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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Superconductivity, Pairing Symmetry, and Disorder in the Doped Topological Insulator Sn 1-x In x Te for x >= 0.10.

The temperature dependence of the London penetration depth Delta lambda(T) in the superconducting doped topological crystalline insulator Sn1-xInxTe was measured down to 450 mK for two different doping levels, x approximate to 0.45 (optimally doped) and x approximate to 0.10 (underdoped), bookending the range of cubic phase in the compound. The results indicate no deviation from fully gapped BCS-like behavior, eliminating several candidate unconventional gap structures. Critical field values below 1 K and other superconducting parameters are also presented. The introduction of disorder by repeated particle irradiation with 5 MeV protons does not enhance T-c, indicating that ferroelectric interactions do not compete with superconductivity.

Smylie, M. P.↗
DOE OSTI2015

Experimental depth dose curves of a 67.5 MeV proton beam for benchmarking and validation of Monte Carlo simulation

Purpose: To measure depth dose curves for a 67.5 ± 0.1 MeV proton beam for benchmarking and validation of Monte Carlo simulation. Methods: Depth dose curves were measured in 2 beam lines. Protons in the raw beam line traversed a Ta scattering foil, 0.1016 or 0.381 mm thick, a secondary emission monitor comprised of thin Al foils, and a thin Kapton exit window. The beam energy and peak width and the composition and density of material traversed by the beam were known with sufficient accuracy to permit benchmark quality measurements. Diodes for charged particle dosimetry from two different manufacturers were used to scan the depth dose curves with 0.003 mm depth reproducibility in a water tank placed 300 mm from the exit window. Depth in water was determined with an uncertainty of 0.15 mm, including the uncertainty in the water equivalent depth of the sensitive volume of the detector. Parallel-plate chambers were used to verify the accuracy of the shape of the Bragg peak and the peak-to-plateau ratio measured with the diodes. The uncertainty in the measured peak-to-plateau ratio was 4%. Depth dose curves were also measured with a diode for a Bragg curve and treatment beam spread out Bragg peak (SOBP) on the beam line used for eye treatment. The measurements were compared to Monte Carlo simulation done with GEANT4 using TOPAS. Results: The 80% dose at the distal side of the Bragg peak for the thinner foil was at 37.47 ± 0.11 mm (average of measurement with diodes from two different manufacturers), compared to the simulated value of 37.20 mm. The 80% dose for the thicker foil was at 35.08 ± 0.15 mm, compared to the simulated value of 34.90 mm. The measured peak-to-plateau ratio was within one standard deviation experimental uncertainty of the simulated result for the thinnest foil and two standard deviations for the thickest foil. It was necessary to include the collimation in the simulation, which had a more pronounced effect on the peak-to-plateau ratio for the thicker foil. The treatment beam, being unfocussed, had a broader Bragg peak than the raw beam. A 1.3 ± 0.1 MeV FWHM peak width in the energy distribution was used in the simulation to match the Bragg peak width. An additional 1.3–2.24 mm of water in the water column was required over the nominal values to match the measured depth penetration. Conclusions: The proton Bragg curve measured for the 0.1016 mm thick Ta foil provided the most accurate benchmark, having a low contribution of proton scatter from upstream of the water tank. The accuracy was 0.15% in measured beam energy and 0.3% in measured depth penetration at the Bragg peak. The depth of the distal edge of the Bragg peak in the simulation fell short of measurement, suggesting that the mean ionization potential of water is 2–5 eV higher than the 78 eV used in the stopping power calculation for the simulation. The eye treatment beam line depth dose curves provide validation of Monte Carlo simulation of a Bragg curve and SOBP with 4%/2 mm accuracy.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Quantitative wood–adhesive penetration with X-ray computed tomography

Micro X-ray computed tomography (XCT) was used to analyze the 3D adhesive penetration behavior of different wood–adhesive bondlines. Three adhesives, a phenol formaldehyde (PF), a polymeric diphenylmethane diisocyanate (pMDI), and a hybrid polyvinyl acetate (PVA), all tagged with iodine for enhanced X-ray attenuation, were used to prepare single-bondline laminates in two softwoods, Douglas-fir and loblolly pine, and one hardwood, a hybrid polar. Adhesive penetration depth was measured with two separate calculations, and results were compared with 2D fluorescent micrographs. A total of 54 XCT scans were collected, representing six replicates of each treatment type; each replicate, however, consisted of approximately 1500 individual, cross-section slices stacked along the specimen length. As these adhesives were highly modified, the presented results do not indicate typical behavior for their broader adhesive classes. Still, clear penetration differences were observed between each adhesive type, and between wood species bonded with both the PF and pMDI adhesives. Furthermore, penetration results depended on the calculation method used. Two adhesive types with noticeably different resin distributions in the cured bondline, showed relatively similar penetration depths when calculated with a traditional effective penetration equation. However, when the same data was calculated with a weighted penetration calculation, which accounts for both adhesive area and depth, the results appeared to better represent the different distributions depicted in the photomicrographs and tomograms. Additionally, individual replicate comparisons showed variation due to specimen anatomy, not easily observed or interpreted from 2D images. Finally, 3D views of segmented 3D adhesive phases offered unique, in-situ views of the cured adhesive structures. In particular, voids formed by CO 2 bubbles generated during pMDI cure were clearly visible in penetrated columns of the solidified adhesive.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2015

Comparisons between tokamak fueling of gas puffing and supersonic molecular beam injection in 2D simulations

Plasma fueling with high efficiency and deep injection is very important to enable fusion power performance requirements. It is a powerful and efficient way to study neutral transport dynamics and find methods of improving the fueling performance by doing large scale simulations. Two basic fueling methods, gas puffing (GP) and supersonic molecular beam injection (SMBI), are simulated and compared in realistic divertor geometry of the HL-2A tokamak with a newly developed module, named trans-neut, within the framework of BOUT++ boundary plasma turbulence code [Z. H. Wang et al., Nucl. Fusion 54, 043019 (2014)]. The physical model includes plasma density, heat and momentum transport equations along with neutral density, and momentum transport equations. Transport dynamics and profile evolutions of both plasma and neutrals are simulated and compared between GP and SMBI in both poloidal and radial directions, which are quite different from one and the other. It finds that the neutrals can penetrate about four centimeters inside the last closed (magnetic) flux surface during SMBI, while they are all deposited outside of the LCF during GP. It is the radial convection and larger inflowing flux which lead to the deeper penetration depth of SMBI and higher fueling efficiency compared to GP.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

STABILITY OF EXTRATERRESTRIAL GLYCINE UNDER ENERGETIC PARTICLE RADIATION ESTIMATED FROM 2 keV ELECTRON BOMBARDMENT EXPERIMENTS

The destruction of solid glycine under irradiation with 2 keV electrons has been investigated by means of IR spectroscopy. Destruction cross sections, radiolysis yields, and half-life doses were determined for samples at 20, 40, 90, and 300 K. The thickness of the irradiated samples was kept below the estimated penetration depth of the electrons. No significant differences were obtained in the experiments below 90 K, but the destruction cross section at 300 K was larger by a factor of 2. The radiolysis yields and half-life doses are in good accordance with recent MeV proton experiments, which confirms that electrons in the keV range can be used to simulate the effects of cosmic rays if the whole sample is effectively irradiated. In the low temperature experiments, electron irradiation leads to the formation of residues. IR absorptions of these residues are assigned to the presence CO{sub 2}, CO, OCN{sup −}, and CN{sup −} and possibly to amide bands I to III. The protection of glycine by water ice is also studied. A water ice film of ∼150 nm is found to provide efficient shielding against the bombardment of 2 keV electrons. The results of this study show also that current Monte Carlo predictions provide a good global description of electron penetration depths. The lifetimes estimated in this work for various environments ranging from the diffuse interstellar medium to the inner solar system, show that the survival of hypothetical primeval glycine from the solar nebula in present solar system bodies is not very likely.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Pore-resolved investigation of turbulent open channel flow over a randomly packed permeable sediment bed

Pore-resolved direct numerical simulations are performed to investigate the interactions between streamflow turbulence and groundwater flow through a randomly packed porous sediment bed for three permeability Reynolds numbers, Re K = 2.56 , 5.17 and 8.94, representative of natural stream or river systems. Time–space averaging is used to quantify the Reynolds stress, form-induced stress, mean flow and shear penetration depths, and mixing length at the sediment–water interface (SWI). Here, the mean flow and shear penetration depths increase with Re K and are found to be nonlinear functions of non-dimensional permeability. The peaks and significant values of the Reynolds stresses, form-induced stresses, and pressure variations are shown to occur in the top layer of the bed, which is also confirmed by conducting simulations of just the top layer as roughness elements over an impermeable wall. The probability distribution functions (p.d.f.s) of normalized local bed stress are found to collapse for all Reynolds numbers, and their root-mean-square fluctuations are assumed to follow logarithmic correlations. The fluctuations in local bed stress and resultant drag and lift forces on sediment grains are mainly a result of the top layer; their p.d.f.s are symmetric with heavy tails, and can be well represented by a non-Gaussian model fit. The bed stress statistics and the pressure data at the SWI potentially can be used in providing better boundary conditions in modelling of incipient motion and reach-scale transport in the hyporheic zone.

turbulence simulation↗
NASA NTRS1978

On the estimation of the vertical ozone distribution from satellite measurements

A simple relationship has been established between the vertical ozone profile above the ozone maximum and satellite measured radiances for wavelengths shorter than 3000 A. The method is based on the computation of the penetration depths for solar radiation entering the atmosphere at wavelengths employed by the BUV satellite. Suitably defined penetration depths are shown to be linear functions of the normalized intensities for typical conditions, eliminating the requirement for iterative solutions and considerably simplifying the error analysis for the system. For ozone distributions which depart significantly from the exponential form, a noniterative extension of the analysis procedure has been developed and tested through application to simulated intensities.

Thomas, R. W. L.↗
DOE OSTI2014

Photoacoustic detection and optical spectroscopy of high-intensity focused ultrasound-induced thermal lesions in biologic tissue

Purpose: The aims of this study are: (a) to investigate the capability of photoacoustic (PA) method in detecting high-intensity focused ultrasound (HIFU) treatments in muscle tissuesin vitro; and (b) to determine the optical properties of HIFU-treated and native tissues in order to assist in the interpretation of the observed contrast in PA detection of HIFU treatments. Methods: A single-element, spherically concaved HIFU transducer with a centre frequency of 1 MHz was utilized to create thermal lesions in chicken breast tissuesin vitro. To investigate the detectability of HIFU treatments photoacoustically, PA detection was performed at 720 and 845 nm on seven HIFU-treated tissue samples. Within each tissue sample, PA signals were acquired from 22 locations equally divided between two regions of interest within two volumes in tissue – a HIFU-treated volume and an untreated volume. Optical spectroscopy was then carried out on 10 HIFU-treated chicken breast specimens in the wavelength range of 500–900 nm, in 1-nm increments, using a spectrophotometer with an integrating sphere attachment. The authors’ optical spectroscopy raw data (total transmittance and diffuse reflectance) were used to obtain the optical absorption and reduced scattering coefficients of HIFU-induced thermal lesions and native tissues by employing the inverse adding-doubling method. The aforementioned interaction coefficients were subsequently used to calculate the effective attenuation coefficient and light penetration depth of HIFU-treated and native tissues in the wavelength range of 500–900 nm. Results: HIFU-treated tissues produced greater PA signals than native tissues at 720 and 845 nm. At 720 nm, the averaged ratio of the peak-to-peak PA signal amplitude of HIFU-treated tissue to that of native tissue was 3.68 ± 0.25 (mean ± standard error of the mean). At 845 nm, the averaged ratio of the peak-to-peak PA signal amplitude of HIFU-treated tissue to that of native tissue was 3.75 ± 0.26 (mean ± standard error of the mean). The authors’ spectroscopic investigation has shown that HIFU-treated tissues have a greater optical absorption and reduced scattering coefficients than native tissues in the wavelength range of 500–900 nm. In fact, at 720 and 845 nm, the ratio of the optical absorption coefficient of HIFU-treated tissues to that of native tissues was 1.13 and 1.17, respectively; on the other hand, the ratio of the reduced scattering coefficient of HIFU-treated tissues to that of native tissues was 13.22 and 14.67 at 720 and 845 nm, respectively. Consequently, HIFU-treated tissues have a higher effective attenuation coefficient and a lower light penetration depth than native tissues in the wavelength range 500–900 nm. Conclusions: Using a PA approach, HIFU-treated tissues interrogated at 720 and 845 nm optical wavelengths can be differentiated from untreated tissues. Based on the authors’ spectroscopic investigation, the authors conclude that the observed PA contrast between HIFU-induced thermal lesions and untreated tissue is due, in part, to the increase in the optical absorption coefficient, the reduced scattering coefficient and, therefore, the deposited laser energy fluence in HIFU-treated tissues.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

The Superconductor-Superinsulator Transition: S-duality and the QCD on the Desktop

We show that the nature of quantum phases around the superconductor-insulator transition (SIT) is controlled by charge-vortex topological interactions, and does not depend on the details of material parameters and disorder. We find three distinct phases, superconductor, superinsulator, and bosonic topological insulator. The superinsulator is a state of matter with infinite resistance in a finite temperature range, which is the S-dual of the superconductor and in which charge transport is prevented by electric strings binding charges of opposite sign. The electric strings ensuring linear confinement of charges are generated by instantons and are dual to superconducting Abrikosov vortices. Material parameters and disorder enter the London penetration depth of the superconductor, the string tension of the superinsulator and the quantum fluctuation parameter driving the transition between them. They are entirely encoded in four phenomenological parameters of a topological gauge theory of the SIT. Finally, we point out that, in the context of strong coupling gauge theories, the many-body localization phenomenon that is often referred to as an underlying mechanism for superinsulation is a mere transcription of the well-known phenomenon of confinement into solid-state physics language and is entirely driven by endogenous disorder embodied by instantons with no need of exogenous disorder.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Advances in Spectro‐Microscopy Methods and their Applications in the Characterization of Perovskite Materials

Perovskite materials are promising contenders as the active layer in light-harvesting and light-emitting applications if their long-term stability can be sufficiently increased. Chemical and structural engineering are shown to enhance long-term stability, but the increased complexity of the material system also leads to inhomogeneous functional properties across various length scales. Thus, scanning probe and high-resolution microscopy characterization techniques are needed to reveal the role of local defects and the results promise to act as the foundation for future device improvements. Here, a look at the parameter space: technique-specific sample penetration depth versus probe size highlights a gap in current methods. High spatial resolution combined with a deep penetration depth is not yet achievable. However, multimodal measurement technique may be the key to covering this parameter space. In this perspective, current advanced spectro-microscopy methods which have been applied to perovskite materials are highlighted.

Luo, Yanqi↗
DOE OSTI2023

Effects of lead and lean in multi-axis directed energy deposition

Here, the present study examines the effect of varying laser incidence angles on textural, microstructural, and geometric characteristics of directed energy deposition (DED) processed materials, providing a more comprehensive outlook on participating laser-matter interaction phenomena and ultimately devising strategies to ameliorate print performance. In this study, single-layer, single-/multi-track specimens were processed to examine the effect of non-orthogonal angular configurations on bead morphology, microstructure, phase composition, and textural representation of DED-processed 316L stainless steel materials. It was observed that bead size decreased at increasing lead and lean angles. Asymmetry in the distribution of the bead morphology as a function of lead angle indicates better catchment for acute lead angle configurations over obtuse configurations. No significant differences in phase composition, texture, and microstructure were observed in moderate off-axis configurations. When the penetration depth for the deposits was below 20 μm, columnar structures dominated the microstructure of the deposited material. At deeper penetration depths, columnar and equiaxed structures were observed at the bead-substrate interface and center of the bead, respectively. Compared to powder-blown DED, wire-DED dilution profiles were found to be asymmetric in both orthogonal and non-orthogonal wire DED samples.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators

The tunability of topological surface states and controllable opening of the Dirac gap are of fundamental and practical interest in the field of topological materials. In the newly discovered topological crystalline insulators (TCIs), theory predicts that the Dirac node is protected by a crystalline symmetry and that the surface state electrons can acquire a mass if this symmetry is broken. Recent studies have detected signatures of a spontaneously generated Dirac gap in TCIs; however, the mechanism of mass formation remains elusive. In this work, we present scanning tunnelling microscopy (STM) measurements of the TCI Pb 1-x Sn x Se for a wide range of alloy compositions spanning the topological and non-topological regimes. The STM topographies reveal a symmetry-breaking distortion on the surface, which imparts mass to the otherwise massless Dirac electrons—a mechanism analogous to the long sought-after Higgs mechanism in particle physics. Interestingly, the measured Dirac gap decreases on approaching the trivial phase, whereas the magnitude of the distortion remains nearly constant. Our data and calculations reveal that the penetration depth of Dirac surface states controls the magnitude of the Dirac mass. At the limit of the critical composition, the penetration depth is predicted to go to infinity, resulting in zero mass, consistent with our measurements. Lastly, we discover the existence of surface states in the non-topological regime, which have the characteristics of gapped, double-branched Dirac fermions and could be exploited in realizing superconductivity in these materials.

36 MATERIALS SCIENCE↗
NASA NTRS1985

Preliminary study of gaseous nitrogen-liquid oxygen mixing and self cleaning

The penetration of gaseous nitrogen into liquid oxygen at a pressure of 150 psi was determined by monitoring the composition of the evaporating liquid in a nitrogen analyzer. For pressurization times of about 1 hr the penetration depth varies between 0.0024 and 0.018 in. at an evaporation rate of about 1 gal/day. These are small compared to the penetration depth of 22.2 in. measured in the 7-inch high temperature tunnel at a pressure of 1500 psi, pressurization time of 5 min, and evaporation rate of 121 gal/day.

Zuckerwar, A. J.↗
DOE OSTI2024

Machine Learning of Performance Space Mapping for the DPD Simulation of Drug Delivery to Endothelial Cells

Despite huge effort over the years, the design of functionalised nanocarriers (NCs) for targeted drug delivery to endothelial cells is still to be completely unveiled. Dissipative particle dynamics (DPD) simulation is used to study the adhesion of NCs to endothelial cells under the influence of series of parameters such as shape, size, and ligand density of the NCs. However, preparing a performance space mapping that illustrates the penetration depths of NCs as a function of variations in their properties requires simulations of all possible NCs with the above-mentioned properties, which is not feasible. This challenge was addressed by leveraging a Gaussian process regression (GPR)-informed active learning strategy and an extensive exploration of numerous samples, each representing different properties of NCs. The performance space mapping reveals that NCs with rod and disc shapes exhibit superior penetration capabilities compared to those with a spherical shape. Furthermore, it demonstrates that smaller-sized rod-shaped NCs and larger-sized disc-shaped NCs tend to achieve better penetration. When considering smaller NCs, the influence of ligand density appears to be limited. On the contrary, for larger NCs, an increase in ligand density correlates with greater penetration depth, underscoring its substantial role in shaping their penetration capabilities.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Large-eddy simulations of surface roughness parameter sensitivity to canopy-structure characteristics

Surface roughness parameters, namely the roughness length and displacement height, are an integral input used to model surface fluxes. However, most models assume these parameters to be a fixed property of plant functional type and disregard the governing structural heterogeneity and dynamics. In this study, we use large-eddy simulations to explore, in silico, the effects of canopy-structure characteristics on surface roughness parameters. We performed a virtual experiment to test the sensitivity of resolved surface roughness to four axes of canopy structure: (1) leaf area index, (2) the vertical profile of leaf density, (3) canopy height, and (4) canopy gap fraction. We found roughness parameters to be highly variable, but uncovered positive relationships between displacement height and maximum canopy height, aerodynamic canopy height and maximum canopy height and leaf area index, and eddy-penetration depth and gap fraction. We also found negative relationships between aerodynamic canopy height and gap fraction, as well as between eddy-penetration depth and maximum canopy height and leaf area index. We generalized our model results into a virtual "biometric" parameterization that relates roughness length and displacement height to canopy height, leaf area index, and gap fraction. Using a decade of wind and canopy-structure observations in a site in Michigan, we tested the effectiveness of our model-driven biometric parameterization approach in predicting the friction velocity over heterogeneous and disturbed canopies. We compared the accuracy of these predictions with the friction-velocity predictions obtained from the common simple approximation related to canopy height, the values calculated with large-eddy simulations of the explicit canopy structure as measured by airborne and ground-based lidar, two other parameterization approaches that utilize varying canopy-structure inputs, and the annual and decadal means of the surface roughness parameters at the site from meteorological observations. We found that the classical representation of constant roughness parameters (in space and time) as a fraction of canopy height performed relatively well. Nonetheless, of the approaches we tested, most of the empirical approaches that incorporate seasonal and interannual variation of roughness length and displacement height as a function of the dynamics of canopy structure produced more precise and less biased estimates for friction velocity than models with temporally invariable parameters.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2012

Comparison of Surface Elevation Changes of the Greenland and Antarctic Ice Sheets from Radar and Laser Altimetry

A primary purpose of satellite altimeter measurements is determination of the mass balances of the Greenland and Antarctic ice sheets and changes with time by measurement of changes in the surface elevations. Since the early 1990's, important measurements for this purpose have been made by radar altimeters on ERS-l and 2, Envisat, and CryoSat and a laser altimeter on ICESat. One principal factor limiting direct comparisons between radar and laser measurements is the variable penetration depth of the radar signal and the corresponding location of the effective depth of the radar-measured elevation beneath the surface, in contrast to the laser-measured surface elevation. Although the radar penetration depth varies significantly both spatially and temporally, empirical corrections have been developed to account for this effect. Another limiting factor in direct comparisons is caused by differences in the size of the laser and radar footprints and their respective horizontal locations on the surface. Nevertheless, derived changes in elevation, dHldt, and time-series of elevation, H(t), have been shown to be comparable. For comparisons at different times, corrections for elevation changes caused by variations in the rate offrrn compaction have also been developed. Comparisons between the H(t) and the average dH/dt at some specific locations, such as the Vostok region of East Antarctic, show good agreement among results from ERS-l and 2, Envisat, and ICESat. However, Greenland maps of dHidt from Envisat and ICESat for the same time periods (2003-2008) show some areas of significant differences as well as areas of good agreement. Possible causes of residual differences are investigated and described.

Zwally, H. Jay↗
DOE OSTI2020

Comparative Analysis of Capacitive Sensors with Different Geometrical layouts for Cable Insulation Degradation Detection

This paper presents a comparative analysis between an Interdigital Capacitor (IDC) sensor and a Serpentine Capacitive (SRC) sensor. The effects of electrode layouts on sensor performance are studied by means of finite element simulation where the geometrical dimensions (except electrode length) and material characteristics of both sensors are identical. Conformal IDC and SRC sensors with equal sensor area are modeled on a cable surface. The simulation results show a tradeoff between IDC and SRC sensors in terms of sensitivity and penetration depth. The SRC sensor shows 13.3% increase in sensitivity and 16.8% increase in capacitance compared to the IDC sensor, though the electric field penetration depth of the SRC sensor is 18.8% lower than the IDC sensor. In addition, the effects of change in electrode width, inter-electrode gap, and number of electrodes on SRC and IDC sensor comparative performance are evaluated.

Interdigital Capacitance, Serpentive Capacitive Se↗
NASA NTRS1994

The Flow Induced by the Coalescence of Two Initially Stationary Drops

The coalescence of two initially stationary drops of different size is investigated by solving the unsteady, axisymmetric Navier-Stokes equations numerically, using a Front-Tracking/Finite Difference method. Initially, the drops are put next to each other and the film between them ruptured. Due to surface tension forces, the drops coalesce rapidly and the fluid from the small drop is injected into the larger one. For low nondimensional viscosity, or Ohnesorge number, little mixing takes place and the small drop fluid forms a blob near the point where the drops touched initially. For low Ohnesorge number, on the other hand, the small drop forms a jet that penetrates far into the large drop. The penetration depth also depends on the size of the drops and shows that for a given fluid of sufficiently low viscosity, there is a maximum penetration depth for intermediate size ratios.

Nobari, M. R.↗