Free Fall of a Sphere in a Partially Lubricated Cylinder

1991 ◽  
Vol 58 (3) ◽  
pp. 812-819
Author(s):  
Roger F. Gans
Keyword(s):  
Contact Force ◽  
Closed System ◽  
Experimental Verification ◽  
Asymptotic Expansions ◽  
Total Mass ◽  
Free Fall ◽  
Matched Asymptotic Expansions ◽  
Biological Applications ◽  
Slider Bearing ◽  
Acceleration Of Gravity

The entrainment of lubricant at the entrance of a lubrication zone, such as that of a partially starved slider bearing, is analyzed in a closed system using the method of matched asymptotic expansions. A sphere falling together with a small lens of lubricant in a closely fitting tube is shown to fall under gravity at a speed V=(Mg−Fc)√[(RC−RS)/RC]/(16π2μRC), where M denotes the total mass of the system, sphere plus lubricant, g the acceleration of gravity, Fc the differential contact force, μ the viscosity of the lubricant, and RC and RS the radii of the tube and the sphere, respectively. Potential biological applications and experimental verification are discussed.

Asymptotic Methods for an Infinite Slider Bearing With a Discontinuity in Film Slope

1976 ◽  
Vol 98 (3) ◽  
pp. 446-452 ◽  
Author(s):  
J. A. Schmitt ◽  
R. C. DiPrima
Keyword(s):  
Boundary Layer ◽  
Film Thickness ◽  
Asymptotic Expansions ◽  
Asymptotic Expression ◽  
Asymptotic Methods ◽  
Matched Asymptotic Expansions ◽  
Slider Bearing ◽  
Trailing Edge ◽  
Slider Bearings ◽  
Special Cases

The method of matched asymptotic expansions is used to develop an asymptotic expression for the pressure for large bearing numbers for the case of an infinite slider bearing with a general film thickness that has a discontinuous slope at a point. It is shown that, in addition to the boundary layer of the pressure at the trailing edge, there is also a boundary layer in the derivative of the pressure at the point of discontinuity. The corresponding load formula is also derived. The special cases of the taper-flat and taper-taper slider bearings are discussed.

Asymptotic Analysis of a Finite Gas Slider Bearing of Narrow Geometry

1983 ◽  
Vol 105 (3) ◽  
pp. 491-495 ◽  
Author(s):  
J. J. Shepherd ◽  
R. C. DiPrima
Keyword(s):  
Steady State ◽  
Asymptotic Analysis ◽  
Pressure Distribution ◽  
Asymptotic Expansions ◽  
Matched Asymptotic Expansions ◽  
Slider Bearing ◽  
Load Bearing ◽  
Bearing Number ◽  
Isothermal Gas ◽  
State Pressure

The method of matched asymptotic expansions is used to analyze the steady state pressure distribution and load bearing properties of a finite rectangular isothermal gas slider bearing when ε, the ratio of transverse to longitudinal dimensions of the bearing, is small and the bearing number Λ is moderate. General expressions for the pressure and load are obtained. Specific results are given for bearings with shallow crowning. The effects of the bearing number becoming large and the interaction between the two effects ε→0 and Λ→∞ are discussed.

Cusp formation for the undercooled Stefan problem in two and three dimensions

1997 ◽  
Vol 8 (1) ◽  
pp. 1-21 ◽  
Author(s):  
JUAN J. L. VELÁZQUEZ
Keyword(s):  
Stefan Problem ◽  
Asymptotic Expansions ◽  
Three Dimensions ◽  
Matched Asymptotic Expansions ◽  
Cusp Formation

We consider in this paper the classical one-phase Stefan problem in dimensions two and three in the undercooled situation. By means of matched asymptotic expansions, a mechanism of cusp formation is presented for interfaces that are initially smooth.

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