lammps/doc/pair_lubricate.txt

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pair_style lubricate command :h3
pair_style lubricate/poly command :h3

[Syntax:]

pair_style style mu flaglog flagfld cutinner cutoff :pre

style = {lubricate} or {lubricate/poly}
mu = dynamic viscosity (dynamic viscosity units)
flaglog = 0/1 log terms in the lubrication approximation off/on
flagfld = 0/1 to include/exclude Fast Lubrication Dynamics effects
cutinner = inner cutoff distance (distance units)
cutoff = outer cutoff for interactions (distance units) :ul

[Examples:] (all assume radius = 1)

pair_style lubricate 1.5 1 1 2.01 2.5
pair_coeff 1 1 2.05 2.8
pair_coeff * * :pre

pair_style lubricate 1.5 1 1 2.01 2.5
pair_coeff * *
variable mu equal ramp(1,2)
fix 1 all adapt 1 pair lubricate mu * * v_mu :pre

[Description:]

Styles {lubricate} and {lubricate/poly} compute hydrodynamic
interactions between mono-disperse spherical particles in a pairwise
fashion.  The interactions have 2 components.  The first is
Ball-Melrose lubrication terms via the formulas in "(Ball and
Melrose)"_#Ball

:c,image(Eqs/pair_lubricate.jpg)

which represents the dissipation W between two nearby particles due to
their relative velocities in the presence of a background solvent with
viscosity mu.  Note that this is dynamic viscosity which has units of
mass/distance/time, not kinematic viscosity.

The Asq (squeeze) term is the strongest and is always included.  It
scales as 1/gap where gap is the separation between the surfaces of
the 2 particles.  The Ash (shear) and Apu (pump) terms are only
include if {flaglog} is set to 1.  Thy are the next strongest
interactions, and the only other singular interaction, and scale as
log(gap).  The Atw (twist) term is currently not included.  It is
typically a very small contribution to the lubrication forces.

{Cutinner} sets the minimum center-to-center separation that will be
used in calculations irrespective of the actual separation.  {Cutoff}
is the maximum center-to-center separation at which an interaction is
computed.  Using a {cutoff} less than 3 radii is recommended if
{flaglog} is set to 1.

The other component is due to the Fast Lubrication Dynamics (FLD)
approximation, described in "(Kumar)"_#Kumar, which can be
represented by the following equation

:c,image(Eqs/fld.jpg)

where U represents the velocities and angular velocities of the
particles, U^{infty} represents the velocity and the angular velocity
of the undisturbed fluid, and E^{infty} represents the rate of strain
tensor of the undisturbed fluid with viscosity mu.  Again, note that
this is dynamic viscosity which has units of mass/distance/time, not
kinematic viscosity.

IMPORTANT NOTE: When using the FLD terms, these pair styles are
designed to be used with explicit time integration and a
correspondingly small timestep.  Thus either "fix
nve/sphere"_fix_nve_sphere.html or "fix
nve/asphere"_fix_nve_asphere.html should be used for time integration.
To perform implicit FLD, see the "pair_style
lubricateU"_pair_lubricateU.html command.

Style {lubricate} requires monodisperse spherical particles; style
{lubricate/poly} allows for polydisperse spherical particles.

The viscosity mu can be varied in a time-dependent manner over the
course of a simluation, in which case in which case the pair_style
setting for mu will be overridden.  See the "fix adapt"_fix_adapt.html
command for details.

If the suspension is sheared via the "fix deform"_fix_deform.html
command then the pair style uses the shear rate to adjust the
hydrodynamic interactions accordingly.

Since lubrication forces are dissipative, it is usually desirable to
thermostat the system at a constant temperature.  If Brownian motion
(at a constant temperature) is desired, it can be set using the
"pair_style brownian"_pair_brownian.html command.  These pair styles
and the {brownian} style should use consistent parameters for {mu},
{flaglog}, {flagfld}, {cutinner}, and {cutoff}.

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The following coefficients must be defined for each pair of atoms
types via the "pair_coeff"_pair_coeff.html command as in the examples
above, or in the data file or restart files read by the
"read_data"_read_data.html or "read_restart"_read_restart.html
commands, or by mixing as described below:

cutinner (distance units)
cutoff (distance units) :ul

The two coefficients are optional.  If neither is specified, the two
cutoffs specified in the pair_style command are used.  Otherwise both
must be specified.

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[Mixing, shift, table, tail correction, restart, rRESPA info]:

For atom type pairs I,J and I != J, the two cutoff distances for this
pair style can be mixed.  The default mix value is {geometric}.  See
the "pair_modify" command for details.

This pair style does not support the "pair_modify"_pair_modify.html
shift option for the energy of the pair interaction.

The "pair_modify"_pair_modify.html table option is not relevant
for this pair style.

This pair style does not support the "pair_modify"_pair_modify.html
tail option for adding long-range tail corrections to energy and
pressure.

This pair style writes its information to "binary restart
files"_restart.html, so pair_style and pair_coeff commands do not need
to be specified in an input script that reads a restart file.

This pair style can only be used via the {pair} keyword of the
"run_style respa"_run_style.html command.  It does not support the
{inner}, {middle}, {outer} keywords.

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[Restrictions:]

These styles are part of the FLD package.  They are only enabled if
LAMMPS was built with that package.  See the "Making
LAMMPS"_Section_start.html#2_3 section for more info.

Only spherical monodisperse particles are allowed for pair_style
lubricate.

Only spherical particles are allowed for pair_style lubricate/poly.

[Related commands:]

"pair_coeff"_pair_coeff.html, "pair_style
lubricateU"_pair_lubricateU.html

[Default:] none

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:link(Ball)
[(Ball)] Ball and Melrose, Physica A, 247, 444-472 (1997).

:link(Kumar)
[(Kumar)] Kumar and Higdon, Phys Rev E, 82, 051401 (2010).