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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Crystalline Organic Compounds as Effective Nuclei in Contact Efflorescence of Ammonium Sulfate

Contact nucleation is believed to play a role in liquid-to-solid phase transitions in the atmosphere including ice nucleation and salt efflorescence. Here, for this work, contact efflorescence of optically levitated ammonium sulfate droplets by collisions with organic particles is probed using a long working-distance optical trap. Two highly viscous water-soluble organic compounds (d-(+)-raffinose and citric acid), and two insoluble highly surface-active organic compounds (stearic acid and cis-pinonic acid) were probed for their ability to induce efflorescence upon contact. While three of the organics showed minimal effectiveness as contact nuclei, cis-pinonic acid showed a remarkable ability to initiate contact efflorescence of ammonium sulfate, occurring near ammonium sulfate’s deliquescence relative humidity. Further analysis of cis-pinonic acid using bright-field microscopy in an electrodynamic balance provided evidence that the cis-pinonic acid particles are crystalline under the laboratory conditions. We suggest that the close lattice match between crystalline ammonium sulfate and crystalline cis-pinonic acid may account for the observed effectiveness in initiating contact efflorescence of ammonium sulfate. In contrast, tests of contact nucleation between cis-pinonic acid and sodium chloride, a pair with a poor lattice match, did not result in efflorescence. These findings suggest that crystalline organic compounds in the atmosphere could act as effective nuclei for contact efflorescence of atmospherically relevant salts, provided they share a compatible lattice structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Identifying impacts of contact tracing on HIV epidemiological inference from phylogenetic data

Abstract Robust sampling methods are foundational to inferences using phylogenies. Yet the impact of using contact tracing, a type of non-uniform sampling used in public health applications such as infectious disease outbreak investigations, has not been investigated in the molecular epidemiology field. To understand how contact tracing influences a recovered phylogeny, we developed a new simulation tool called SEEPS (Sequence Evolution and Epidemiological Process Simulator) that allows for the simulation of contact tracing and the resulting transmission tree, pathogen phylogeny, and corresponding virus genetic sequences. Importantly, SEEPS takes within-host evolution into account when generating pathogen phylogenies and sequences from transmission histories. Using SEEPS, we demonstrate that contact tracing can significantly impact the structure of the resulting tree, as described by popular tree statistics. Contact tracing generates phylogenies that are less balanced than the underlying transmission process, less representative of the larger epidemiological process, and affects the internal/external branch length ratios that characterize specific epidemiological scenarios. We also examined real data from a 2007–2008 Swedish HIV-1 outbreak and the broader 1998–2010 European HIV-1 epidemic to highlight the differences in contact tracing and expected phylogenies. Aided by SEEPS, we show that the data collection of the Swedish outbreak was strongly influenced by contact tracing even after downsampling, while the broader European Union epidemic showed little evidence of universal contact tracing, agreeing with the known epidemiological information about sampling and spread. Overall, our results highlight the importance of including possible non-uniform sampling schemes when examining phylogenetic trees. For that, SEEPS serves as a useful tool to evaluate such impacts, thereby facilitating better phylogenetic inferences of the characteristics of a disease outbreak. SEEPS is available at https://github.com/MolEvolEpid/SEEPS.

Virology↗
NASA NTRS1981

Dynamics of solid dispersions in oil during the lubrication of point contacts. Part 1: Graphite

A Hertzian contact was lubricated with dispersed graphite in mineral oils under boundary lubrication conditions. The contact was optically observed under pure rolling, combined rolling and sliding, and pure sliding conditions. The contact was formed with a steel ball on the flat surface of a glass disk. Photomicrographs are presented which show the distribution of the graphite in and around the contact. Friction and surface damage are also shown for conditions when the base oils are used alone and when graphite is added to the base oils. Under pure rolling and combined rolling and sliding conditions, it is found that, for low speeds, a graphite film can form which will separate the contacting surfaces. Under pure sliding conditions, graphite accumulates at the inlet and sweeps around the contact, but very little of the graphite passes through the contact. The accumulated graphite appears to act as a barrier which reduces the supply of oil available to the contact for boundary lubrication. Friction data show no clear short term beneficial or detrimental effect caused by addition of graphite to the base oil. However, during pure sliding, more abrasion occurs on the polished balls lubricated with the dispersion than on those lubricated with the base oil alone. All observations were for the special case of a highly-polished ball on a glass surface and may not be applicable to other geometries and materials, or to rougher surfaces.

Cusano, C.↗
NASA NTRS1990

Influence of linear profile modification and loading conditions on the dynamic tooth load and stress of high contact ratio gears

A computer simulation for the dynamic response of high-contact-ratio spur gear transmissions is presented. High contact ratio gears have the potential to produce lower dynamic tooth loads and minimum root stress but they can be sensitive to tooth profile errors. The analysis presented examines various profile modifications under realistic loading conditions. The effect of these modifications on the dynamic load (force) between mating gear teeth and the dynamic root stress is presented. Since the contact stress is dependent on the dynamic load, minimizing dynamic loads will also minimize contact stresses. It is shown that the combination of profile modification and the applied load (torque) carried by a gear system has a significant influence on gear dynamics. The ideal modification at one value of applied load will not be the best solution for a different load. High-contact-ratio gears were found to require less modification than standard low-contact-ratio gears. High-contact-ratio gears are more adversely affected by excess modification than by under modification. In addition, the optimal profile modification required to minimize the dynamic load (hence the contact stress) on a gear tooth differs from the optimal modification required to minimize the dynamic root (bending) stress. Computer simulation can help find the design tradeoffs to determine the best profile modification to satisfy the conflicting constraints of minimizing both the load and root stress in gears which must operate over a range of applied loads.

Lee, Chinwai↗
NASA NTRS1995

Sensitivity analysis of frictional contact response of axisymmetric composite structures

A computational procedure is presented for evaluating the sensitivity coefficients of the static frictional contact response of axisymmetric composite structures. The structures are assumed to consist of an arbitrary number of perfectly bonded homogeneous anisotropic layers. The material of each layer is assumed to be hyperelastic, and the effect of geometric nonlinearity is included. The sensitivity coefficients measure the sensitivity of the response variations in different material, lamination and geometric parameters of the structure. A displacement finite element model is used for the discretization. The normal contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of nodal displacements, and Lagrange multipliers associated with the contact conditions. The Lagrange multipliers are allowed to be discontinuous at interelement boundaries. Tangential contact conditions are incorporated by using a penalty method in conjunction with the classical Coulomb's friction model. The Newton-Raphson iterative scheme is used for the solution of the resulting nonlinear algebraic equations, and for the determination of the contact region, contact conditions (sliding or sticking), and the contact pressures. The sensitivity coefficients are evaluated by using a direct differentiation approach. Numerical results are presented for the frictional contact of a composite spherical cap pressed against a rigid plate.

Karaoglan, I.↗
NASA NTRS2000

Effects of Evaporation/Condensation on Spreading and Contact Angle of a Volatile Liquid Drop

Effects of evaporation/condensation on spreading and contact angle were experimentally studied. A sessile drop of R-113 was tested at different vapor environments to determine the effects of evaporation/condensation on the evolution of contact diameter and contact angle of the drop. Condensation on the drop surface occurs at both the saturated and a nonsaturated vapor environments and promotes the spreading. When the drop is placed in the saturated vapor environment it tends to completely wetting and spreads rapidly. In a nonsaturated vapor environment, the evolution of the sessile drop is divided three stages: condensation-spreading stage, evaporation-retracting stage and rapid contracting stage. In the first stage the drop behaves as in the saturated environment. In the evaporation -retracting stage, the competition between spreading and evaporation of the drop determines the evolution characteristics of the contact diameter and the contact angle. A lower evaporation rate struggles against the spreading power to turn the drop from spreading to retracting with a continuous increase of the contact angle. The drop placed in open air has a much higher evaporation rate. The strong evaporation suppresses the spreading and accelerates the retraction of the drop with a linear decrease of the contact diameter. The contraction of the evaporating drops is gradually accelerated when the contact diameter decreases to 3 min and less till drying up, though the evaporation rate is gradually slowing down.

Zhang, Nengli↗
NASA NTRS2001

Study of Electrical Contacts and Devices in Advanced Semiconductors

Research conducted at Tuskegee University concentrates on electrical contacts to GaN films and their characterization with the objective of understanding contact formation and realizing low-resistance metal contacts. Contact properties are known to be strongly related to surface preparation. It appears that the as-received material had a thin oxide film on the surface of the GaN film. Various cleaning treatments were employed in order to render the surface contamination free and removal of the oxide film. Metal films were then deposited by e-beam evaporation. Electrical characteristics of these contacts indicated that the optimal treatment was an organic solvent cleaning followed by etching in buffered oxide solution. Contacts established with Al were observed to be ohmic in nature, whereas Au, Cr, Ti, and Pt exhibit rectifying contacts. Platinum contacts were almost ideal as shown by an ideality factor of 1.02.

Hall, H. P.↗
NASA NTRS2004

Subsurface Stress Fields in FCC Single Crystal Anisotropic Contacts

Single crystal superalloy turbine blades used in high pressure turbomachinery are subject to conditions of high temperature, triaxial steady and alternating stresses, fretting stresses in the blade attachment and damper contact locations, and exposure to high-pressure hydrogen. The blades are also subjected to extreme variations in temperature during start-up and shutdown transients. The most prevalent high cycle fatigue (HCF) failure modes observed in these blades during operation include crystallographic crack initiation/propagation on octahedral planes, and non-crystallographic initiation with crystallographic growth. Numerous cases of crack initiation and crack propagation at the blade leading edge tip, blade attachment regions, and damper contact locations have been documented. Understanding crack initiation/propagation under mixed-mode loading conditions is critical for establishing a systematic procedure for evaluating HCF life of single crystal turbine blades. This paper presents analytical and numerical techniques for evaluating two and three dimensional subsurface stress fields in anisotropic contacts. The subsurface stress results are required for evaluating contact fatigue life at damper contacts and dovetail attachment regions in single crystal nickel-base superalloy turbine blades. An analytical procedure is presented for evaluating the subsurface stresses in the elastic half-space, based on the adaptation of a stress function method outlined by Lekhnitskii. Numerical results are presented for cylindrical and spherical anisotropic contacts, using finite element analysis (FEA). Effects of crystal orientation on stress response and fatigue life are examined. Obtaining accurate subsurface stress results for anisotropic single crystal contact problems require extremely refined three-dimensional (3-D) finite element grids, especially in the edge of contact region. Obtaining resolved shear stresses (RSS) on the principal slip planes also involves considerable post-processing work. For these reasons it is very advantageous to develop analytical solution schemes for subsurface stresses, whenever possible.

Arakere, Nagaraj K.↗
NASA NTRS1999

Precision contact of the fingertip reduces postural sway of individuals with bilateral vestibular loss

Contact of the hand with a stationary surface attenuates postural sway in normal individuals even when the level of force applied is mechanically inadequate to dampen body motion. We studied whether subjects without vestibular function would be able to substitute contact cues from the hand for their lost labyrinthine function and be able to balance as well as normal subjects in the dark without finger contact. We also studied the relative contribution of sight of the test chamber to the two groups. Subjects attempted to maintain a tandem Romberg stance for 25 s under three levels of fingertip contact: no contact; light-touch contact, up to 1 N (approximately 100 g) force; and unrestricted contact force. Both eyes open and eyes closed conditions were evaluated. Without contact, none of the vestibular loss subjects could stand for more than a few seconds in the dark without falling; all the normals could. The vestibular loss subjects were significantly more stable in the dark with light touch of the index finger than the normal subjects in the dark without touch. They also swayed less in the dark with light touch than when permitted sight of the test chamber without touch, and less with sight and touch than just sight. The normal subjects swayed less in the dark with touch than without, and less with sight and touch than sight alone. These findings show that during quiet stance light touch of the index finger with a stationary surface can be as effective or even more so than vestibular function for minimizing postural sway.

NASA Discipline Neuroscience↗
NASA NTRS1998

Cell contact as an independent factor modulating cardiac myocyte hypertrophy and survival in long-term primary culture

Cardiac myocytes maintained in cell culture develop hypertrophy both in response to mechanical loading as well as to receptor-mediated signaling mechanisms. However, it has been shown that the hypertrophic response to these stimuli may be modulated through effects of intercellular contact achieved by maintaining cells at different plating densities. In this study, we show that the myocyte plating density affects not only the hypertrophic response and features of the differentiated phenotype of isolated adult myocytes, but also plays a significant role influencing myocyte survival in vitro. The native rod-shaped phenotype of freshly isolated adult myocytes persists in an environment which minimizes myocyte attachment and spreading on the substratum. However, these conditions are not optimal for long-term maintenance of cultured adult cardiac myocytes. Conditions which promote myocyte attachment and spreading on the substratum, on the other hand, also promote the re-establishment of new intercellular contacts between myocytes. These contacts appear to play a significant role in the development of spontaneous activity, which enhances the redevelopment of highly differentiated contractile, junctional, and sarcoplasmic reticulum structures in the cultured adult cardiomyocyte. Although it has previously been shown that adult cardiac myocytes are typically quiescent in culture, the addition of beta-adrenergic agonists stimulates beating and myocyte hypertrophy, and thereby serves to increase the level of intercellular contact as well. However, in densely-plated cultures with intrinsically high levels of intercellular contact, spontaneous contractile activity develops without the addition of beta-adrenergic agonists. In this study, we compare the function, morphology, and natural history of adult feline cardiomyocytes which have been maintained in cultures with different levels of intercellular contact, with and without the addition of beta-adrenergic agonists. Intercellular contact, communication, and transmission of contractile forces between myocytes appears to play a primary role in remodeling the 2-dimensional cell layer into a parallel alignment of elongated myocytes with highly developed intercalated disk-like junctions. This highly differentiated state is very stable, and cultures which achieve this state exhibit significantly greater longevity than more sparsely plated myocytes. These myocytes typically continue beating, and survive from 6 to more than 12 weeks in culture. When this level of contact and differentiation are not achieved, even among beta-adrenergic stimulated myocytes, contractile activity is not sustained, myofibrils atrophy, there is little or no development of junctional complexes, and the period of myocyte viability is typically no more than 5 weeks in vitro.

Non-NASA Center↗
DOE OSTI2026

C‐Cracking of Brittle‐Material Spheres From Eccentric Hertzian Contact

Contact of brittle-material spheres can occur while they are manufactured, handled, or used in operation as roller elements or in deformably processed composite material. Statistically, the directional contact between two spheres will nearly always be oblique or eccentric in an unconfined and mobile sphere population. Although analyses of oblique contact exist, the portrayal of its maximum (tensile) first principal stress ( S 1 ) field is lacking. This information is needed for improved judgment of the prospect of crack initiation. Given these, the S 1 due to eccentric contact and subsequent crack initiation was analyzed using finite element analysis (FEA) and corroborative demonstration of c-crack creation. The FEA shows that an asymmetric S 1 field is created about the contact patch and is caused by superimposed shear intrinsic to eccentric contact. A crack will initiate if the maximum S 1 exceeds the material's tensile strength, and its field will cause the crack to propagate and arrest to form a C-shaped crack, or c-crack. C-crack initiation trends with lower applied forces, with greater amount of contact eccentricity, higher coefficient of friction, and smaller spherical radius. Finally, these metrics deserve recognition, especially when c-cracked brittle-material spheres are used in a system whose functionality or reliability is potentially compromised by the c-cracks.

Hertzian contact↗
DOE OSTI2026

Algebraic Multigrid with Filtering: An Efficient Preconditioner for Interior Point Methods in Large-Scale Contact Mechanics Optimization

Large-scale contact mechanics simulations are crucial in many engineering fields such as structural design and manufacturing. In the frictionless case, contact can be modeled by minimizing an energy functional; however, these problems are often nonlinear, nonconvex, and increasingly difficult to solve as mesh resolution increases. In this work, we employ a Newton-based interior-point (IP) filter line-search method, an effective approach for large-scale constrained optimization. While this method converges rapidly, each iteration requires solving a large saddle-point linear system that becomes ill-conditioned as the optimization process converges, largely due to IP treatment of the contact constraints. Such ill-conditioning can hinder solver scalability and increase iteration counts with mesh refinement. Here, to address this, we introduce a novel preconditioner, algebraic multigrid with filtering (AMGF), tailored to the Schur complement of the saddle-point system. Building on the classical AMG solver, commonly used for elasticity, we augment it with a specialized subspace correction that filters near null space components introduced by contact interface constraints. Through theoretical analysis and numerical experiments on a range of linear and nonlinear contact problems, we demonstrate that the proposed solver achieves mesh independent convergence and maintains robustness against the ill-conditioning that notoriously plagues IP methods. These results indicate that AMGF makes contact mechanics simulations more tractable and broadens the applicability of Newton-based IP methods in challenging engineering scenarios. More broadly, AMGF is well suited for problems, optimization or otherwise, where solver performance is limited by a low-dimensional subspace, such as those arising from localized constraints, interface conditions, or model heterogeneities. This makes the method widely applicable beyond contact mechanics and constrained optimization.

Mathematics and Computing↗
DOE OSTI2025

Characterization of Performance Degradation Mechanisms in Low-Cost High Throughput DI-O3 Layer for Passivated Contact Silicon Solar Cells

Characterization and mitigating performance limiting defects in Silicon (Si) PV is one of key areas to be addressed to improve PV hardware costs and energy yield in order to lower the levelized cost of energy (LCOE) of installed PV cost to $0.02/kWh. As Si PV cells efficiencies have surpassed 22% and approaching 23%, the recombination at the metal contacts have become the focus point to be addressed. Passivated contact technologies—having a heterojunction with a band-gap larger than silicon between the metal and silicon—have emerged as a great potential for future highand ultrahigh-efficiency solar cells, as it concurrently reduces recombination and increases carrier selectivity, by incorporating thin films within the contact structure. Passivated contact Si solar cell technologies use a wide variety of tunnel layers—playing a crucial role to passivate metal contacts and tunnel charge carriers—including stoichiometric silicon oxide (SiO 2 ) grown by thermal oxidation and Low-Pressure Chemical Vapor Deposition (LPCVD) technique and silicon oxide (SiO x ) by hot nitric acid. However, thorough investigations on understanding the failure and performance degradation mechanisms associated with tunnel layers are still limited to date. Unlocking those degradation characteristics in crucial tunnel layers could improve the reliability and energy yield of passivated contact Si solar cells. Besides, the technique of growing aforementioned tunneling layers are low throughput, and requires high temperature processes and/or a vacuum environment. In this project, we investigated the performance degradation mechanisms of a low-cost high-throughput ozonated oxide (DI-O 3 ) tunnel layer for the passivated contact Si solar cells.

14 SOLAR ENERGY↗
DOE OSTI2025

Methods to Observe Tribological Failures in Self-Mated Steel Contacts

Scuffing, a type of wear found in highly stressed or poorly lubricated contacts, is characterized by a rapid increase in friction and severe plastic deformation of the near-surface material. Scuffing has proven difficult to study because it initiates unpredictably, progresses rapidly, and typically develops within an inaccessible contact interface. Although there have been successful in-situ studies of scuffing in real-time, the transparent counter body needed for these studies changes the interactions between the surfaces and the lubricant, which affects the scuffing process in unknown ways. This paper describes the development of X-ray-compatible tribometry to study the scuffing of self-mated steels in-situ and in real-time. The method uses a crossed cylinders configuration with a thin (500 μm thick) stationary component and a small (≈200 μm) contact width to maximize X-ray interactions with atoms within the stress field generated by the contact. The resulting instrument and method are used to benchmark the scuffing response of self-mated 52,100 steel under tribologically challenging ‘oil-off’ lubrication conditions. The results demonstrate reliable scuffing in this configuration despite the relatively small contact areas and loads used. Following scuffing, gross plastic deformation was observed on both surfaces along with significant subsurface grain refinement and flow only on the stationary surface, which experienced constant contact. Interestingly, high friction initiated at specific locations of the migratory surface, which experienced intermittent contact, and then propagated across the track over time, suggesting that local conditions of the migratory surface dominated friction leading into the failure event.

36 MATERIALS SCIENCE↗
DOE OSTI2024

A multiscale model to understand the interface chemistry, contacts, and dynamics during lithium stripping

A reversible Li-metal electrode, paired with a solid electrolyte, is critical for attaining higher energy density and safer batteries beyond the current lithium-ion cells. A stable stripping process may be even harder to attain as the stripping process will remove Li-atoms from the surface, and naturally reduce surface contact area, if not self-corrected by other mechanisms, such as diffusion and plastic deformation under an applied external stack pressure. Here, we capture these mechanisms occurring at multiple length- and time- scales, i.e., interface interactions, vacancy hopping, and plastic deformation, by integrating density functional theory (DFT) simulations, kinetic Monte Carlo (KMC), and continuum finite element method (FEM). By assuming the self-affine nature of multiscale contacts, we predict the steady-state contact area as a function of stripping current density, interface wettability, and stack pressure. We further estimate the exponential increase of overpotential due to contact area loss to maintain the same stripping current density. We demonstrate that a lithiophilic interface requires less stack pressure to reach the same steady-state contact area fraction than a lithiophobic interface. A “tolerable steady-state” contact area loss for maintaining stable stripping is estimated at 20 %, corresponding to a 10 % increase in overpotential. To constrain contact loss within the tolerance, the required stack pressure is 0.1, 0.5, and 2 times the yield strength of lithium metal for three distinct interfaces, lithiophilic Li/lithium oxide(Li2O), Li/lithium lanthanum zirconium oxide(LLZO), and lithiophoblic Li/lithium fluoride(LiF), respectively. The modeling results agree with experiments on the impact of the stack pressure quantitatively, while the discrepancy in stripping rate sensitivity is attributed to the simplifying interface interaction in our simulations. Overall, this multiscale simulation framework demonstrates the importance of electrochemical-mechanical coupling in understanding the dynamics of the Li/SE interface during stripping.

Feng, Min↗
NASA NTRS1972

Solar cell contact pull strength as a function of pull-test temperature

Four types of solar cell contacts were given pull-strength tests at temperatures between -173 and +165 C. Contacts tested were: (1) solder-coated titanium-silver contacts on n-p cells, (2) palladium-containing titanium-silver contacts on n-p cells, (3) titanium-silver contacts on 0.2-mm-thick n-p cells, and (4) solder-coated electroless-nickel-plated contacts on p-n cells. Maximum pull strength was demonstrated at temperatures significantly below the air mass zero cell equilibrium temperature of +60 C. At the lowest temperatures, the chief failure mechanism was silicon fracture along crystallographic planes; at the highest temperatures, it was loss of solder strength. In the intermediate temperatures, many failure mechanisms operated. Pull-strength tests give a good indication of the suitability of solar cell contact systems for space use. Procedures used to maximize the validity of the results are described.

Yasui, R. K.↗
NASA NTRS1978

An exact derivation of contact resistance to planar devices

A mixed boundary-value problem is formulated for an imperfect rectangular contact to a semiconducting sheet (layer). An exact model for derivation of contact resistance is developed and its solution by conformal mapping and eigenfunction expansion is presented. The expression for contact resistance is similar to that for a perfect (lossless) contact but includes an additional term containing the lowest-order coefficient in the infinite series expansion of the complex potential function. The calculated contact resistances are compared with those obtained from three approximate models: lossless contact, transmission line, and extended transmission line models. The extended transmission line model appears to be a very satisfactory approximation provided the ratio of contact length to sheet thickness is no less than 0.5.

Schuldt, S. B.↗
NASA NTRS1981

Elastohydrodynamic lubrication of elliptical contacts

The determination of the minimum film thickness within contact is considered for both fully flooded and starved conditions. A fully flooded conjunction is one in which the film thickness is not significantly changed when the amount of lubricant is increased. The fully flooded results presented show the influence of contact geometry on minimum film thickness as expressed by the ellipticity parameter and the dimensionless speed, load, and materials parameters. These results are applied to materials of high elastic modulus (hard EHL), such as metal, and to materials of low elastic modulus(soft EHL), such as rubber. In addition to the film thickness equations that are developed, contour plots of pressure and film thickness are given which show the essential features of elastohydrodynamically lubricated conjunctions. The crescent shaped region of minimum film thickness, with its side lobes in which the separation between the solids is a minimum, clearly emerges in the numerical solutions. In addition to the 3 presented for the fully flooded results, 15 more cases are used for hard EHL contacts and 18 cases are used for soft EHL contacts in a theoretical study of the influence of lubricant starvation on film thickness and pressure. From the starved results for both hard and soft EHL contacts, a simple and important dimensionless inlet boundary distance is specified. This inlet boundary distance defines whether a fully flooded or a starved condition exists in the contact. Contour plots of pressure and film thickness in and around the contact are shown for conditions.

Hamrock, B. J.↗