A binary coalescence model of a two-component system of mixed oil drops in water is established. The original coalescence driving force directly connected to the chemical potential difference of the coalesced oil drops has been investigated under a mimetic "weightlessness" condition. Gravitation is minimized nearly to zero to overcome drop deformation by mixing hydrocarbon compounds and carbon tetrachloride. Any external force out of the drops is reduced nearly to zero, when one liquid drop goes near enough to be tangential to another. The coalescence time, defined as the binary coalescence time (t(bi-coal)), can be expressed as ink(d)sigma (1/r(1) - 1/r(2)) = k(b)t(bi-coal) + b'. [1] The coalescence phenomenon was first proposed as initiated by chemical potential differences between liquid drops (B. Y. Yu, Ph.D. dissertation, Swiss Fed. lost. Technol., Zurich, 1995). The greater the chemical potential difference between two liquid drops, the larger the factor sigma (1/r(1) - 1/r(2)); as a result, the coalescence tendency will increase (i.e., t(bi-coal) decreases). Equation [1], including interfacial tension, drop size difference, and thin-film coefficient supported by the experimental data, is quantitatively established.