<p>Styles <em>lubricateU</em> and <em>lubricateU/poly</em> compute velocities and
angular velocities for finite-size spherical particles such that the
hydrodynamic interaction balances the force and torque due to all
other types of interactions.</p>
<p>The interactions have 2 components. The first is
Ball-Melrose lubrication terms via the formulas in <a class="reference internal" href="#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 velocities and the angular
velocities of the undisturbed fluid, and E^<em>infty</em> represents the rate
of strain tensor of the undisturbed fluid flow 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 if <em>flagVF</em> is set to 1 (default).</p>
<p>F<em>rest</em> represents the forces and torques due to all other types of
interactions, e.g. Brownian, electrostatic etc. Note that this
algorithm neglects the inertial terms, thereby removing the
restriction of resolving the small interial time scale, which may not
be of interest for colloidal particles. This pair style solves for
the velocity such that the hydrodynamic force balances all other types
of forces, thereby resulting in a net zero force (zero inertia limit).
When defining this pair style, it must be defined last so that when
this style is invoked all other types of forces have already been
computed. For the same reason, it won’t work if additional non-pair
styles are defined (such as bond or Kspace forces) as they are
calculated in LAMMPS after the pairwise interactions have been
computed.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">When using these styles, the these pair styles are designed to
be used with implicit time integration and a correspondingly larger
timestep. Thus either <a class="reference internal" href="fix_nve_noforce.html"><span class="doc">fix nve/noforce</span></a> should
be used for spherical particles defined via <a class="reference internal" href="atom_style.html"><span class="doc">atom_style sphere</span></a> or <a class="reference internal" href="fix_nve_asphere_noforce.html"><span class="doc">fix nve/asphere/noforce</span></a> should be used for
spherical particles defined via <a class="reference internal" href="atom_style.html"><span class="doc">atom_style ellipsoid</span></a>. This is because the velocity and angular
momentum of each particle is set by the pair style, and should not be
<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
<p>These styles are part of the COLLOID package. They are only enabled
if LAMMPS was built with that package. See the <a class="reference internal" href="Section_start.html#start-2-3"><span class="std std-ref">Making LAMMPS</span></a> section for more info.</p>
<p>Currently, these pair styles assume that all other types of
forces/torques on the particles have been already been computed when
it is invoked. This requires this style to be defined as the last of
the pair styles, and that no fixes apply additional constraint forces.
One exception is the <a class="reference internal" href="fix_wall.html"><span class="doc">fix wall/colloid</span></a> commands, which
has an “fld” option to apply their wall forces correctly.</p>
<p>Only spherical monodisperse particles are allowed for pair_style
lubricateU.</p>
<p>Only spherical particles are allowed for pair_style lubricateU/poly.</p>
<p>For sheared suspensions, it is assumed that the shearing is done in
the xy plane, with x being the velocity direction and y being the
velocity-gradient direction. In this case, one must use <a class="reference internal" href="fix_deform.html"><span class="doc">fix deform</span></a> with the same rate of shear (erate).</p>
Built with <a href="http://sphinx-doc.org/">Sphinx</a> using a <a href="https://github.com/snide/sphinx_rtd_theme">theme</a> provided by <a href="https://readthedocs.org">Read the Docs</a>.