(a) At equilibrium the downward flux balances the diffusion flux . Use the profile to…

PHYSICS · Subjective · Fermi University Physics · Fluids & Continuum Physics · Condensed Matter, Materials & Soft Matter · Solid continuum mechanics and complex fluids

Condensed Matter Physics, Ch Soft matter: when entropy, not bonding, sets the structure

Problem

(a) At equilibrium the downward flux

n_cv_{\rm sed}

balances the diffusion flux

-D\,\mathrm{d}n_c/\mathrm{d}z

. Use the profile

n_c\propto e^{-z/\ell_g}

to derive

D=v_{\rm sed}\ell_g

. Then substitute

v_{\rm sed}=\Delta\rho V_{\rm p}g/6\pi\eta r_{\rm p}

and

\ell_g=k_BT/(\Delta\rho V_{\rm p}g)

, and explain why the result contains no reference to gravity, even though gravity was used to derive it. (b) Iron oxide nanoparticles of radius

40\,\mathrm{nm}

are suspended in water at

293\,\mathrm{K}

(

\eta=1.0\,\mathrm{mPa\,s}

). Find their diffusion coefficient.

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