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At least 703 records · Page 39

Implementation and Comparison of Acoustic Travel-Time Measurement Procedures for the Helioseismic and Magnetic Imager Time-Distance Helioseismology Pipeline

The Helioseismic and Magnetic Imager (HMI) instrument on board the Solar Dynamics Observatory (SDO) satellite is designed to produce high-resolution Doppler velocity maps of oscillations at the solar surface with high temporal cadence. To take advantage of these high-quality oscillation data, a time-distance helioseismology pipeline has been implemented at the Joint Science Operations Center (JSOC) at Stanford University. The aim of this pipeline is to generate maps of acoustic travel times from oscillations on the solar surface, and to infer subsurface 3D flow velocities and sound-speed perturbations. The wave travel times are measured from cross covariances of the observed solar oscillation signals. For implementation into the pipeline we have investigated three different travel-time definitions developed in time-distance helioseismology: a Gabor wavelet fitting (Kosovichev and Duvall, 1997), a minimization relative to a reference cross-covariance function (Gizon and Birch, 2002), and a linearized version of the minimization method (Gizon and Birch, 2004). Using Doppler velocity data from the Michelson Doppler Imager (MDI) instrument on board SOHO, we tested and compared these definitions for the mean and difference travel-time perturbations measured from reciprocal signals. Although all three procedures return similar travel times in a quiet Sun region, the method of Gizon and Birch (2004) gives travel times that are significantly different from the others in a magnetic (active) region. Thus, for the pipeline implementation we chose the procedures of Kosovichev and Duvall (1997) and Gizon and Birch (2002). We investigated the relationships among these three travel-time definitions, their sensitivities to fitting parameters, and estimated the random errors they produce

Couvidat, S.↗

Increased panel height enhances cooling for photovoltaic solar farms

We report solar photovoltaic (PV) systems suffer substantial efficiency loss due to environmental and internal heating. However, increasing the canopy height of these systems promotes surface heat transfer and boosts production. This work represents the first wind tunnel experiments to explore this concept in terms of array flow behavior and relative convective heat transfer, comparing model solar arrays of varied height arrangements - a nominal height, extended height, and a staggered height configuration. Analyses of surface thermocouple data show average Nusselt number (Nu) to increase with array elevation, where panel convection at double height improved up to 1.88 times that of the nominal case. This behavior is an effect of sub-array entrainment of high velocity flow and panel interactions as evidenced through flow statistics and mean kinetic energy budgets on particle image velocimetry (PIV) data. The staggered height arrangement encourages faster sub-panel flow than in the nominal array. Despite sub-array blockage due to the lower panel interaction, heat shedding at panel surfaces promotes improvements on over 1.3 times that of the nominal height case.

14 SOLAR ENERGY↗

Coupled neutronics and species transport simulation of the Molten Salt Reactor Experiment

This paper presents the development of coupling between the molten salt reactor species transport code Mole and the reactor physics code Griffin. Here, in this study, tracking of delayed neutron precursors was investigated in the Molten-Salt Reactor Experiment (MSRE), accounting for changes in fuel flow velocity as a function of position in the primary loop. The neutron transport calculations in Griffin were performed using 11 energy groups, and the species advection calculations in Mole used 6 delayed neutron precursor groups to predict spatial distribution of the neutron flux and neutron precursors in the MSRE. Mole–Griffin was used to calculate $k$ eff and $β$ eff in the reactor as a function of different volumetric flow rates.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Variable-grid-size transformation for solving nonsimilar laminar and turbulent boundary-layers

A numerical code has been developed to calculate nonsimilar boundary-layers (either laminar, transitional, or turbulent). The formulation of the equations of motion employs two transformations for the y-coordinate which provide a dense spacing of points near the wall and, therefore, can provide engineering solutions using relatively few points in the y-direction. The turbulent viscosity is correlated in terms of a length scale, which is in turn a function of the physical y-coordinate and of the mean-flow velocity gradient at that point. The boundary-layer solutions computed using the present code are compared with theoretical solutions presented by other investigators and with data from the literature. Comparisons with the data indicate that the theoretical solutions provide suitable values for the pitot-pressure profiles and the displacement thickness. Significant differences exist in the one comparison between the theoretical and the experimental heat-transfer rates for hypersonic flow past a flat plate.

Bertin, J. J.↗

Implementation and Comparison of Acoustic Travel-Time Measurement Procedures for the Solar Dynamics Observatory-Helioseismic and Magnetic Imager Time-Distance Helioseismology Pipeline

The Helioseismic and Magnetic Imager (HMI) instrument onboard the Solar Dynamics Observatory (SDO) satellite is designed to produce high-resolution Doppler-velocity maps of oscillations at the solar surface with high temporal cadence. To take advantage of these high-quality oscillation data, a time - distance helioseismology pipeline (Zhao et al., Solar Phys. submitted, 2010) has been implemented at the Joint Science Operations Center (JSOC) at Stanford University. The aim of this pipeline is to generate maps of acoustic travel times from oscillations on the solar surface, and to infer subsurface 3D flow velocities and sound-speed perturbations. The wave travel times are measured from cross-covariances of the observed solar oscillation signals. For implementation into the pipeline we have investigated three different travel-time definitions developed in time - distance helioseismology: a Gabor-wavelet fitting (Kosovichev and Duvall, SCORE'96: Solar Convection and Oscillations and Their Relationship, ASSL, Dordrecht, 241, 1997), a minimization relative to a reference cross-covariance function (Gizon and Birch, Astrophys. J. 571, 966, 2002), and a linearized version of the minimization method (Gizon and Birch, Astrophys. J. 614, 472, 2004). Using Doppler-velocity data from the Michelson Doppler Imager (MDI) instrument onboard SOHO, we tested and compared these definitions for the mean and difference traveltime perturbations measured from reciprocal signals. Although all three procedures return similar travel times in a quiet-Sun region, the method of Gizon and Birch (Astrophys. J. 614, 472, 2004) gives travel times that are significantly different from the others in a magnetic (active) region. Thus, for the pipeline implementation we chose the procedures of Kosovichev and Duvall (SCORE'96: Solar Convection and Oscillations and Their Relationship, ASSL, Dordrecht, 241, 1997) and Gizon and Birch (Astrophys. J. 571, 966, 2002). We investigated the relationships among these three travel-time definitions, their sensitivities to fitting parameters, and estimated the random errors that they produce.

HMI↗

Nonresonant particle acceleration in strong turbulence: Comparison to kinetic and MHD simulations

Collisionless, magnetized turbulence offers a promising framework for the generation of nonthermal high-energy particles in various astrophysical sites. Yet, the detailed mechanism that governs particle acceleration has remained subject to debate. By means of 2D and 3D particle-in-cell, as well as 3D (incompressible) magnetohydrodynamic (MHD) simulations, we test here a recent model of nonresonant particle acceleration in strongly magnetized turbulence, which ascribes the energization of particles to their continuous interaction with the random velocity flow of the turbulence, in the spirit of the original Fermi model. To do so, we compare, for a large number of particles that were tracked in the simulations, the predicted and the observed histories of particles momenta. The predicted history is that derived from the model, after extracting from the simulations, at each point along the particle trajectory, the three force terms that control acceleration: the acceleration of the field line velocity projected along the field line direction, its shear projected along the same direction, and its transverse compressive part. Overall, we find a clear correlation between the model predictions and the numerical experiments, indicating that this nonresonant model can successfully account for the bulk of particle energization through Fermi-type processes in strongly magnetized turbulence. Additionally we also observe that the parallel shear contribution tends to dominate the physics of energization in the particle-in-cell simulations, while in the magnetohydrodynamic incompressible simulation, both the parallel shear and the transverse compressive term provide about equal contributions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Finite Gyroradius Effects Observed in Pickup Oxygen Ions at Venus

On the dayside of Venus, the hot oxygen corona extending above the ionopause is the principal source of pickup oxygen ions. The ions are born here and picked up by the ionosheath plasma as it is deflected around the planet. These pickup ions have been observed by the Orbiter Plasma Analyzer (OPA) throughout the Pioneer Venus Orbiter (PVO) mission. They were observed over a region extending from their dayside source to great distances downstream (about 10 Venus radii), in the solar wind wake, as PVO passed through apoapsis. Finite gyroradius effects in the velocity distribution of the oxygen pickup ions are expected in the source region because the gyroradius is several times larger than the scale height of the hot oxygen source. Such effects are also expected in those regions of the ionosheath where the scale lengths of the magnetic field and the ambient plasma velocity field are less than the pickup ion gyroradius. While explicitly accounting for the spatial distribution of the hot oxygen source, an analytic expression for the pickup oxygen ion velocity distribution is developed to study how it is affected by finite gyroradii. The analysis demonstrates that as the gyroradius increases by factors of three to six above the hot oxygen scale height, the peak of the pickup oxygen ion flux distribution decreases 25 to 50% below the maximum allowed speed, which is twice the speed of the ambient plasma times the sine of the angle between the magnetic field and the flow velocity. The pickup oxygen ion flux distribution observed by OPA is shown to follow this behavior in the source region. It is also shown that this result is consistent with the pickup ion distributions observed in the wake, downstream of the source, where the flux peaks are usually well below the maximum allowed speed.

Hartle, Richard E.↗

An experimental investigation of flow-induced oscillations of the Bruel and Kjaer in-flow microphone

One source contributing to wind tunnel background noise is microphone self-noise. An experiment was conducted to investigate the flow-induced acoustic oscillations of Bruel & Kjaer (B&K) in-flow microphones. The results strongly suggest the B&K microphone cavity behaves more like an open cavity. Their cavity acoustic oscillations are likely caused by strong interactions between the cavity shear layer and the cavity trailing edge. But the results also suggest that cavity shear layer oscillations could be coupled with cavity acoustic resonance to generate tones. Detailed flow velocity measurements over the cavity screen have shown inflection points in the mean velocity profiles and high disturbance and spectral intensities in the vicinity of the cavity trailing edge. These results are the evidence for strong interactions between cavity shear layer oscillations and the cavity trailing edge. They also suggest that beside acoustic signals, the microphone inside the cavity has likely recorded hydrodynamic pressure oscillations, too. The results also suggest that the forebody shape does not have a direct effect on cavity oscillations. For the FITE (Flow Induced Tone Eliminator) microphone, it is probably the forebody length and the resulting boundary layer turbulence that have made it work. Turbulence might have thickened the boundary layer at the separation point, weakened the shear layer vortices, or lifted them to miss impinging on the cavity trailing edge. In addition, the study shows that the cavity screen can modulate the oscillation frequency but not the cavity acoustic oscillation mechanisms.

Fields, Richard S., Jr.↗

Spacecraft Cabin Ventilation Fan: Wake Measurements Results

Quiet, efficient fans with minimal vibrations are required for revitalization system fans used for human support system in long duration space exploration missions. A spacecraft cabin ventilation fan suitable for aerodynamic and acoustic ground tests was designed in NASA Glenn research center. Two copies of the fan assembly were fabricated and tested for aerodynamic performance and acoustic levels in the NASA Glenn Research Center Acoustical Testing Laboratory. A new test rig for small axial flow fans was designed to accommodate the instrumentation and back-pressure adjustments. Measurements acquired were from: static pressures for measuring performance, a 72-channel in-duct microphone array, external microphone measurements for acoustics, and inter-stage hot-wire measurements of the fan wake. Hot-wire measurements were obtained by radially traversing a x-wire probe downstream of the rotor. This report documents the phase-locked wake velocity, flow angle and turbulence measurements from the hot-wire surveys as part of a series of reports.

Hotwire Measurement↗

Sound scattering from atmospheric turbulence

Sound propagation through a turbulent flow field with nonvanishing mean-flow velocity has been studied. The effects of compressibility on sound scattering are discussed. Using an analysis describing moving sources in a fixed frame, particular results are obtained for the far-field scattered sound intensity due to uniformly moving scattering turbulence. A formula is obtained showing the factor by which the scattered sound intensity is amplified due to the motion of the turbulence. In addition, this analysis was extended to include wave propagating through mean flow with constant gradient.

Huang, M. N.↗

Convection and dendrite crystallization

The convection and thermal conditions in aqueous and metallic liquid systems under conditions of the Dendrite Remelting Rocket Experiment were assessed to help establish the relevance of the rocket experiment to the metals casting phenomena. The results of the study indicate that aqueous or metallic convection velocities in the cell are of insignificant magnitudes at the 0.0001 to 0.00001 g levels of the experiment. The crystallization phenomena observed in the rocket experiment, therefore, may be indicative of how metals will solidify in low-g. The influence of possibly differing thermal fields, however, remains to be assessed. The rocket experiment may also be relevant to how metals solidify on the ground at temperature differences and in cell configurations such that the flow velocities are not high enough to break or bend delicate dendrite arms. Again, however, the influence of the thermal fields must be assessed.

Grodzka, P. G.↗

Magnetohydrodynamics (MHD) Aerocapture System for Enabling Faster-Larger Planetary Science & Human Exploration Missions

Since our completing the NIAC Phase I NIAC on this Advanced Aerocapture System, NASA Langley Research Center has funded or supported a number of studies and code enhancements through its Center Innovation Fund (CIF) and NASA’s NSTGRO and Internship Programs to mature the analysis capabilities and quantify the merits of the MHD Aerocapture System technology. These efforts have resulted in a plug and play analysis capability for assessing MHD aerocapture system performance for arrival at many planetary bodies of interest. Our efforts have especially focused on the potential mass savings for improving the capacity for science observations at Neptune and Triton. A re-cent Forbes article published “‘Orbital mechanics is probably going to decide for us whether we go to Uranus or Neptune because we need to flyby Jupiter,’ said Kunio Sayanagi at Hampton University, Virginia, who also worked on the Neptune Odyssey proposal…. Exactly when a mission can be sent to Uranus, or Neptune, depends on the relative position of Jupiter, which can help give a spacecraft a gravitational slingshot. That drastically shortens the cruise phase.” [1] Since shortening the cruise phase is important for these science missions, any mass savings enabled by the MHD Aerocapture System could be reallocated to increasing Thermal Protection System mass to allow faster arrival speeds and/or for onboarding additional payloads such as science instruments, batteries, or propellant for conducting more science for longer durations in the desired orbits. The analysis steps and codes for conducting trades and sizing vehicles for aerocapture are as follows: Step 1 is to conduct aeroheating analysis using LAURA of the selected entry vehicle shape to identify locations on the forebody where ionization and flow velocity are sufficient for producing Lo-rentz forces. LAURA is a multiblock structured grid finite-volume CFD solver developed at the NASA Langley Research Center. [2] LAURA has been used for aerothermal analysis support of the entry, de-scent and landing (EDL) phase of interplanetary missions over the last three decades [3-7]. Step 2 is to port the LAURA results into CFDWARP to calcu-late electrical and thermal conductivities of ionized flow for sizing MHD patch system and calculating Lorentz forces needed for controls analysis. CFDWARP is a CFD code that uses advanced nu-merical methods that enable the simulation of the full coupling between the aerodynamics, the magne-tohydrodynamics, and the non-neutral plasma sheaths. CFDWARP has the unique capability to simulate efficiently the non-neutral sheaths (near the electrodes) in coupled form with the quasi-neutral bulk MHD flow [8-11]. Step 3 is to link re-sults from LAURA and CFDWARP into POST2 for calculating entry trajectories and comparing MHD control results with other aerodynamic control strategies. The Program to Optimize Simulated Tra-jectories II (POST2) is a generalized point mass, discrete parameter targeting and optimization pro-gram. POST2 provides the capability to target and optimize point mass trajectories for multiple pow-ered or un-powered vehicles near an arbitrary rotat-ing, oblate planet [12]. Step 4: TPS sizing was per-formed using the Fully Implicit Ablation and Ther-mal-response code (FIAT) tool which computes the transient one-dimensional thermal response and surface thermochemistry of a multilayer stackup of thermal protection, bonding, and structural materi-als subject to aeroheating on one surface [13]. The sizing and margining methodology used was based on the approach documented by Mahzari and Milos [14] for the dual-layered heatshield for extreme entry environment technology (DL-HEEET) TPS concept. TPS analysis utilizes trajectory information from POST2. Using this step-wise plug and play MHD Aerocapture performance assessment process, our analysis targets a Neptune aerocapture trajectory that will place the spacecraft in an observation orbit for Triton. [15]. Magnetohydrodynamic (MHD) control of a 4.5-meter diameter MSL-style capsule resulted in TPS mass savings of nearly 2000 kg when using an MHD system mass of under 200 kg. The flight path for a vehicle using the MHD control strategy has a much lower heat rate and heat load compared to the conventional aerodynamic aerocapture strategies known as bank angle con-trolled (BAC) and direct force controlled (DFC). Both BAC and DFC have heat rates significantly greater than 1500 W/cm2 typically used as an upper limit for PICA. Thus, DL-HEEET TPS concept was required for the BAC and DFC control strategies. However, considering the more benign environ-ments for the MHD case, additional TPS concepts with improved mass efficiency were also assessed. PICA was considered for the MHD controlled strat-egy since the maximum heat rate was well within the limits (<1500 W/cm2) of PICA. TPS sizing re-sulted in a significant mass reduction. The PICA layer for this sizing case was about 7.8 cm. As a point of reference, the Mars 2020 mission, which used this same PICA concept, had a PICA thickness of 3.18 cm [16]. The trajectories used for the TPS sizing originat-ed from the POST2 simulations. The current, I, to an electromagnet configuration can be manipulated to allow for active control of the vehicle. Manipula-tion of the current, I, changes the magnetic field, B, which affects the Lorentz force and therefore the MHD drag force on the vehicle. Our analysis in-cluded both open-loop and close-loop control. Closed-loop control will enable improved overall performance when taking into account mission level uncertainties, such as interplanetary delivery errors and atmospheric modeling uncertainties. The open-loop and closed-loop MHD control cases do not dip as deep into the atmosphere as the aerodynamic cases. Three types of aerodynamic-only approach-es are investigated: bank angle modulation (BAM), director force control (DFC), and Drag Modulated. BAM and DFC make use of vehicle aerodynamic angles to steer the vehicle. Thus, changing the aer-odynamic forces acting on the vehicle for control, aerodynamic drag modulated case requires a vary-ing drag area to modulate the drag force. The MHD drag modulated case modulates MHD generated drag force that adds to the aerodynamic drag. This higher atmospheric activation of drag forces by the MHD patch results in significantly less heat flux on the vehicle. The MHD technology will enable shorter cruise times and deceleration of larger payloads for increasing the capacity for science at the Ice Giants or for returning astronauts to Earth from cislunar space or from Mars. The purpose of this presentation is to provide more details about this work and to highlight plans for further research and development including a flight demonstration.

R. W. Moses↗

Experimental investigation of the radiation of sound from an unflanged duct and a bellmouth, including the flow effect

The radiation of sound from an inlet as a function of flow velocity, frequency, duct mode structure, and inlet geometry was examined by using a spinning mode synthesizer to insure a given space-time structure inside the duct. Measurements of the radiation pattern (amplitude and phase) and of the pressure reflection coefficient were obtained over an azimuthal wave number range of 0 to 6 and a frequency range up to 5000 Hz for an unflanged duct and a bellmouth. The measured radiated field and pressure reflection coefficient without flow for the unflanged duct agree reasonably well with theory. The influence of the inlet contour appears to be very drastic near the cut-on frequency of a mode and reasonable agreement is found between the bellmouth pressure reflection coefficient and a infinite hyperboloidal inlet theory. It is also shown that the flow has a weak effect on the amplitude of the directivity factor but significantly shifts the directivity factor phase. The influence of the flow on the modulus of the pressure reflection coefficient is found to be well described by a theoretical prediction.

Ville, J. M.↗

Fin Buffeting Features of an Early F-22 Model

Fin buffeting is an aeroelastic phenomenon encountered by high performance aircraft, especially those with twin vertical tails that must operate at high angles of attack. This buffeting is a concern from fatigue and inspection points of view. To date, the buffet (unsteady pressures) and buffeting (structural response) characteristics of the F-15 and F/A-18 fins have been studied extensively using flow visualization, flow velocity measurements, pressure transducers, and response gages. By means of windtunnel and flight tests of the F-15 and F/A-18, this phenomenon is well studied to the point that buffet loads can be estimated and fatigue life can he increased by structural enhancements to these airframes. However, prior to the present research, data was not available outside the F-22 program regarding fin buffeting on the F-22 configuration. During a test in the Langley Transonic Dynamics Tunnel, flow visualization and unsteady fin surface pressures were recorded for a 13.3%-scale F-22 model at high angles of attack for the purpose of comparing with results available for similar aircraft configurations. Details of this test and fin buffeting are presented herein.

Moses, Robert W.↗

High Enthalpy Studies of Capsule Heating in an Expansion Tunnel Facility

Measurements were made on an Orion heat shield model to demonstrate the capability of the new LENS-XX expansion tunnel facility to make high quality measurements of heat transfer distributions at flow velocities from 3 km/s (h(sub 0) = 5 MJ/kg) to 8.4 km/s (h(sub 0) = 36 MJ/kg). Thirty-nine heat transfer gauges, including both thin-film and thermocouple instruments, as well as four pressure gauges, and high-speed Schlieren were used to assess the aerothermal environment on the capsule heat shield. Only results from laminar boundary layer runs are reported. A major finding of this test series is that the high enthalpy, low-density flows displayed surface heating behavior that is observed to be consistent with some finite-rate recombination process occurring on the surface of the model. It is too early to speculate on the nature of the mechanism, but the response of the gages on the surface seems generally repeatable and consistent for a range of conditions. This result is an important milestone in developing and proving a capability to make measurements in a ground test environment and extrapolate them to flight for conditions with extreme non-equilibrium effects. Additionally, no significant, isolated stagnation point augmentation ("bump") was observed in the tests in this facility. Cases at higher Reynolds number seemed to show the greatest amount of overall increase in heating on the windward side of the model, which may in part be due to small-scale particulate.

Dufrene, Aaron↗

A Method of Estimating Low Turbulence Levels in Near Real Time Using Laser Anemometry

Laser anemometry was used to make two independent measurements of the flow velocity by capturing individual Doppler signals with high-speed digitizing boards. The two independent measurements were cross-correlated to reduce the contribution of photo detector shot noise on the frequency determination and subsequently on the turbulence estimate. In addition, criteria were developed to eliminate "bad" Doppler bursts from the data set, which then allowed reasonable low turbulence estimates to be made. The laser anemometer measurements were obtained at the inlet of an annular cascade and at the exit of a flow calibration nozzle and were compared with hot-wire data.

Goldman, Louis J.↗

Time-Distance Helioseismology Data-Analysis Pipeline for Helioseismic and Magnetic Imager Onboard Solar Dynamics Observatory (SDO-HMI) and Its Initial Results

The Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory (SDO/HMI) provides continuous full-disk observations of solar oscillations. We develop a data-analysis pipeline based on the time-distance helioseismology method to measure acoustic travel times using HMI Doppler-shift observations, and infer solar interior properties by inverting these measurements. The pipeline is used for routine production of near-real-time full-disk maps of subsurface wave-speed perturbations and horizontal flow velocities for depths ranging from 0 to 20 Mm, every eight hours. In addition, Carrington synoptic maps for the subsurface properties are made from these full-disk maps. The pipeline can also be used for selected target areas and time periods. We explain details of the pipeline organization and procedures, including processing of the HMI Doppler observations, measurements of the travel times, inversions, and constructions of the full-disk and synoptic maps. Some initial results from the pipeline, including full-disk flow maps, sunspot subsurface flow fields, and the interior rotation and meridional flow speeds, are presented.

Sun: helioseismology↗

Simulation and analysis of slip flow of water at hydrophobic silica surfaces of nanometer slit pores

Water flow in nanopores is controlled fundamentally by pore wettability and interfacial water features. In the research herein reported, Molecular dynamics (MD) was used to simulate water flow in nanometer slit pores of silica surfaces with variable wetting characteristics. Compared to Couette flow, the simulated slit-pores of the talc (001) and octadecyltrichlorosilane (OTS) monolayer surfaces exhibited water flow enhancement and a positive slip length at the interface, whereas water flow velocity at the quartz (001) and amorphous silica surfaces was zero, adhering to the no slip condition. More intensive interactions between the interfacial water and hydrophilic silica surfaces were confirmed by MD simulation and sum-frequency vibrational spectroscopy (SFVS) results. A water exclusion zone of approximately 3 Å was found at the hydrophobic silica surfaces by quantitative MD interfacial water analysis and validated by SFVS. This exclusion zone dimension was similar in magnitude to the slip length (4–5 Å) as determined from simulated water flow in hydrophobic silica slit pores. The simulated slip lengths at the hydrophobic surfaces (0.2–1 nm) were significantly less than the experimental slip lengths (>40 nm) reported in the literature. In the case of the experimental results, this difference appears to be due to nanobubbles expected to be present at hydrophobic surfaces.

42 ENGINEERING↗