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

Adhesional Wetting, Dupre equation $W_A$ = $\frac{-(\Delta G_a)}{a}$ = ${\gamma }_{\mathrm{LG}}+{\gamma }_{\mathrm{SG}}-{\gamma }_{\mathrm{SL}}$, Young-Dupre equation $W_a$ = ${\gamma }_{\mathrm{LG}}(1+\cos \theta )$

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

Adsorption Isotherms, Langmuir Isotherm $q$ = $K_a{q}_m\frac{c}{1+K_{a}c}$ , Freundlich Isotherm $q$ = $K_{f}c^{\left(\frac{1}{n}\right)}$, where $q$ = $\frac{x}{m}$

Gouy-Chapman $\mathrm{\psi \prime \prime }(x)$ = $\frac{2e{n}_{0}z}{\epsilon }\sinh \left(\frac{e\psi z}{Tk}\right)$, $\mathrm{\psi \prime }(x)$ = $\sqrt{\frac{8Tk{n}_0}{\epsilon }}\sinh \left(\frac{e\psi z}{2Tk}\right)$, $\psi$ = $\frac{2kt}{ez}\ln \left(\frac{1+\gamma e^{-(\kappa x)}}{1-\gamma e^{-(\kappa x)}}\right)$, where $\gamma$ = $\frac{-1+e^{\frac{e{\psi }_{0}z}{2Tk}}}{1+e^{\frac{e{\psi }_{0}z}{2Tk}}}$, and $\kappa$ = $\sqrt{\frac{2e^2{n}_{0}z^2}{T\epsilon k}}$ = $\sqrt{\frac{2N_{A}ce^{2}z^2}{T\epsilon k}}$ = $\sqrt{\frac{2F^{2}cz^2}{T\epsilon k}}$, in which $F$ is coulombs/volts, at 25°C $\kappa$ = $3.29E9\sqrt{\frac{cz^2}{\mathrm{moldm}^{-3}}}m^{-1}$.${\sigma }_0$ = $\sqrt{8T\epsilon k{n}_0}\sinh \left(\frac{e{\psi }_{0}z}{2Tk}\right)$

Debye-Huckel Approximation, When $\frac{e{\psi }_{0}z}{2Tk}$ is far less than $1$ then $e^{\frac{e{\psi }_{0}z}{2Tk}}\approx 1+\frac{e{\psi }_{0}z}{2Tk}$, $\psi$ = ${\psi }_{0}e^{-(\kappa x)}$, ${\sigma }_0$ = $\epsilon \kappa {\psi }_0$

Stern Layer, As above substitute ${\psi }_0$ with ${\psi }_d$.${\sigma }_1$ = $\frac{{\sigma }_m}{1+e^{\frac{\phi +e{\psi }_{d}z}{Tk}}\frac{N_A}{n_0{v}_m}}$

Capacitances $C_1$ = $\frac{{\sigma }_0}{{\psi }_0-{\psi }_d}$ = $\frac{\mathrm{\epsilon \prime }}{\delta }$, $C_2$ = $\frac{{\sigma }_0}{{\psi }_d}$, ${\psi }_d$ = $\frac{C_1{\psi }_0}{C_1+C_2}$, at low potentials, 25°C $C_2$ = $\epsilon \kappa$ = $2.28\sqrt{\frac{cz^2}{\mathrm{moldm}^{-3}}}Fm^{-2}$

Surface Potentials $\mathrm{\zeta \prime }(p(Ag))$ = ${\mathrm{\psi \prime }}_0(p(Ag)){\mathrm{\psi \prime }}_d({\psi }_0)$ = $-(59\frac{C_1}{C_1+C_2}\mathrm{mV})$

Huckel Equation $u_E$ = $\frac{v_E}{E}$ = $\frac{\epsilon \zeta }{1.5\eta }$, Smoluchowski Equation $u_E$ = $\frac{v_E}{E}$ = $\frac{\epsilon \zeta }{\eta }$, Electro-Osmosis ${\mathrm{V\prime }}_{\mathrm{EO}}(t)$ = $A{V}_{\mathrm{EO}}(t)$ = $\frac{AE\epsilon \zeta }{\eta }$

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

$A_{132}$ = $(\sqrt{A_{11}}-\sqrt{A_{33}})(\sqrt{A_{22}}-\sqrt{A_{33}})$, $A_{131}$ = $(\sqrt{A_{11}}-\sqrt{A_{33}})^2$

Coagulation Kinetics $-\mathrm{n\prime }(t)$ = $k_{2}n(t)^2$, $\frac{1}{n}-\frac{1}{n_0}$ = $k_{2}t$, $k_2$ = $\frac{4Tk}{3\eta }$, $W$ = $\frac{k_2}{k_2}$