\(\renewcommand{\AA}{\text{Å}}\)

# fix rheo/viscosity command

## Syntax

    fix ID group-ID rheo/viscosity type1 pstyle1 args1 ... typeN pstyleN argsN

- ID, group-ID are documented in fix command

- rheo/viscosity = style name of this fix command

- one or more types and viscosity styles must be appended

- types = lists of types (see below)

- vstyle = constant or power

      constant args = eta
        eta = viscosity

      power args = eta, gd0, K, n
        eta = viscosity
        gd0 = critical strain rate
        K = consistency index
        n = power-law exponent

## Examples

    fix 1 all rheo/viscosity * constant 1.0
    fix 1 all rheo/viscosity 1 constant 1.0 2 power 0.1 5e-4 0.001 0.5

## Description

Added in version 29Aug2024.

This fix defines a viscosity for RHEO particles. One can define different viscosities for different atom types, but a viscosity must be specified for every atom type.

One first defines the atom types. A wild-card asterisk can be used in place of or in conjunction with the types argument to set values for multiple atom types. This takes the form “*” or “*n” or “m*” or “m*n”. If \(N\) is the number of atom types, then an asterisk with no numeric values means all types from 1 to \(N\). A leading asterisk means all types from 1 to n (inclusive). A trailing asterisk means all types from m to \(N\) (inclusive). A middle asterisk means all types from m to n (inclusive).

The types definition is followed by the viscosity style, vstyle. Two options are available, constant and power. Style constant simply applies a constant value of the viscosity eta to each particle of the assigned type. Style power is a Hershchel-Bulkley constitutive equation for the stress \(\tau\)

\[\tau = \left(\frac{\tau_0}{\dot{\gamma}} + K \dot{\gamma}^{n - 1}\right) \dot{\gamma}, \tau \ge \tau_0\]

where \(\dot{\gamma}\) is the strain rate and \(\tau_0\) is the critical yield stress, below which \(\dot{\gamma} = 0.0\). To avoid divergences, this expression is regularized by defining a critical strain rate gd0. If the local strain rate on a particle falls below this limit, a constant viscosity of eta is assigned. This implies a value of

\[\tau_0 = \eta \dot{\gamma}_0 - K \dot{\gamma}_0^N\]

## Restart, fix_modify, output, run start/stop, minimize info

No information about this fix is written to binary restart files. None of the fix_modify options are relevant to this fix. No global or per-atom quantities are stored by this fix for access by various output commands. No parameter of this fix can be used with the start/stop keywords of the run command. This fix is not invoked during energy minimization.

## Restrictions

This fix must be used with an atom style that includes viscosity such as atom_style rheo or rheo/thermal. This fix must be used in conjunction with fix rheo. The fix group must be set to all. Only one instance of fix rheo/viscosity can be defined.

This fix is part of the RHEO package. It is only enabled if LAMMPS was built with that package. See the Build package page for more info.

## Related commands

fix rheo, pair rheo, compute rheo/property/atom

## Default

none