scholarly journals Distribution of Gaps and Adhesive Interaction between Contacting Rough Surfaces

2021 ◽  
Author(s):  
Joseph M. Monti ◽  
Antoine Sanner ◽  
Lars Pastewka
Keyword(s):  
Rough Surfaces ◽  
Characteristic Scale ◽  
Surface Slope ◽  
Adhesive Interaction ◽  
Frictionless Contact ◽  
Quantitative Estimates ◽  
The Mean ◽  
Fine Resolution ◽  
Adhesive Contacts ◽  
Adhesive Forces

Abstract Understanding the distribution of interfacial separations between contacting rough surfaces is integral for providing quantitative estimates for adhesive forces between them. Assuming nonadhesive, frictionless contact of self-affine surfaces, we derive the distribution of separations p(g) between surfaces near the contact edge. The distribution diverges as g-1/3 for small gaps, and we use numerical simulations with fine resolution to confirm the scaling. The characteristic scale over which the prediction persists is h0' drep, the product of the rms surface slope and the mean diameter of contacting regions. We show that these results remain valid for weakly adhesive contacts and connect these observations to recent theories for adhesion between rough surfaces.

Contact Model of Two Rough Surfaces Based on a Visco-Elasto-Adhesive Interaction

2010 ◽  
Author(s):  
Ali Sepehri ◽  
Kambiz Farhang
Keyword(s):  
Normal Force ◽  
Rough Surfaces ◽  
Mathematical Formulation ◽  
Contact Model ◽  
Force Component ◽  
Adhesive Interaction ◽  
Normal Contact ◽  
Rate Dependent ◽  
Statistical Consideration ◽  
Adhesive Forces

Mathematical formulae are derived for normal contact force component between two nominally flat rough surfaces. The development of the contact model is based on the asperity level interaction in which adhesive forces between two asperities as well as elastic and rate-dependent forces are included. Statistical consideration of rough surfaces yields the mathematical formulation of total normal force due to adhesion, elastic and rate-dependent properties of the surfaces in contact.

Leakage Prediction in Mechanical Seals Under Hydrostatic Operating Condition

2007 ◽  
Author(s):  
S. Elhanafi ◽  
K. Farhang
Keyword(s):  
Closed Form ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Rough Surfaces ◽  
Mechanical Seals ◽  
Operating Condition ◽  
Form Equation ◽  
Macro Scale ◽  
The Mean

This paper considers leakage in mechanical seals under hydrostatic operating condition. A contact model based on the Greenwood and Williamson contact of rough surfaces is developed for treating problems involving mechanical seals in which both the micron scale roughness of the seal face and its macro scale profile are used to obtain either a closed-form equation or a nonlinear equation relating mean plane separation to the mass flow rate. The equations involve the micron scale geometry of the rough surfaces and physical parameter of the seal and carriage. Under hydrostatic condition, it is shown that there is an approximate closed-form solution in which mass flow rate in terms of the mean plane separation, or alternatively, the mean plane separation in terms of the leakage mass flow rate is found. Equations pertaining to leakage in nominally flat seal macro profile is considered and closed form equation relating to leakage flow rate to pressure difference is obtained that contain macro and micron geometries of the seal.

THE TERMINAL GROUPS OF RIBONUCLEATE CHAINS IN EACH OF THE 16S AND 23S COMPONENTS OF ESCHERICHIA COLI RIBOSOMAL RNA

1967 ◽  
Vol 45 (6) ◽  
pp. 937-948 ◽  
Author(s):  
J. L. Nichols ◽  
B. G. Lane
Keyword(s):  
Escherichia Coli ◽  
Chain Length ◽  
Ribosomal Rna ◽  
Gradient Centrifugation ◽  
Sucrose Density Gradient ◽  
Sucrose Density Gradient Centrifugation ◽  
Quantitative Estimates ◽  
16S Rna ◽  
The Mean ◽  
End Group

Ribosomal ribonucleates from Escherichia coli have been resolved into 16S and 28S components by sucrose density-gradient centrifugation, and the chain termini in each of the 16S and 23S RNA components have been analyzed by hydrolysis with alkali. The principal 5′-linked end group of 16S RNA was found to be adenosine, and the principal 5′-linked end group of 23S RNA was found to be uridine. The principal 3′-linked end group of 16S RNA was also found to be adenosine, whereas the principal 3′-linked end group of 23S RNA was found to be guanosine. Quantitative estimates of chain length based on analyses for 5′-iinked terminals indicate that the mean chain length for 16S RNA is about 1.3 × 103nucleotide residues and the mean chain length for 23S RNA is about 2.1 × 103nucleotide residues.

scholarly journals Spatial model of the gecko foot hair: functional significance of highly specialized non-uniform geometry

2015 ◽  
Vol 5 (1) ◽  
pp. 20140065 ◽  
Author(s):  
Alexander E. Filippov ◽  
Stanislav N. Gorb
Keyword(s):  
Functional Significance ◽  
Spatial Model ◽  
Rough Surfaces ◽  
Three Dimensional ◽  
Intermolecular Forces ◽  
Dimensional Structure ◽  
Fractal Surface ◽  
Flexible Form ◽  
Spatial Geometry ◽  
Adhesive Contacts

One of the important problems appearing in experimental realizations of artificial adhesives inspired by gecko foot hair is so-called clusterization. If an artificially produced structure is flexible enough to allow efficient contact with natural rough surfaces, after a few attachment–detachment cycles, the fibres of the structure tend to adhere one to another and form clusters. Normally, such clusters are much larger than original fibres and, because they are less flexible, form much worse adhesive contacts especially with the rough surfaces. Main problem here is that the forces responsible for the clusterization are the same intermolecular forces which attract fibres to fractal surface of the substrate. However, arrays of real gecko setae are much less susceptible to this problem. One of the possible reasons for this is that ends of the seta have more sophisticated non-uniformly distributed three-dimensional structure than that of existing artificial systems. In this paper, we simulated three-dimensional spatial geometry of non-uniformly distributed branches of nanofibres of the setal tip numerically, studied its attachment–detachment dynamics and discussed its advantages versus uniformly distributed geometry.

scholarly journals Accumulation and Temperature on The Inland Ice of North Greenland, 1959

1961 ◽  
Vol 3 (30) ◽  
pp. 1017-1044 ◽  
Author(s):  
Chester C. Langway
Keyword(s):  
Snow Accumulation ◽  
Surface Slope ◽  
Empirical Correlations ◽  
Altitude Gradient ◽  
Local Climate ◽  
The Mean ◽  
Inland Ice ◽  
Deep Pits ◽  
North Greenland ◽  
Linear Trends

AbstractTwelve deep pits (5 to 5.5 m.) revealed between 6 and 13 years of snow accumulation. The results show an average net accumulation of 18.5 g./cm.2per year. Accumulation decreases inland at a mean rate of 1.5 g./cm.2per 100 m. rise in elevation. Temperature measurements at 100 m. in all pits give a mean temperature-altitude gradient of 0.77° C. per 100 m. Evidence of melt was observed in all pits, the most pronounced melt occurring in 1954. The mean density reflects the local climate. Other empirical correlations of these data show linear trends that vary systematically with surface slope and local climate.

Females of a solitary bee reject males to collect food for offspring

2020 ◽  
Vol 31 (4) ◽  
pp. 884-891 ◽  
Author(s):  
Ana Laura Dutra ◽  
Clemens Schlindwein ◽  
Reisla Oliveira
Keyword(s):  
Natural Habitat ◽  
Model Organisms ◽  
Male Mating ◽  
Solitary Bee ◽  
Female Reproductive Success ◽  
Offspring Production ◽  
Quantitative Estimates ◽  
Foraging Performance ◽  
In The Wild ◽  
The Mean

Abstract The time dedicated to courtship and copulation is the most general cost of mating for females. However, quantitative estimates of this cost and the consequences for female mating behavior have been investigated for only a few model organisms and mostly under laboratory conditions. We determined the costs of copulations and persistent courtship by males in terms of time for females of the solitary bee Anthrenoides micans. We estimated the rate and duration of male mating behaviors and the consequences for sexual interactions for females with respect to the loss of foraging opportunity in the wild. Males invested most of their time searching for mates and intercepted foraging females every 3 min. Copulas lasted, on average, 10 times longer than the time females took to resist male mating attempts. Despite the high frequency of these rejections (82%), females spent 3-fold more time copulating than rejecting males. Considering the rate of encounters with males and the mean duration of flower visits by females, we estimated that females would perform 64% fewer flower visits per hour if they accepted all copulation attempts. The loss of time is especially significant in the natural habitat of the species, where host cacti blossom for extraordinary short periods of time and females compete with other cacti-specialized bees and conspecifics. Because the offspring production of a female solitary bee depends on its pollen collection capacity, reduced foraging performance directly influences female reproductive success.

scholarly journals Parametric forcing approach to rough-wall turbulent channel flow

2012 ◽  
Vol 712 ◽  
pp. 169-202 ◽  
Author(s):  
A. Busse ◽  
N. D. Sandham
Keyword(s):  
Numerical Simulations ◽  
Channel Flow ◽  
Stokes Equations ◽  
Rough Surfaces ◽  
Turbulent Channel Flow ◽  
Rough Wall ◽  
Force Term ◽  
Shape Functions ◽  
Mean Flow ◽  
The Mean

AbstractThe effects of rough surfaces on turbulent channel flow are modelled by an extra force term in the Navier–Stokes equations. This force term contains two parameters, related to the density and the height of the roughness elements, and a shape function, which regulates the influence of the force term with respect to the distance from the channel wall. This permits a more flexible specification of a rough surface than a single parameter such as the equivalent sand grain roughness. The effects of the roughness force term on turbulent channel flow have been investigated for a large number of parameter combinations and several shape functions by direct numerical simulations. It is possible to cover the full spectrum of rough flows ranging from hydraulically smooth through transitionally rough to fully rough cases. By using different parameter combinations and shape functions, it is possible to match the effects of different types of rough surfaces. Mean flow and standard turbulence statistics have been used to compare the results to recent experimental and numerical studies and a good qualitative agreement has been found. Outer scaling is preserved for the streamwise velocity for both the mean profile as well as its mean square fluctuations in all but extremely rough cases. The structure of the turbulent flow shows a trend towards more isotropic turbulent states within the roughness layer. In extremely rough cases, spanwise structures emerge near the wall and the turbulent state resembles a mixing layer. A direct comparison with the study of Ashrafian, Andersson & Manhart (Intl J. Heat Fluid Flow, vol. 25, 2004, pp. 373–383) shows a good quantitative agreement of the mean flow and Reynolds stresses everywhere except in the immediate vicinity of the rough wall. The proposed roughness force term may be of benefit as a wall model for direct and large-eddy numerical simulations in cases where the exact details of the flow over a rough wall can be neglected.

Machining Forces: Some Effects of Removing a Wavy Surface

1966 ◽  
Vol 8 (2) ◽  
pp. 129-140 ◽  
Author(s):  
P. W. Wallace ◽  
C. Andrew
Keyword(s):  
Chip Thickness ◽  
Shear Plane ◽  
Shear Angle ◽  
Surface Slope ◽  
Experimental Conditions ◽  
Undeformed Chip Thickness ◽  
Cutting Force Components ◽  
The Mean ◽  
Force Components ◽  
Made In

Previous work has shown that during the removal of a surface waveform oscillating cutting force components arise which may have a phase difference with respect to the oscillating component of undeformed chip thickness; it has also shown that the shear angle is affected by the slopes of the surface waveform. However, no attempt to predict the oscillating force behaviour from the geometry of cutting has been reported. The present work attempts to achieve such a prediction by means of an analysis of the phase and magnitude of the oscillating force components acting in two directions; in the directions of the mean shear plane and of the tool rake face. In the analysis it is assumed that the shear angle oscillates in phase with and proportionally to the surface slope, and that the curvature of the chip varies with the undeformed chip thickness. An experimental technique for cutting with variable undeformed chip thickness is described, together with a method for recording and measuring the oscillating components of force and undeformed chip thickness. Experimental results are presented which show the assumptions made in the analysis to be substantially valid; the predicted oscillating forces are shown to be in adequate agreement with experiment over a range of experimental conditions. It is shown that the oscillation of the shear angle is primarily dependent on the surface slope and that the frictional force behaviour is consistent with the characteristics of the two regions of friction, sticking and sliding, as found in work on cutting with constant undeformed chip thickness.

scholarly journals Height of convective layer in planetary atmospheres with condensable and non-condensable greenhouse substances

2003 ◽  
Vol 3 (6) ◽  
pp. 6701-6720 ◽  
Author(s):  
A. M. Makarieva ◽  
V. G. Gorshkov ◽  
T. Pujol
Keyword(s):  
Thermal Radiation ◽  
Surface Temperature ◽  
Optical Thickness ◽  
Analytical Formula ◽  
Lower Atmosphere ◽  
Quantitative Estimates ◽  
Convective Processes ◽  
Low Latitudes ◽  
The Mean ◽  
Convective Layer

Abstract. Convection reduces greenhouse effect by transporting a certain amount of non-radiative dynamic energy to the upper atmosphere, where this energy dissipates and radiates into space without interaction with greenhouse substances in the lower atmosphere. In this paper we show that the height of the convective layer zc is finite and independent of atmospheric optical thickness τs at large values of the latter. We derive an analytical formula for zc at large values of τs for condensable and non-condensable greenhouse substances. The formula obtained yields reasonable quantitative estimates of the observed height of convective layer on Venus and at low latitudes on Earth, where atmospheric thickness of water vapor is maximum. The dissipative power of dynamic convective processes is limited by the incoming flux of solar radiation. Height of convective layer being finite, values of optical depth at the top of the convective layer and at the mean height of convective energy dissipation increase proportionally to the atmospheric optical thickness, while the contribution of convective energy fluxes to formation of the outgoing flux of thermal radiation proportionally diminishes. As far as optical thickness of condensable greenhouse substances grows exponentially with increasing surface temperature, the obtained results lead to the conclusion that the outgoing thermal radiation into space in the presence of convection tends exponentially to zero with increasing surface temperature, instead of reaching a finite plateau as suggested by earlier radiative-convective studies.

scholarly journals Continuum approximations for lattice-free multi-species models of collective cell migration

2017 ◽  
Author(s):  
Oleksii M Matsiaka ◽  
Catherine J Penington ◽  
Ruth E Baker ◽  
Matthew J Simpson
Keyword(s):  
Cell Migration ◽  
Discrete Model ◽  
Mean Field ◽  
Mean Field Approximation ◽  
Collective Cell Migration ◽  
Moment Equations ◽  
The Mean ◽  
Continuum Description ◽  
The Moment ◽  
Adhesive Forces

AbstractCell migration within tissues involves the interaction of many cells from distinct subpopulations. In this work, we present a discrete model of collective cell migration where the motion of individual cells is driven by random forces, short range repulsion forces to mimic crowding, and longer range attraction forces to mimic adhesion. This discrete model can be used to simulate a population of cells that is composed of K ≥ 1 distinct subpopulations. To analyse the discrete model we formulate a hierarchy of moment equations that describe the spatial evolution of the density of agents, pairs of agents, triplets of agents, and so forth. To solve the hierarchy of moment equations we introduce two forms of closure: (i) the mean field approximation, which effectively assumes that the distributions of individual agents are independent; and (ii) a moment dynamics description that is based on the Kirkwood superposition approximation. The moment dynamics description provides an approximate way of incorporating spatial patterns, such as agent clustering, into the continuum description. Comparing the performance of the two continuum descriptions confirms that both perform well when adhesive forces are sufficiently weak. In contrast, the moment dynamics description outperforms the mean field model when adhesive forces are sufficiently large. This is a first attempt to provide an accurate continuum description of a lattice-free, multi-species model of collective cell migration.

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