Equation Sheets
Equation Sheets

CHEM E 455 Surface and Colloid Science Laboratory

  
Contents
Description Equations
Surface tension σ=dFdl\sigma = \dfrac{dF}{dl}
Description Equations
Eotovs law σv2/3=kE(Tc−T)\sigma v^{2/3} = k_E (T_c - T)
Guggenheim law σ=σ∗(1−TTc)11/9\sigma = \sigma^* \left(1 - \dfrac{T}{T_c}\right)^{11/9}
Empirical linear equation
★ Modest T		 σ=a−bTb=dσdT=−0.1 mM/m⋅K\sigma =a-bT \newline b = \dfrac{d\sigma}{dT} = -0.1 \ \mathrm{mM/m \cdot K}
Description Equations
van der Waals attraction ΦvdW=−BvdWr6\Phi_{\text{vdW}} = -\dfrac{B_{\text{vdW}}}{r^6}
Born repulsion Φrep=Brepr12\Phi_{\text{rep}} = \dfrac{B_{\text{rep}}}{r^{12}}
Lennard-Jones potential Φ=4ε[(δr)12−(δr)6]\Phi = 4\varepsilon \left[\left(\dfrac{\delta }{r}\right)^{12}-\left(\dfrac{\delta }{r}\right)^6\right]
Lennard-Jones attractive force Fattr=−24εr[2(δr)12−(δr)6]F_{\text{attr}} = -\dfrac{24\varepsilon }{r}\left[2\left(\dfrac{\delta }{r}\right)^{12}-\left(\dfrac{\delta }{r}\right)^6\right]
Bakker’s equation σ=∫−∞∞(p−pT)dz\sigma = \displaystyle\int_{-\infty}^\infty (p - p_T) dz
Description Equations
Components of surface tension σ=σdisperison+σdipole+σinduced dipole+σH-bond+σmetallic bond+⋯\sigma = \sigma^{\text{disperison}} + \sigma^{\text{dipole}} + \sigma^{\text{induced dipole}} + \sigma^{\text{H-bond}} + \sigma^{\text{metallic bond}} + \cdots
Surface tension of liquid σ=σdisperison+σacid-base\sigma = \sigma^{\text{disperison}} + \sigma^{\text{acid-base}}
Surface tension of molten salt σ=σdisperison+σmetallic bond\sigma = \sigma^{\text{disperison}} + \sigma^{\text{metallic bond}}
Description Equations
Antanov σAB=∣σA(B)−σB(A)∣\sigma_{AB} = \vert \sigma_{A(B)} - \sigma_{B(A)} \vert
Girifalco & Good σAB=σA+σB−2ΦσAσB\sigma_{AB} = \sigma_A + \sigma_B - 2\Phi \sqrt{\sigma_A \sigma_B}
Fowkes σAB=σA+σB−2σAdσBd\sigma_{AB} = \sigma_A + \sigma_B - 2 \sqrt{\sigma_A^d \sigma_B^d}
Description Equations
Curvature of a plane curve κ=dϕdS\kappa = \dfrac{d\phi}{dS}
Curvature of a plane curve κ=±y′′[1+(y′)2]−3/2\kappa = \pm y'' [1+(y')^2]^{-3/2}
Curvature of a line κ=0\kappa = 0
Curvature of a circle κ=1R\kappa = \dfrac{1}{R}
Description Equations
Curvature of a surface κ=±(1R1+1R2)=±2Rmean\kappa = \pm \left(\dfrac{1}{R_1}+\dfrac{1}{R_2}\right)=\pm \dfrac{2}{R_{\text{mean}}}
Curvature of a surface κ=±zxx[1+(zy)2]−2zxzyzxy+zyy[1+(zx)2][1+(zx)2+(zy)2]3/2\kappa = \pm \dfrac{z_{xx}\left[1+\left(z_y\right)^2\right]-2z_xz_yz_{xy}+z_{yy}\left[1+\left(z_x\right)^2\right]}{\left[1+\left(z_x\right)^2+\left(z_y\right)^2\right]^{3/2}}
Curvature of a sphere κ=2R\kappa = \dfrac{2}{R}
Curvature of a circular cylinder κ=1R\kappa = \dfrac{1}{R}
Curvature of a cylindrical surface κ=±y′′[1+(y′)2]−3/2\kappa = \pm y'' [1+(y')^2]^{-3/2}
Curvature of an axially symmetric surface κ=\kappa =
Description Equations
Young-Laplace equation Δp=p′′−p′=σκ\Delta p = p'' - p' = \sigma\kappa
Updated on 2022-04-04
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