A silica dispersion in water at (viscosity ) has particle radius

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Soft condensed matter · Soft condensed matter

Soft Matter at the Thermal Scale, Ch Forces between colloids and the stability of a dispersion

Problem

A silica dispersion in water at

298\,\mathrm{K}

(viscosity

\eta = 8.9\times10^{-4}\,\mathrm{Pa\,s}

) has particle radius

a = 250\,\mathrm{nm}

, number density

n_0 = 2\times10^{16}\,\mathrm{m^{-3}}

, a DLVO barrier of

U_{\max} = 14\,k_BT

, and Debye length

\lambda_{\rm D} = 1.5\,\mathrm{nm}

at the salt concentration used. Using the Reerink-Overbeek estimate

W \approx e^{U_{\max}/k_BT}/(2a/\lambda_{\rm D})

for the stability ratio and the fast-coagulation half-life

t_{1/2,\rm fast} = 3\eta/(4k_BTn_0)

, estimate the stability ratio

W

(quote it to two significant figures, since it is exponential in the barrier) and the actual coagulation half-life

t_{1/2} = W\,t_{1/2,\rm fast}