Surface of revolution never negative, the area is given by If the curve is described by the function , , then the integral becomes for revolution around the -axis, and for revolution around the "y"-axis (using ). These come from the above formula. For example, the spherical surface with unit radius is generated by the curve , , when ranges over . Its area is therefore For the case of the spherical curve with radius , rotated about the -axis A minimal surface of revolution is the surface of revolution of the curve between two given points which minimizes surface area. A basic
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