An Elliptical Integral (A. W. Gillies)

SIAM Review ◽  
1970 ◽  
Vol 12 (4) ◽  
pp. 591-592
Author(s):  
J. K. M. Jansen
Keyword(s):  
Elliptical Integral

scholarly journals The adhesion model considering capillarity for gecko attachment system

2007 ◽  
Vol 5 (20) ◽  
pp. 319-327 ◽  
Author(s):  
Tae Wan Kim ◽  
Bharat Bhushan
Keyword(s):  
Capillary Force ◽  
Adhesion Force ◽  
Adhesive Force ◽  
Contact Angles ◽  
Adhesion Forces ◽  
Real Area Of Contact ◽  
Wide Range ◽  
Elliptical Integral ◽  
Gecko Adhesion ◽  
Surface Construction

Geckos make use of approximately a million microscale hairs (setae) that branch off into hundreds of nanoscale spatulae to cling to different smooth and rough surfaces and detach at will. This hierarchical surface construction gives the gecko the adaptability to create a large real area of contact with surfaces. It is known that van der Waals force is the primary mechanism used to adhere to surfaces, and capillary force is a secondary effect that can further increase adhesive force. To investigate the effects of capillarity on gecko adhesion, we considered the capillary force as well as the solid-to-solid interaction. The capillary force expressed in terms of elliptical integral is calculated by numerical method to cope with surfaces with a wide range of contact angles. The adhesion forces exerted by a single gecko spatula in contact with planes with different contact angles for various relative humidities are calculated, and the contributions of capillary force to total adhesion force are evaluated. The simulation results are compared with experimental data. Finally, using the three-level hierarchical model recently developed to simulate a gecko seta contacting with random rough surface, the effect of the relative humidity and the hydrophobicity of surface on the gecko adhesion is investigated.

A NOVEL METHOD OF CALCULATING THE INTERACTION ENERGIES OF DOUBLE LAYERS

2006 ◽  
Vol 13 (01) ◽  
pp. 127-133
Author(s):  
SHIMIN ZHANG
Keyword(s):  
Power Series ◽  
Surface Potential ◽  
Efficient Method ◽  
Double Layers ◽  
Parameter Method ◽  
Interaction Energies ◽  
Plane Parallel ◽  
Elliptical Integral ◽  
Novel Method

A novel, simple, and efficient method to calculate the interaction energies of double layers, λ parameter method, is presented by introducing a parameter λ in the elliptical integral. The interaction energies between two similar plane parallel double layers are expanded in the power series with such a method. The series converge very fast. When the dimensionless surface potential of double layers is less than or equal to 30, the number of the series terms required does not exceed 3 to obtain the interaction energies with six significant digits.

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