Contact axisymmetric

The axisymmetric drop shape analysis (see Section II-7B) developed by Neumann and co-workers has been applied to the evaluation of sessile drops or bubbles to determine contact angles between 50° and 180° [98]. In two such studies, Li, Neumann, and co-workers [99, 100] deduced the line tension from the drop size dependence of the contact angle and a modified Young equation... 

It is worth pointing out that the fluid flow in our calculations of the merger (Rosswog et al. 2003) never becomes axisymmetric during the simulation and therefore Cowlings anti-dynamo theorem does not apply here. When the surfaces of the neutron stars come into contact, a vortex sheet forms between them... 

T. W. Shield and D. M. Bogy, Some Axisymmetric Problems for Layered Elastic Media Part I — Multiple Region Contact Solutions for Simply-Connected Indenters, Thansac-tions of the ASME, vol. 56, pp. 798-806, Dec 1989. 

Contact Angle Measurements. Axisymmetric drop shape analysis - profile (ADSA-P) The hydrophobicity/ hydrophilicity of a solid surface is usually expressed in terms of wettability, which can be quantified by contact angle measurements. ADSA-P is a technique to determine liquid-fluid interfacial tensions and contact angles... 

When the gap width between two particles becomes very small, numerical calculations involved in both the bispherical coordinate method and the boundary collocation technique are computationally intensive because the number of terms in the series required to be retained to achieve a desired accuracy increases tremendously. To solve this near-contact motion more effectively and accurately, Loewenberg and Davis [43] developed a lubrication solution for the electrophoretic motion of two spherical particles in near contact along their line of centers with the assumption of infinitely thin ion cloud. The axisymmetric motion of the two particles in near contact can be approximated as the pairwise motion of the spheres in point contact plus a deviation stemming from their relative motion caused by the contact force. The lubrication results agree very well with those obtained from the collocation method. It is shown that near contact electrophoretic interparticle... 

Figure 2.16 Axisymmetric finite element model of a threaded connection showing (a) thread contact (b) distortion and stress state. (Reprinted with permission from ASM International. All rights reserved www.asminternational.org)...

Kwok, D.Y., Gietzelt, T., Grundke, K., Jacobasch, H.J., and Neumann, A.W. (1997). Contact angle measurements and contact angle interpretation. 1. Contact angle measurements by axisymmetric drop shape analysis and a goniometer sessile drop technique. Langmuir, 13, 2880-2894. 

D. Li, P. Cheng and A.W. Neumann, Contact Angle Measurement by Axisymmetric Drop Shape Analysis (ADSA), Adv. Colloid Interface Set 39 (1992) 347, and references to the Neumann group in sec. 5.12 D.Y. Kwok, A.W. Neumann, Contact Angle Measurement and Contact Angle Interpretation, Adv. Colloid Interface Set 81 (1999) 167-249. 

Mehdizadeh and Dukovic (5) expanded the theoretical treatment and included mass transport effects in an axisymmetric system as well as a 3-D geometry. In the 3-D geometry, they assumed four peripheral low-contact-area terminals and have shown the effect of peripheral point contacts on the thickness distribution of a 200 mm wafer. Initially, the thickness near the four point contacts is very high, whereas between the contacts is very low. A time series of a growing deposit with four peripheral point contact terminals is shown in (6). Point contacts result in azimuthal nonuniformity. However, the nonuniformity in the vicinity of the contacts becomes appreciably better as the plated thickness builds up. In applications such as Damascene electroplating where the final plated thickness is usually not more than l/im, azimuthal nonuniformity can be a problem. Our solution was to implement an almost continuous peripheral contact terminal and to assume that the system is axisymmetric and that only the radial nonuniformity needs improvement. 

Figure 8. Nonuniformity transient for a wafer with a peripheral axisymmetric contact for different values of the intial sheet conductance (C ) ...

The general expression for the dimensionless spreading (constriction) resistance 4kaRs for a circular contact subjected to an arbitrary axisymmetric flux distribution f(u) [131-133] is obtained from the series... 

The maximum temperature is reached at the contact with the over-pack, after about 30 years of heating. Three-dimensional models predict a value within the range of 75 to SOX, whereas the axisymmetric model (JNC) leads to about 90°C. The evolution of temperature at point B4 is summarized on Figure 2. On this figure, the ISEG curve relates to a purely TM calculation. 

When the fluid approaches the sphere from above, the fluid initially contacts the sphere at 0 = 0 (i.e., the stagnation point) because polar angle 6 is defined relative to the positive z axis. This is convenient because the mass transfer boundary layer thickness Sc is a function of 6, and 5c = 0 at 0 = 0. In the laminar and creeping flow regimes, the two-dimensional fluid dynamics problem is axisymmetric (i.e., about the z axis) with... 

In this paper, we approach this problem by utilizing an axisymmetric adhesion test involving the contact of a rigid glass hemispherical indenter with an elastomeric substrate. Application of these types of tests has been reviewed recently... 

Once a specific event in the load-displacement curve has been associated with a particular phase transition, the pressure at which it occurs can be estimated by considering the elastoplastic behavior of the material under the indenter. For the point-force contact, the Sneddon s solution [39] to the problem of the penetration of an axisymmetric punch into an elastic half space predicts the following relation between the applied load P and the indenter displacement A ... 

The elastic problem for an elastic half-space contacted by a normal point force P was solved by Boussinesq in 1885. The stress field is axisymmetric around the force direction and has the general form, in spherical coordinates. 

To quantify the effects of mixed waste con sition on wettability and interfacial tension equilibrium, aqueous phase receding contact angle and interfacial tension were measured. Inter cial tension was measured ida a spinning drop tensiometer Model 500 (University of Texas, Austin, TX) and contact angles were obtained using axisymmetric drop shape analysis (17) on quartz slides. Contact angles are reported through the aqueous phase. 

Contact Angle Measurements by Axisymmetric Drop Shape Analysis... 

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