Model-free hydrodynamic theory of the colloidal glass transition

We present a phenomenological, model-free theory for the large-distance hydrodynamic response of a viscous fluid hosting colloidal particles. The flow of the host fluid is affected by the presence of the particles, thus reflecting their liquid or solid state. On the liquid side of the glass transition we identify a dynamic length scale $\ell$ beyond which the host fluid's response is that of a viscous fluid with increased effective viscosity $\eta$. As the glass transition is approached, $\ell$ increases indefinitely as $\ell \sim \eta^{1/2}$. At the transition the large-distance response changes qualitatively, marking the host fluid's loss of translation invariance. On the solid side of the transition we identify another dynamic length, $\ell_s$, beyond which the host fluid responds as a viscous fluid of increased effective viscosity $\eta^+$, confined in a porous medium of effective pore size $\ell_s$. As the glass transition is approached from the solid side, $\ell_s$ grows indefinitely, more sharply than $(\eta^+)^{1/2}$. We discuss various experimental implications of the results and their possible relation to microscopic theories of the colloidal glass transition.