<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 <a class="reference internal" href="pair_lubricateU.html#ball"><span class="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>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="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 <a class="reference internal" href="fix_nve_sphere.html"><span class="doc">fix nve/sphere</span></a> or <a class="reference internal" href="fix_nve_asphere.html"><span class="doc">fix nve/asphere</span></a> should be used for time integration.
To perform implicit FLD, see the <a class="reference internal" href="pair_lubricateU.html"><span class="doc">pair_style lubricateU</span></a> command.</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 <a class="reference internal" href="pair_modify.html"><span class="doc">pair_modify</span></a>
shift option for the energy of the pair interaction.</p>
<p>The <a class="reference internal" href="pair_modify.html"><span class="doc">pair_modify</span></a> table option is not relevant
for this pair style.</p>
<p>This pair style does not support the <a class="reference internal" href="pair_modify.html"><span class="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 <a class="reference internal" href="restart.html"><span class="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
<a class="reference internal" href="run_style.html"><span class="doc">run_style respa</span></a> command. It does not support the
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