Young equation statement

The exact treatment of capillary rise must take into account the deviation of the meniscus from sphericity, that is, the curvature must correspond to the AP = Ap gy at each point on the meniscus, where y is the elevation of that point above the flat liquid surface. The formal statement of the condition is obtained by writing the Young-Laplace equation for a general point (x, y) on the meniscus, with R and R2 replaced by the expressions from analytical geometry given in... 

Elastomers are solids, even if they are soft. Their atoms have distinct mean positions, which enables one to use the well-established theory of solids to make some statements about their properties in the linear portion of the stress-strain relation. For example, in the theory of solids the Debye or macroscopic theory is made compatible with lattice dynamics by equating the spectral density of states calculated from either theory in the long wavelength limit. The relation between the two macroscopic parameters, Young s modulus and Poisson s ratio, and the microscopic parameters, atomic mass and force constant, is established by this procedure. The only differences between this theory and the one which may be applied to elastomers is that (i) the elastomer does not have crystallographic symmetry, and (ii) dissipation terms must be included in the equations of motion. 

Good job " "Way to go " "Well done " "Congratulations " These are common statements parents make to show approval of their child s performance. Because such expressions feel so affirming, the young child often equates parental approval with parental love "They love me when I do well."... 

Note that E is the Young modulus and v is the Poisson ratio for the material of interest. We are now ready to turn to the concrete implementation of the variational statement of eqn (2.70). Evaluation of 9 IT/9a results in the equation of motion... 

The phenomenon of the hysteresis of the contact angle has been mosdy associated with physical or chemical heterogeneities on the sohd surface or with impurities in any of the components of the system. It was thought that Young s equation was stiU applicable locally this statement was only proved for particular situations, for example choosing the shape of the liquid-fluid interface as a spherical cup, but not in general due to the mathematical difficulty to describe all the possible states of the system. 

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