Solid angle to the unit sphere with center P, which can be calculated as the surface integral: where formula_5 is the unit vector corresponding to formula_6, the position vector of an infinitesimal area of surface with respect to point P, and where formula_7 represents the unit normal vector to . Even if the projection on the unit sphere to the surface S is not isomorphic, the multiple folds are correctly considered according to the surface orientation described by the sign of the scalar product formula_8. Thus one can approximate the solid angle subtended by a small facet having flat surface area ,
Polymeric surface processing proclude it from being a competitive surface modification method within industry. The process begins with production of plasma via ionization either by deposition on monomer mixtures or gaseous carrier ions. The power required to produce the necessary plasma flux can be derived from the active volume mass/energy balance: formula_1 where formula_2 where formula_3 denotes the surface energy of the solid–liquid, liquid–gas, or solid–gas interface formula_4 is the measured contact angle A series of solutions with known surface tension (e.g., Dyne solutions) can be used to estimate the surface energy of the polymer substrate qualitatively by observing the wettability of