<p>Styles <em>lubricate</em> and <em>lubricate/poly</em> compute hydrodynamic
interactions between mono-disperse finite-size spherical particles in
a pairwise fashion. The interactions have 2 components. The first is
Ball-Melrose lubrication terms via the formulas in <aclass="reference internal"href="pair_lubricateU.html#ball"><spanclass="std std-ref">(Ball and Melrose)</span></a></p>
<p>where U represents the velocities and angular velocities of the
particles, U^<em>infty</em> represents the velocity and the angular velocity
of the undisturbed fluid, and E^<em>infty</em> represents the rate of strain
tensor of the undisturbed fluid with viscosity <em>mu</em>. Again, note that
this is dynamic viscosity which has units of mass/distance/time, not
kinematic viscosity. Volume fraction corrections to R_FU are included
as long as <em>flagVF</em> is set to 1 (default).</p>
<divclass="admonition note">
<pclass="first admonition-title">Note</p>
<pclass="last">When using the FLD terms, these pair styles are designed to be
used with explicit time integration and a correspondingly small
timestep. Thus either <aclass="reference internal"href="fix_nve_sphere.html"><spanclass="doc">fix nve/sphere</span></a> or <aclass="reference internal"href="fix_nve_asphere.html"><spanclass="doc">fix nve/asphere</span></a> should be used for time integration.
To perform implicit FLD, see the <aclass="reference internal"href="pair_lubricateU.html"><spanclass="doc">pair_style lubricateU</span></a> command.</p>
<em>lubricate/poly</em> allows for polydisperse spherical particles.</p>
<p>The viscosity <em>mu</em> 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 <em>mu</em> will be overridden. See the <aclass="reference internal"href="fix_adapt.html"><spanclass="doc">fix adapt</span></a>
command for details.</p>
<p>If the suspension is sheared via the <aclass="reference internal"href="fix_deform.html"><spanclass="doc">fix deform</span></a>
command then the pair style uses the shear rate to adjust the
hydrodynamic interactions accordingly. Volume changes due to fix
deform are accounted for when computing the volume fraction
corrections to R_FU.</p>
<p>When computing the volume fraction corrections to R_FU, the presence
of walls (whether moving or stationary) will affect the volume
fraction available to colloidal particles. This is currently accounted
for with the following types of walls: <aclass="reference internal"href="fix_wall.html"><spanclass="doc">wall/lj93</span></a>,
<aclass="reference internal"href="fix_wall.html"><spanclass="doc">wall/lj126</span></a>, <aclass="reference internal"href="fix_wall.html"><spanclass="doc">wall/colloid</span></a>, and
<aclass="reference internal"href="fix_wall.html"><spanclass="doc">wall/harmonic</span></a>. For these wall styles, the correct
volume fraction will be used when walls do not coincide with the box
boundary, as well as when walls move and thereby cause a change in the
volume fraction. Other wall styles will still work, but they will
result in the volume fraction being computed based on the box
boundaries.</p>
<p>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
<aclass="reference internal"href="pair_brownian.html"><spanclass="doc">pair_style brownian</span></a> command. These pair styles
and the brownian style should use consistent parameters for <em>mu</em>,
<em>flaglog</em>, <em>flagfld</em>, <em>cutinner</em>, <em>cutoff</em>, <em>flagHI</em> and <em>flagVF</em>.</p>
<hrclass="docutils"/>
<p>The following coefficients must be defined for each pair of atoms
types via the <aclass="reference internal"href="pair_coeff.html"><spanclass="doc">pair_coeff</span></a> command as in the examples
above, or in the data file or restart files read by the
<aclass="reference internal"href="read_data.html"><spanclass="doc">read_data</span></a> or <aclass="reference internal"href="read_restart.html"><spanclass="doc">read_restart</span></a>
commands, or by mixing as described below:</p>
<ulclass="simple">
<li>cutinner (distance units)</li>
<li>cutoff (distance units)</li>
</ul>
<p>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.</p>
<hrclass="docutils"/>
<p>Styles with a <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
functionally the same as the corresponding style without the suffix.
They have been optimized to run faster, depending on your available
hardware, as discussed in <aclass="reference internal"href="Section_accelerate.html"><spanclass="doc">this section</span></a> of
the manual. The accelerated styles take the same arguments and should
produce the same results, except for round-off and precision issues.</p>
<p>These accelerated styles are part of the GPU, USER-INTEL, KOKKOS,
USER-OMP and OPT packages, respectively. They are only enabled if
LAMMPS was built with those packages. See the <aclass="reference internal"href="Section_start.html#start-3"><spanclass="std std-ref">Making LAMMPS</span></a> section for more info.</p>
<p>You can specify the accelerated styles explicitly in your input script
by including their suffix, or you can use the <aclass="reference internal"href="Section_start.html#start-7"><spanclass="std std-ref">-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
use the <aclass="reference internal"href="suffix.html"><spanclass="doc">suffix</span></a> command in your input script.</p>
<p>See <aclass="reference internal"href="Section_accelerate.html"><spanclass="doc">this section</span></a> of the manual for more
instructions on how to use the accelerated styles effectively.</p>
<p>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 <em>geometric</em>. See
the “pair_modify” command for details.</p>
<p>This pair style does not support the <aclass="reference internal"href="pair_modify.html"><spanclass="doc">pair_modify</span></a>
shift option for the energy of the pair interaction.</p>
<p>The <aclass="reference internal"href="pair_modify.html"><spanclass="doc">pair_modify</span></a> table option is not relevant
for this pair style.</p>
<p>This pair style does not support the <aclass="reference internal"href="pair_modify.html"><spanclass="doc">pair_modify</span></a>
tail option for adding long-range tail corrections to energy and
pressure.</p>
<p>This pair style writes its information to <aclass="reference internal"href="restart.html"><spanclass="doc">binary restart files</span></a>, so pair_style and pair_coeff commands do not need
to be specified in an input script that reads a restart file.</p>
<p>This pair style can only be used via the <em>pair</em> keyword of the
<aclass="reference internal"href="run_style.html"><spanclass="doc">run_style respa</span></a> command. It does not support the
<p>These styles are part of the COLLOID package. They are only enabled
if LAMMPS was built with that package. See the <aclass="reference internal"href="Section_start.html#start-2-3"><spanclass="std std-ref">Making LAMMPS</span></a> section for more info.</p>
<p>Only spherical monodisperse particles are allowed for pair_style
lubricate.</p>
<p>Only spherical particles are allowed for pair_style lubricate/poly.</p>
<p>These pair styles will not restart exactly when using the
<aclass="reference internal"href="read_restart.html"><spanclass="doc">read_restart</span></a> command, though they should provide
statistically similar results. This is because the forces they
compute depend on atom velocities. See the
<aclass="reference internal"href="read_restart.html"><spanclass="doc">read_restart</span></a> command for more details.</p>
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