Analysis of the viscosity of dilute suspensions beyond Einstein’s formula. (English) Zbl 1454.76101
Summary: We provide a mathematical analysis of the effective viscosity of suspensions of spherical particles in a Stokes flow, at low solid volume fraction \(\phi\). Our objective is to go beyond Einstein’s approximation \(\mu_{eff} = (1 + \frac{5}{2} \phi) \mu\). Assuming a lower bound on the minimal distance between the \(N\) particles, we are able to identify the \(O(\phi^2)\) correction to the effective viscosity, which involves pairwise particle interactions. Applying the methodology developped over the last years on Coulomb gases, we are able to tackle the limit \(N \rightarrow +\infty\) of the \(O(\phi^2)\)-correction, and provide an explicit formula for this limit when the particles centers can be described by either periodic or stationary ergodic point processes.
MSC:
| 76T20 | Suspensions |
| 76D07 | Stokes and related (Oseen, etc.) flows |
| 82B21 | Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics |
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