Constitutive laws for dense granular flows and suspensions

4 problems

• A well-posed continuum theory of dense granular flow

  Partially resolved

  The standard equations for flowing grains predict, for some flow conditions, that tiny ripples grow infinitely fast, which means the equations have no sensible solutions there (they are ill-posed). A version that is mathematically sound in every regime and still matches experiments is not known.

• A nonlocal constitutive law for slow granular flows

  Partially resolved

  A simple local friction law describes fast flows of grains well but fails when the flow is slow: grains creep below the expected stopping point and thin layers stop earlier than thick ones. The correct replacement law, and its basis in grain-scale physics, is not established.

• Predicting the onset of discontinuous shear thickening in dense suspensions

  Partially resolved

  Some dense suspensions, such as cornstarch in water, become almost solid when stirred hard. The accepted explanation is that particles switch from slipping past each other to touching with friction, but the stress at which this happens cannot yet be predicted from particle properties.

• Is there a critical outlet size for clogging of granular silos?

  Contested

  Grains pouring through a small hole in a silo eventually jam by forming an arch. It is disputed whether there is a hole size above which jamming never happens, or whether jamming only becomes extremely rare.