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### fix viscosity command

Syntax:

    fix ID group-ID viscosity N vdim pdim Nbin keyword value ...

- ID, group-ID are documented in fix command
- viscosity = style name of this fix command
- N = perform momentum exchange every N steps
- vdim = x or y or z = which momentum component to exchange
- pdim = x or y or z = direction of momentum transfer
- Nbin = # of layers in pdim direction (must be even number)
- zero or more keyword/value pairs may be appended
- keyword = swap or target

        swap value = Nswap = number of swaps to perform every N steps
        vtarget value = V or INF = target velocity of swap partners (velocity units)

Examples:

    fix 1 all viscosity 100 x z 20
    fix 1 all viscosity 50 x z 20 swap 2 vtarget 1.5

Description:

Use the Muller-Plathe algorithm described in this paper to exchange momenta between two particles in different regions of the simulation box every N steps. This induces a shear velocity profile in the system. As described below this enables a viscosity of the fluid to be calculated. This algorithm is sometimes called a reverse non-equilibrium MD (reverse NEMD) approach to computing viscosity. This is because the usual NEMD approach is to impose a shear velocity profile on the system and measure the response via an off-diagonal component of the stress tensor, which is proportional to the momentum flux. In the Muller-Plathe method, the momentum flux is imposed, and the shear velocity profile is the system's response.

The simulation box is divided into Nbin layers in the pdim direction, where the layer 1 is at the low end of that dimension and the layer Nbin is at the high end. Every N steps, Nswap pairs of atoms are chosen in the following manner. Only atoms in the fix group are considered. Nswap atoms in layer 1 with positive velocity components in the vdim direction closest to the target value V are selected. Similarly, Nswap atoms in the "middle" layer (see below) with negative velocity components in the vdim direction closest to the negative of the target value V are selected. The two sets of Nswap atoms are paired up and their vdim momenta components are swapped within each pair. This resets their velocities, typically in opposite directions. Over time, this induces a shear velocity profile in the system which can be measured using commands such as the following, which writes the profile to the file tmp.profile:

    fix f1 all ave/spatial 100 10 1000 z lower 0.05 vx &
        file tmp.profile units reduced

Note that by default, Nswap = 1 and vtarget = INF, though this can be changed by the optional swap and vtarget keywords. When vtarget = INF, one or more atoms with the most positive and negative velocity components are selected. Setting these parameters appropriately, in conjunction with the swap rate N, allows the momentum flux rate to be adjusted across a wide range of values, and the momenta to be exchanged in large chunks or more smoothly.

The "middle" layer for momenta swapping is defined as the Nbin/2 + 1 layer. Thus if Nbin = 20, the two swapping layers are 1 and 11. This should lead to a symmetric velocity profile since the two layers are separated by the same distance in both directions in a periodic sense. This is why Nbin is restricted to being an even number.

As described below, the total momentum transferred by these velocity swaps is computed by the fix and can be output. Dividing this quantity by time and the cross-sectional area of the simulation box yields a momentum flux. The ratio of momentum flux to the slope of the shear velocity profile is proportional to the viscosity of the fluid, in appropriate units. See the Muller-Plathe paper for details.

IMPORTANT NOTE: If your system is periodic in the direction of the momentum flux, then the flux is going in 2 directions. This means the effective momentum flux in one direction is reduced by a factor of 2. You will see this in the equations for viscosity in the Muller-Plathe paper. LAMMPS is simply tallying momentum which does not account for whether or not your system is periodic; you must use the value appropriately to yield a viscosity for your system.

IMPORTANT NOTE: After equilibration, if the velocity profile you observe is not linear, then you are likely swapping momentum too frequently and are not in a regime of linear response. In this case you cannot accurately infer a viscosity and should try increasing the Nevery parameter.

An alternative method for calculating a viscosity is to run a NEMD simulation, as described in Section_howto 13 of the manual. NEMD simulations deform the simmulation box via the fix deform command. Thus they cannot be run on a charged system using a PPPM solver since PPPM does not currently support non-orthogonal boxes. Using fix viscosity keeps the box orthogonal; thus it does not suffer from this limitation.

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.

This fix computes a global scalar which can be accessed by various output commands. The scalar is the cummulative momentum transferred between the bottom and middle of the simulation box (in the pdim direction) is stored as a scalar quantity by this fix. This quantity is zeroed when the fix is defined and accumlates thereafter, once every N steps. The units of the quantity are momentum = mass*velocity. The scalar value calculated by this fix is "intensive".

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:

Swaps conserve both momentum and kinetic energy, even if the masses of the swapped atoms are not equal. Thus you should not need to thermostat the system. If you do use a thermostat, you may want to apply it only to the non-swapped dimensions (other than vdim).

LAMMPS does not check, but you should not use this fix to swap velocities of atoms that are in constrained molecules, e.g. via fix shake or fix rigid. This is because application of the constraints will alter the amount of transferred momentum. You should, however, be able to use flexible molecules. See the Maginn paper for an example of using this algorithm in a computation of alcohol molecule properties.

When running a simulation with large, massive particles or molecules in a background solvent, you may want to only exchange momenta bewteen solvent particles.

Related commands:

fix ave/spatial, fix thermal/conductivity

Default:

The option defaults are swap = 1 and vtarget = INF.

(Muller-Plathe) Muller-Plathe, Phys Rev E, 59, 4894-4898 (1999).

(Maginn) Kelkar, Rafferty, Maginn, Siepmann, Fluid Phase Equilibria, 260, 218-231 (2007).