fluid and small perturbation amplitudes, exactly evaluates the BP effects in finite-thickness shells through acceleration and deceleration phases. The time-dependent dispersion equations determining the “instantaneous growth rate” are derived. It is demonstrated that by integrating this approximate growth rate over time, one can accurately evaluate the number of perturbation e-foldings during the inward acceleration phase of the implosion. As a result, in the limit of small shell thickness, exact thin-shell perturbationequations and approximate thin-shell dispersion equations are obtained, generalizing the earlier results [E. G. Harris, Phys. Fluids 5, 1057 (1962); E. Ott, Phys. Rev. Lett. 29, 1429 (1972); A. B. Bud'ko et al., Phys. Fluids B 2, 1159 (1990)].
Combination of the classical density functional theory with kinetics modeling and the Navier–Stokes equation enables a quantitative description of the convoluted effects of fluid flow, surface reactions, interfacial structure and mass transport.
This milestone report discusses improvements to CTF closure models for modeling of bubbly and annular mist two-phase flow conditions, which are important for accurate modeling and simulation for boiling water reactor (BWR) conditions. Models that were improved include the two-phase wall shear, wall boiling, and phase mass and heat transfer. A new flow regime map was implemented to improve on the prediction of transition to annular flow, which was generally largely over-predicted by the legacy CTF flow regime map. The annular mist interfacial drag models were also reviewed and new models were proposed for implementation into the code. In addition to implementing new models, an activity was performed to calibrate these new models to experimental data using a Markov Chain Monte Carlo technique, thus further improving their accuracy. Finally, new experiments were implemented into the CTF validation matrix which add more two-phase pressure drop and void measurements for the assessment of CTF for modeling of BWRs. The results show that the Chisholm model, which was implemented and then calibrated, results in significantly improved comparison against the Riso two-phase pressure drop data. Furthermore, improvements in the implicit heat transfer and wall boiling models resulted in good agreement with the void measurement data.
An experimental investigation of thermocapillary flow in droplets of a vegetable oil (partially hydrogenated soybean oil) immersed in silicone oil was conducted in a test cell with a heated top wall and a cooled bottom wall. The liquids are nearly immiscible and have equal densities at a temperature below the room temperature, thus providing a simulation of low-gravity conditions by reducing the buoyancy forces. The interfacial tension between the two oils was measured in the temperature range 20 to 50 C using a capillary tube and (d sigma)/(d T) was determined to be negative. Droplets ranging in sizes from 3 mm to 1 cm diameter were injected into the silicone oil. The vertical temperature profile in the bulk liquid (silicone oil) produces temperature variations along the interface which induce variations in the interfacial tension. The flow inside the droplet driven by the resulting interfacial shear stresses was observed using a laser light-sheet flow visualization technique. The flow direction is consistent with the sign of (d sigma)/(d T). The observed maximum surface velocities are compared to the theoretical predictions of Young et al. (1959).
An experimental investigation of thermocapillary flow in droplets of a vegetable oil (partially hydrogenated soybean oil) immersed in silicone oil was conducted in a test cell with a heated top wall and a cooled bottom wall. The liquids are nearly immiscible and have equal densities at a temperature below the room temperature, thus providing a simulation of low-gravity conditions by reducing the buoyancy forces. The interfacial tension between the two oils was measured in the temperature range 20 to 50 C using a capillary tube and (d sigma)/(d T) was determined to be negative. Droplets ranging in sizes from 3 mm to 1 cm diameter were injected into the silicone oil. The vertical temperature profile in the bulk liquid (silicone oil) produces temperature variations along the interface which induce variations in the interfacial tension. The flow inside the droplet driven by the resulting interfacial shear stresses was observed using a laser light-sheet flow visualization technique. The flow direction is consistent with the sign of (d sigma)/(d T). The observed maximum surface velocities are compared to the theoretical predictions of Young et al. (1959).
The objective of the present study is to develop a two-fluid model formulation with interfacial area transport equation applicable for microgravity conditions. The new model is expected to make a leapfrog improvement by furnishing the constitutive relations for the interfacial interaction terms with the interfacial area transport equation, which can dynamically model the changes of the interfacial structures. In the first year of this three-year project supported by the U.S. NASA, Office of Biological and Physics Research, the primary focus is to design and construct a ground-based, microgravity two-phase flow simulation facility, in which two immiscible fluids with close density will be used. In predicting the two-phase flow behaviors in any two-phase flow system, the interfacial transfer terms are among the most essential factors in the modeling. These interfacial transfer terms in a two-fluid model specify the rate of phase change, momentum exchange, and energy transfer at the interface between the two phases. For the two-phase flow under the microgravity condition, the stability of the fluid particle interface and the interfacial structures are quite different from those under normal gravity condition. The flow structure may not reach an equilibrium condition and the two fluids may be loosely coupled such that the inertia terms of each fluid should be considered separately by use of the two-fluid model. Previous studies indicated that, unless phase-interaction terms are accurately modeled in the two-fluid model, the complex modeling does not necessarily warrant an accurate solution.
We consider the genesis and dynamics of interfacial instability in vertical gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream. To make contact with existing studies in the literature, the effect of various density contrasts is also examined. Energy budget analyses based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low density contrast. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. Direct numerical simulations of the same system (low density contrast) show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. For high density contrasts, corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. The same linear stability theory predicts when the direction of travel of the waves changes — from downwards to upwards. We outline the practical implications of this change in terms of loading and flooding. The change in direction of the wave propagation is represented graphically in terms of a flow map based on the liquid and gas flow rates and the prediction carries over to the nonlinear regime with only a small deviation.
A model problem is posed to study the influence of flow on the interfacial stability of a nearly cylindrical liquid bridge for lengths near its circumference (the Plateau-Rayleigh limit). The flow is generated by a shear stress imposed on the deformable interface. The symmetry of the imposed shear stress mimics the thermocapillary stress induced on a float-zone by a ring heater (i.e. a full zone). Principal assumptions are (1) zero gravity, (2) creeping flow, and (3) that the imposed coupling at the free surface between flow and temperature fields is the only such coupling. A numerical solution, complemented by a bifurcation analysis, shows that bridges substantially longer than the Plateau-Rayleigh limit are possible. An interaction of the first two capillary instabilities through the stress-induced flow is responsible. Time-periodic standing waves are also predicted in certain parameter ranges. Motivation comes from extra-long float-zones observed in MEPHISTO space lab experiments (June 1994).
Interfaces impede heat flow in micro/nanostructured systems. Conventional theories for interfacial thermal transport were derived based on bulk phonon properties of the materials making up the interface without explicitly considering the atomistic interfacial details, which are found critical to correctly describing thermal boundary conductance. Recent theoretical studies predicted the existence of localized phonon modes at the interface which can play an important role in understanding interfacial thermal transport. However, experimental validation is still lacking. Through a combination of Raman spectroscopy and high-energy-resolution electron energy-loss spectroscopy in a scanning transmission electron microscope, we report the experimental observation of localized interfacial phonon modes at ~12 THz at a high-quality epitaxial Si-Ge interface. These modes are further confirmed using molecular dynamics simulations with a high-fidelity neural network interatomic potential, which also yield thermal boundary conductance agreeing well with that measured in time-domain thermoreflectance experiments. Simulations find that the interfacial phonon modes have an obvious contribution to the total thermal boundary conductance. Our findings significantly contribute to the understanding of interfacial thermal transport physics and have impact on engineering thermal boundary conductance at interfaces in applications such as electronics thermal management and thermoelectric energy conversion.
Redox flow batteries are attractive technologies for grid energy storage since they use solutions of redox-active molecules that enable a superior scalability and the decoupling of power and energy density. However, the reaction mechanisms of the redox active components at RFB electrodes are complex, and there is currently a pressing need to understand how interfacial processes impact the kinetics and operational reversibility of RFB systems. Here, we developed a combined electrochemical imaging methodology rooted in scanning electrochemical microscopy (SECM) and atomic force microscopy (AFM) for exploring the impact of electrode structure and conditioning on the electron transfer properties of model redox-active dialkoxybenzene derivatives, 2,5-di-tert-butyl-1,4-bis(2-methoxyethoxy)benzene (C1) and 2,3-dimethyl-1,4-dialkoxybenzene (C7). Using AFM and secondary-ion mass spectrometry (SIMS), we observed the formation of interfacial films with distinct mechanical properties compared to those of cleaved graphitic surfaces, and exclusively during reduction of electrogenerated radical cations. These films had an impact on the median rate and distribution of the electron transfer rate constant at the basal plane of multilayer and single layer graphene electrodes, displaying kinetically-limited values that did not yield the activation expected per the Butler–Volmer model with a transfer coefficient ~0.5. These changes were dependent on redoxmer structure: furthermore, SECM showed strong attenuation of C7 kinetics by a surface layer on MLG and SLG, while C1 kinetics were only affected by SLG. SECM and AFM results together show that these limiting films operate exclusively on the basal plane of graphite, with the edge plane showing a relative insensitivity to cycling and operation potential. Ultimately, this integrated electrochemical imaging methodology creates new opportunities to understand the unique role of interfacial processes on the heterogeneous reactivity of redoxmers at electrodes for RFBs, with a future role in elucidating phenomena at high active concentrations and spatiotemporal variations in electrode dynamics.