In the forms given in Introduction to Colloid and Surface Chemistry by Duncan J. Shaw, publisher Butterworth-Heinemann. Data entry by Dienkuan Donn. Markup by meditor.

Brownian Motion $x$ = $\sqrt{2Dt}$, $Df$ = $Tk$, $f$ = $6a\eta \pi$

Spreading Wetting $S$ = $\frac{-\Delta {G}_{s}}{A}$ = ${\gamma }_{\mathrm{SG}}-\left({\gamma }_{\mathrm{LG}}+{\gamma }_{\mathrm{SL}}\right)$, Young's equation 0 = $-{\gamma }_{S}+{\gamma }_{\mathrm{SL}}+{\pi }_{\mathrm{SG}}+{\gamma }_{\mathrm{LG}}\mathrm{cos}\left(\theta \right)$

Adhesional Wetting, Dupre equation ${W}_{A}$ = $\frac{-\Delta {G}_{a}}{a}$ = ${\gamma }_{\mathrm{LG}}+{\gamma }_{\mathrm{SG}}-{\gamma }_{\mathrm{SL}}$, Young-Dupre equation ${W}_{a}$ = ${\gamma }_{\mathrm{LG}}\left(1+\mathrm{cos}\left(\theta \right)\right)$

Immersional Wetting $-\Delta {G}_{i}$ = ${\gamma }_{\mathrm{SG}}-{\gamma }_{\mathrm{SL}}$ = ${\gamma }_{\mathrm{LG}}\left(\mathrm{cos}\left(\theta \right)\right)$, Contact Angles p = $\frac{2\gamma \mathrm{cos}\left(\theta \right)}{r}$, ${p}^{\prime }$ = $\frac{2{\gamma }^{\prime }}{r}$

Adsorption Isotherms, Langmuir Isotherm q = ${K}_{a}{q}_{m}\frac{c}{1+{K}_{a}c}$ , Freundlich Isotherm q = ${K}_{f}\sqrt[n]{c}$, where q = $\frac{x}{m}$

Gouy-Chapman $\frac{{d}^{2}\psi }{d{x}^{2}}$ = $\frac{2e{n}_{0}z}{\epsilon }\mathrm{sinh}\left(\frac{e\psi z}{Tk}\right)$, $\frac{d\psi }{dx}$ = $\mathrm{sinh}\left(\frac{e\psi z}{2Tk}\right)\sqrt{\frac{8Tk{n}_{0}}{\epsilon }}$, $\psi$ = $\frac{2kt}{ez}\mathrm{ln}\left(\frac{1+\gamma {e}^{-\kappa x}}{1-\gamma {e}^{-\kappa x}}\right)$, where $\gamma$ = $\frac{-1+{e}^{\frac{e{\psi }_{0}z}{2Tk}}}{1+{e}^{\frac{e{\psi }_{0}z}{2Tk}}}$, and $\kappa$ = $\sqrt{\frac{2{e}^{2}{n}_{0}{z}^{2}}{T\epsilon k}}$ = $\sqrt{\frac{2{N}_{A}c{e}^{2}{z}^{2}}{T\epsilon k}}$ = $\sqrt{\frac{2{F}^{2}c{z}^{2}}{T\epsilon k}}$, in which F is coulombs/volts, at 25 C $\kappa$ = 0.329e+10$\sqrt[2]{\frac{c{z}^{2}}{\mathrm{mol}{\mathrm{dm}}^{-3}}}{m}^{-1}$.${\sigma }_{0}$ = $\mathrm{sinh}\left(\frac{e{\psi }_{0}z}{2Tk}\right)\sqrt{8T\epsilon k{n}_{0}}$

Debye-Huckel Approximation, When $\frac{e{\psi }_{0}z}{2Tk}$ is far less than 1 then ${e}^{\frac{e{\psi }_{0}z}{2Tk}}$ ~= $1+\frac{e{\psi }_{0}z}{2Tk}$, $\psi$ = ${\psi }_{0}{e}^{-\kappa x}$, ${\sigma }_{0}$ = $\epsilon \kappa {\psi }_{0}$

Stern Layer, As above substitute ${\psi }_{0}$ with ${\psi }_{d}$.${\sigma }_{1}$ = $\frac{{\sigma }_{m}}{1+{e}^{\frac{\phi +e{\psi }_{d}z}{Tk}}\left(\frac{{N}_{A}}{{n}_{0}{v}_{m}}\right)}$

Capacitances ${C}_{1}$ = $\frac{{\sigma }_{0}}{{\psi }_{0}-{\psi }_{d}}$ = $\frac{{\epsilon }^{\prime }}{\delta }$, ${C}_{2}$ = $\frac{{\sigma }_{0}}{{\psi }_{d}}$, ${\psi }_{d}$ = $\frac{{C}_{1}{\psi }_{0}}{{C}_{1}+{C}_{2}}$, at low potentials, 25 C ${C}_{2}$ = $\epsilon \kappa$ = 2.28$\sqrt[2]{\frac{c{z}^{2}}{\mathrm{mol}{\mathrm{dm}}^{-3}}}F{m}^{-2}$

Surface Potentials $\frac{d\zeta }{d\mathrm{pAg}}\left(\mathrm{\zeta ->0}\right)$ = $\frac{d{\psi }_{0}}{d\mathrm{pAg}}\frac{d{\psi }_{d}}{d{\psi }_{0}}\left(\mathrm{\zeta ->0}\right)$ = $-59\left(\frac{{C}_{1}}{{C}_{1}+{C}_{2}}\right)\mathrm{mV}$

Huckel Equation ${u}_{E}$ = $\frac{{v}_{E}}{E}$ = $\frac{\epsilon \zeta }{\mathrm{1.5}\eta }$, Smoluchowski Equation ${u}_{E}$ = $\frac{{v}_{E}}{E}$ = $\frac{\epsilon \zeta }{\eta }$, Electro-Osmosis $\frac{d{V}_{\mathrm{EO}}}{dt}$ = $A{V}_{\mathrm{EO}}$ = $\frac{AE\epsilon \zeta }{\eta }$

Colloidal Stability V = ${V}_{A}+{V}_{R}$ where ${V}_{R}$ = ${e}^{-H\kappa }\left(\frac{32{T}^{2}a\epsilon {\gamma }^{2}{k}^{2}\pi }{{e}^{2}{z}^{2}}\right)$, and ${V}_{A}$ = $\left(\frac{1}{2x}\right)\left(-\frac{A}{12}\right)$ = $\frac{-Aa}{12H}$

${A}_{132}$ = $\left(\sqrt[2]{{A}_{11}}-\sqrt[2]{{A}_{33}}\right)\left(\sqrt[2]{{A}_{22}}-\sqrt[2]{{A}_{33}}\right)$, ${A}_{131}$ = ${\left(\sqrt[2]{{A}_{11}}-\sqrt[2]{{A}_{33}}\right)}^{2}$

Coagulation Kinetics $-\frac{dn}{dt}$ = ${k}_{2}{n}^{2}$, $\frac{1}{n}-\frac{1}{{n}_{0}}$ = ${k}_{2}t$, ${k}_{2}$ = $\frac{4Tk}{3\eta }$, W = $\frac{{k}_{2}}{{k}_{2}}$