Polystyrene spheres across ( ) are suspended in water ( , ) at .

PHYSICS · Multi-part · 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

Polystyrene spheres 200 nm200\,\mathrm{nm} across (ρ=1050 kg m−3\rho=1050\,\mathrm{kg\,m^{-3}}) are suspended in water (ρ=1000 kg m−3\rho=1000\,\mathrm{kg\,m^{-3}}, η=1.0 mPa s\eta=1.0\,\mathrm{mPa\,s}) at 293 K293\,\mathrm{K}. ((a)) Find the diffusion coefficient DD and the root-mean-square distance 6Dt\sqrt{6Dt} such a sphere wanders in 10 s10\,\mathrm{s}. ((b)) Find the gravitational length ℓg\ell_g and say whether the spheres settle out in a sample cell 1 mm1\,\mathrm{mm} deep.

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