2011-10-27 00:59:49 +08:00
|
|
|
<HTML>
|
|
|
|
|
<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
|
|
|
|
|
</CENTER>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<HR>
|
|
|
|
|
|
|
|
|
|
<H3>pair_style lubricateU command
|
|
|
|
|
</H3>
|
|
|
|
|
<H3>pair_style lubricateU/poly command
|
|
|
|
|
</H3>
|
|
|
|
|
<P><B>Syntax:</B>
|
|
|
|
|
</P>
|
2012-05-24 01:47:58 +08:00
|
|
|
<PRE>pair_style style mu flaglog cutinner cutoff gdot flagHI flagVF
|
2011-10-27 00:59:49 +08:00
|
|
|
</PRE>
|
|
|
|
|
<UL><LI>style = <I>lubricateU</I> or <I>lubricateU/poly</I>
|
|
|
|
|
<LI>mu = dynamic viscosity (dynamic viscosity units)
|
2013-05-25 05:55:29 +08:00
|
|
|
<LI>flaglog = 0/1 to exclude/include log terms in the lubrication approximation
|
2011-10-27 00:59:49 +08:00
|
|
|
<LI>cutinner = inner cut off distance (distance units)
|
|
|
|
|
<LI>cutoff = outer cutoff for interactions (distance units)
|
2012-05-24 01:47:58 +08:00
|
|
|
<LI>gdot = shear rate (1/time units)
|
2013-05-25 05:55:29 +08:00
|
|
|
<LI>flagHI (optional) = 0/1 to exclude/include 1/r hydrodynamic interactions
|
|
|
|
|
<LI>flagVF (optional) = 0/1 to exclude/include volume fraction corrections in the long-range isotropic terms
|
2011-10-27 00:59:49 +08:00
|
|
|
</UL>
|
|
|
|
|
<P><B>Examples:</B> (all assume radius = 1)
|
|
|
|
|
</P>
|
2012-05-24 01:47:58 +08:00
|
|
|
<PRE>pair_style lubricateU 1.5 1 2.01 2.5 0.01 1 1
|
2011-10-27 00:59:49 +08:00
|
|
|
pair_coeff 1 1 2.05 2.8
|
|
|
|
|
pair_coeff * *
|
|
|
|
|
</PRE>
|
|
|
|
|
<P><B>Description:</B>
|
|
|
|
|
</P>
|
|
|
|
|
<P>Styles <I>lubricateU</I> and <I>lubricateU/poly</I> compute velocities and
|
|
|
|
|
angular velocities 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 HREF = "#Ball">(Ball and
|
|
|
|
|
Melrose)</A>
|
|
|
|
|
</P>
|
|
|
|
|
<CENTER><IMG SRC = "Eqs/pair_lubricate.jpg">
|
|
|
|
|
</CENTER>
|
|
|
|
|
<P>which represents the dissipation W between two nearby particles due to
|
|
|
|
|
their relative velocities in the presence of a background solvent with
|
2012-05-24 01:47:58 +08:00
|
|
|
viscosity <I>mu</I>. Note that this is dynamic viscosity which has units of
|
2011-10-27 00:59:49 +08:00
|
|
|
mass/distance/time, not kinematic viscosity.
|
|
|
|
|
</P>
|
2012-05-24 01:47:58 +08:00
|
|
|
<P>The Asq (squeeze) term is the strongest and is included as long as
|
|
|
|
|
<I>flagHI</I> is set to 1 (default). 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 included if <I>flaglog</I> is set to 1. They
|
|
|
|
|
are the next strongest interactions, and the only other singular
|
|
|
|
|
interaction, and scale as log(gap). Note that <I>flaglog</I> = 1 and
|
|
|
|
|
<I>flagHI</I> = 0 is invalid, and will result in a warning message, after
|
|
|
|
|
which <I>flagHI</I> will be set to 1. The Atw (twist) term is currently not
|
|
|
|
|
included. It is typically a very small contribution to the lubrication
|
|
|
|
|
forces.
|
|
|
|
|
</P>
|
|
|
|
|
<P>The <I>flagHI</I> and <I>flagVF</I> settings are optional. Neither should be
|
|
|
|
|
used, or both must be defined.
|
2011-10-27 00:59:49 +08:00
|
|
|
</P>
|
|
|
|
|
<P><I>Cutinner</I> sets the minimum center-to-center separation that will be
|
|
|
|
|
used in calculations irrespective of the actual separation. <I>Cutoff</I>
|
|
|
|
|
is the maximum center-to-center separation at which an interaction is
|
|
|
|
|
computed. Using a <I>cutoff</I> less than 3 radii is recommended if
|
|
|
|
|
<I>flaglog</I> is set to 1.
|
|
|
|
|
</P>
|
|
|
|
|
<P>The other component is due to the Fast Lubrication Dynamics (FLD)
|
2011-10-27 01:21:47 +08:00
|
|
|
approximation, described in <A HREF = "#Kumar">(Kumar)</A>. The equation being
|
2011-10-27 00:59:49 +08:00
|
|
|
solved to balance the forces and torques is
|
|
|
|
|
</P>
|
|
|
|
|
<CENTER><IMG SRC = "Eqs/fld2.jpg">
|
|
|
|
|
</CENTER>
|
|
|
|
|
<P>where U represents the velocities and angular velocities of the
|
2012-05-24 01:47:58 +08:00
|
|
|
particles, U^<I>infty</I> represents the velocities and the angular
|
|
|
|
|
velocities of the undisturbed fluid, and E^<I>infty</I> represents the rate
|
|
|
|
|
of strain tensor of the undisturbed fluid flow with viscosity
|
|
|
|
|
<I>mu</I>. 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 <I>flagVF</I> is set to 1 (default).
|
2011-10-27 00:59:49 +08:00
|
|
|
</P>
|
|
|
|
|
<P>F<I>rest</I> 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>
|
|
|
|
|
<P>IMPORTANT NOTE: 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 HREF = "fix_nve_noforce.html">fix
|
|
|
|
|
nve/noforce</A> should be used for spherical
|
|
|
|
|
particles defined via <A HREF = "atom_style.html">atom_style sphere</A> or <A HREF = "fix_nve_asphere_noforce.html">fix
|
|
|
|
|
nve/asphere/noforce</A> should be used for
|
|
|
|
|
spherical particles defined via <A HREF = "atom_style.html">atom_style
|
|
|
|
|
ellipsoid</A>. This is because the velocity and angular
|
|
|
|
|
momentum of each particle is set by the pair style, and should not be
|
|
|
|
|
reset by the time integration fix.
|
|
|
|
|
</P>
|
|
|
|
|
<P>Style <I>lubricateU</I> requires monodisperse spherical particles; style
|
|
|
|
|
<I>lubricateU/poly</I> allows for polydisperse spherical particles.
|
|
|
|
|
</P>
|
|
|
|
|
<P>If the suspension is sheared via the <A HREF = "fix_deform.html">fix deform</A>
|
|
|
|
|
command then the pair style uses the shear rate to adjust the
|
2012-05-24 01:47:58 +08:00
|
|
|
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: <A HREF = "fix_wall.html">wall/lj93</A>,
|
|
|
|
|
<A HREF = "fix_wall.html">wall/lj126</A>, <A HREF = "fix_wall.html">wall/colloid</A>, and
|
|
|
|
|
"wall/harmonic_fix_wall.html". 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. To use these wall styles with pair_style <I>lubricateU</I>
|
|
|
|
|
or <I>lubricateU/poly</I>, the <I>fld yes</I> option must be specified in the
|
|
|
|
|
fix wall command.
|
2011-10-27 00:59:49 +08:00
|
|
|
</P>
|
|
|
|
|
<P>Since lubrication forces are dissipative, it is usually desirable to
|
2012-05-24 01:47:58 +08:00
|
|
|
thermostat the system at a constant temperature. If Brownian motion
|
2011-10-27 00:59:49 +08:00
|
|
|
(at a constant temperature) is desired, it can be set using the
|
2012-05-24 01:47:58 +08:00
|
|
|
<A HREF = "pair_brownian.html">pair_style brownian</A> command. These pair styles
|
|
|
|
|
and the brownian style should use consistent parameters for <I>mu</I>,
|
|
|
|
|
<I>flaglog</I>, <I>flagfld</I>, <I>cutinner</I>, <I>cutoff</I>, <I>flagHI</I> and <I>flagVF</I>.
|
2011-10-27 00:59:49 +08:00
|
|
|
</P>
|
|
|
|
|
<HR>
|
|
|
|
|
|
|
|
|
|
<P>The following coefficients must be defined for each pair of atoms
|
|
|
|
|
types via the <A HREF = "pair_coeff.html">pair_coeff</A> command as in the examples
|
|
|
|
|
above, or in the data file or restart files read by the
|
|
|
|
|
<A HREF = "read_data.html">read_data</A> or <A HREF = "read_restart.html">read_restart</A>
|
|
|
|
|
commands, or by mixing as described below:
|
|
|
|
|
</P>
|
|
|
|
|
<UL><LI>cutinner (distance units)
|
|
|
|
|
<LI>cutoff (distance units)
|
|
|
|
|
</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>
|
|
|
|
|
<HR>
|
|
|
|
|
|
|
|
|
|
<P><B>Mixing, shift, table, tail correction, restart, rRESPA info</B>:
|
|
|
|
|
</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 <I>geometric</I>. See
|
|
|
|
|
the "pair_modify" command for details.
|
|
|
|
|
</P>
|
|
|
|
|
<P>This pair style does not support the <A HREF = "pair_modify.html">pair_modify</A>
|
|
|
|
|
shift option for the energy of the pair interaction.
|
|
|
|
|
</P>
|
|
|
|
|
<P>The <A HREF = "pair_modify.html">pair_modify</A> table option is not relevant
|
|
|
|
|
for this pair style.
|
|
|
|
|
</P>
|
|
|
|
|
<P>This pair style does not support the <A HREF = "pair_modify.html">pair_modify</A>
|
|
|
|
|
tail option for adding long-range tail corrections to energy and
|
|
|
|
|
pressure.
|
|
|
|
|
</P>
|
|
|
|
|
<P>This pair style writes its information to <A HREF = "restart.html">binary restart
|
|
|
|
|
files</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 <I>pair</I> keyword of the
|
|
|
|
|
<A HREF = "run_style.html">run_style respa</A> command. It does not support the
|
|
|
|
|
<I>inner</I>, <I>middle</I>, <I>outer</I> keywords.
|
|
|
|
|
</P>
|
|
|
|
|
<HR>
|
|
|
|
|
|
|
|
|
|
<P><B>Restrictions:</B>
|
|
|
|
|
</P>
|
|
|
|
|
<P>These styles are part of the FLD package. They are only enabled if
|
|
|
|
|
LAMMPS was built with that package. See the <A HREF = "Section_start.html#2_3">Making
|
|
|
|
|
LAMMPS</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.
|
2012-05-24 01:47:58 +08:00
|
|
|
One exception is the <A HREF = "fix_wall.html">fix wall/colloid</A> commands, which
|
|
|
|
|
has an "fld" option to apply their wall forces correctly.
|
2011-10-27 00:59:49 +08:00
|
|
|
</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 HREF = "fix_deform.html">fix
|
|
|
|
|
deform</A> with the same rate of shear (erate).
|
|
|
|
|
</P>
|
|
|
|
|
<P><B>Related commands:</B>
|
|
|
|
|
</P>
|
|
|
|
|
<P><A HREF = "pair_coeff.html">pair_coeff</A>, <A HREF = "pair_lubricate.html">pair_style
|
|
|
|
|
lubricate</A>
|
|
|
|
|
</P>
|
2012-05-24 01:47:58 +08:00
|
|
|
<P><B>Default:</B>
|
|
|
|
|
</P>
|
|
|
|
|
<P>The default settings for the optional args are flagHI = 1 and flagVF =
|
|
|
|
|
1.
|
2011-10-27 00:59:49 +08:00
|
|
|
</P>
|
|
|
|
|
<HR>
|
|
|
|
|
|
|
|
|
|
<A NAME = "Ball"></A>
|
|
|
|
|
|
|
|
|
|
<P><B>(Ball)</B> Ball and Melrose, Physica A, 247, 444-472 (1997).
|
|
|
|
|
</P>
|
2011-10-27 01:21:47 +08:00
|
|
|
<A NAME = "Kumar"></A>
|
2011-10-27 00:59:49 +08:00
|
|
|
|
2011-10-27 01:21:47 +08:00
|
|
|
<P><B>(Kumar)</B> Kumar and Higdon, Phys Rev E, 82, 051401 (2010).
|
2011-10-27 00:59:49 +08:00
|
|
|
</P>
|
|
|
|
|
</HTML>
|
