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<HTML>
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<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>
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</CENTER>
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<HR>
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<H3>pair_style lubricate command
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</H3>
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<H3>pair_style lubricate/omp command
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</H3>
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<H3>pair_style lubricate/poly command
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</H3>
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<H3>pair_style lubricate/poly/omp command
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</H3>
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<P><B>Syntax:</B>
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</P>
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<PRE>pair_style style mu flaglog flagfld cutinner cutoff flagHI flagVF
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</PRE>
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<UL><LI>style = <I>lubricate</I> or <I>lubricate/poly</I>
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<LI>mu = dynamic viscosity (dynamic viscosity units)
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<LI>flaglog = 0/1 to exclude/include log terms in the lubrication approximation
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<LI>flagfld = 0/1 to exclude/include Fast Lubrication Dynamics (FLD) effects
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<LI>cutinner = inner cutoff distance (distance units)
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<LI>cutoff = outer cutoff for interactions (distance units)
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<LI>flagHI (optional) = 0/1 to exclude/include 1/r hydrodynamic interactions
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<LI>flagVF (optional) = 0/1 to exclude/include volume fraction corrections in the long-range isotropic terms
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</UL>
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<P><B>Examples:</B> (all assume radius = 1)
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</P>
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<PRE>pair_style lubricate 1.5 1 1 2.01 2.5
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pair_coeff 1 1 2.05 2.8
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pair_coeff * *
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</PRE>
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<PRE>pair_style lubricate 1.5 1 1 2.01 2.5
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pair_coeff * *
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variable mu equal ramp(1,2)
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fix 1 all adapt 1 pair lubricate mu * * v_mu
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</PRE>
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<P><B>Description:</B>
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</P>
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<P>Styles <I>lubricate</I> and <I>lubricate/poly</I> compute hydrodynamic
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interactions between mono-disperse spherical particles in a pairwise
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fashion. The interactions have 2 components. The first is
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Ball-Melrose lubrication terms via the formulas in <A HREF = "#Ball">(Ball and
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Melrose)</A>
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</P>
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<CENTER><IMG SRC = "Eqs/pair_lubricate.jpg">
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</CENTER>
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<P>which represents the dissipation W between two nearby particles due to
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their relative velocities in the presence of a background solvent with
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viscosity <I>mu</I>. Note that this is dynamic viscosity which has units of
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mass/distance/time, not kinematic viscosity.
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</P>
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<P>The Asq (squeeze) term is the strongest and is included if <I>flagHI</I> is
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set to 1 (default). It scales as 1/gap where gap is the separation
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between the surfaces of the 2 particles. The Ash (shear) and Apu
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(pump) terms are only included if <I>flaglog</I> is set to 1. They are the
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next strongest interactions, and the only other singular interaction,
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and scale as log(gap). Note that <I>flaglog</I> = 1 and <I>flagHI</I> = 0 is
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invalid, and will result in a warning message, after which <I>flagHI</I> will
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be set to 1. The Atw (twist) term is currently not included. It is
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typically a very small contribution to the lubrication forces.
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</P>
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<P>The <I>flagHI</I> and <I>flagVF</I> settings are optional. Neither should be
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used, or both must be defined.
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</P>
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<P><I>Cutinner</I> sets the minimum center-to-center separation that will be
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used in calculations irrespective of the actual separation. <I>Cutoff</I>
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is the maximum center-to-center separation at which an interaction is
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computed. Using a <I>cutoff</I> less than 3 radii is recommended if
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<I>flaglog</I> is set to 1.
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</P>
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<P>The other component is due to the Fast Lubrication Dynamics (FLD)
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approximation, described in <A HREF = "#Kumar">(Kumar)</A>, which can be
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represented by the following equation
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</P>
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<CENTER><IMG SRC = "Eqs/fld.jpg">
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</CENTER>
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<P>where U represents the velocities and angular velocities of the
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particles, U^<I>infty</I> represents the velocity and the angular velocity
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of the undisturbed fluid, and E^<I>infty</I> represents the rate of strain
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tensor of the undisturbed fluid with viscosity <I>mu</I>. Again, note that
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this is dynamic viscosity which has units of mass/distance/time, not
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kinematic viscosity. Volume fraction corrections to R_FU are included
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as long as <I>flagVF</I> is set to 1 (default).
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</P>
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<P>IMPORTANT NOTE: When using the FLD terms, these pair styles are
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designed to be used with explicit time integration and a
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correspondingly small timestep. Thus either <A HREF = "fix_nve_sphere.html">fix
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nve/sphere</A> or <A HREF = "fix_nve_asphere.html">fix
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nve/asphere</A> should be used for time integration.
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To perform implicit FLD, see the <A HREF = "pair_lubricateU.html">pair_style
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lubricateU</A> command.
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</P>
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<P>Style <I>lubricate</I> requires monodisperse spherical particles; style
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<I>lubricate/poly</I> allows for polydisperse spherical particles.
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</P>
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<P>The viscosity <I>mu</I> can be varied in a time-dependent manner over the
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course of a simluation, in which case in which case the pair_style
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setting for <I>mu</I> will be overridden. See the <A HREF = "fix_adapt.html">fix adapt</A>
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command for details.
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</P>
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<P>If the suspension is sheared via the <A HREF = "fix_deform.html">fix deform</A>
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command then the pair style uses the shear rate to adjust the
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hydrodynamic interactions accordingly. Volume changes due to fix
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deform are accounted for when computing the volume fraction
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corrections to R_FU.
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</P>
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<P>When computing the volume fraction corrections to R_FU, the presence
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of walls (whether moving or stationary) will affect the volume
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fraction available to colloidal particles. This is currently accounted
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for with the following types of walls: <A HREF = "fix_wall.html">wall/lj93</A>,
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<A HREF = "fix_wall.html">wall/lj126</A>, <A HREF = "fix_wall.html">wall/colloid</A>, and
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<A HREF = "fix_wall.html">wall/harmonic</A>. For these wall styles, the correct
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volume fraction will be used when walls do not coincide with the box
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boundary, as well as when walls move and thereby cause a change in the
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volume fraction. Other wall styles will still work, but they will
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result in the volume fraction being computed based on the box
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boundaries.
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</P>
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<P>Since lubrication forces are dissipative, it is usually desirable to
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thermostat the system at a constant temperature. If Brownian motion
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(at a constant temperature) is desired, it can be set using the
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<A HREF = "pair_brownian.html">pair_style brownian</A> command. These pair styles
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and the brownian style should use consistent parameters for <I>mu</I>,
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<I>flaglog</I>, <I>flagfld</I>, <I>cutinner</I>, <I>cutoff</I>, <I>flagHI</I> and <I>flagVF</I>.
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</P>
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<HR>
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<P>The following coefficients must be defined for each pair of atoms
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types via the <A HREF = "pair_coeff.html">pair_coeff</A> command as in the examples
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above, or in the data file or restart files read by the
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<A HREF = "read_data.html">read_data</A> or <A HREF = "read_restart.html">read_restart</A>
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commands, or by mixing as described below:
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</P>
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<UL><LI>cutinner (distance units)
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<LI>cutoff (distance units)
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</UL>
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<P>The two coefficients are optional. If neither is specified, the two
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cutoffs specified in the pair_style command are used. Otherwise both
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must be specified.
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</P>
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<HR>
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<P>Styles with a <I>cuda</I>, <I>gpu</I>, <I>intel</I>, <I>kk</I>, <I>omp</I>, or <I>opt</I> suffix are
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functionally the same as the corresponding style without the suffix.
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They have been optimized to run faster, depending on your available
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hardware, as discussed in <A HREF = "Section_accelerate.html">this section</A> of
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the manual. The accelerated styles take the same arguments and should
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produce the same results, except for round-off and precision issues.
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</P>
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<P>These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
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KOKKOS, USER-OMP and OPT packages, respectively. They are only
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enabled if LAMMPS was built with those packages. See the <A HREF = "Section_start.html#start_3">Making
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LAMMPS</A> section for more info.
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</P>
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<P>You can specify the accelerated styles explicitly in your input script
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by including their suffix, or you can use the <A HREF = "Section_start.html#start_7">-suffix command-line
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switch</A> when you invoke LAMMPS, or you can
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use the <A HREF = "suffix.html">suffix</A> command in your input script.
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</P>
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<P>See <A HREF = "Section_accelerate.html">this section</A> of the manual for more
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instructions on how to use the accelerated styles effectively.
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</P>
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<HR>
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<P><B>Mixing, shift, table, tail correction, restart, rRESPA info</B>:
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</P>
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<P>For atom type pairs I,J and I != J, the two cutoff distances for this
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pair style can be mixed. The default mix value is <I>geometric</I>. See
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the "pair_modify" command for details.
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</P>
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<P>This pair style does not support the <A HREF = "pair_modify.html">pair_modify</A>
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shift option for the energy of the pair interaction.
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</P>
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<P>The <A HREF = "pair_modify.html">pair_modify</A> table option is not relevant
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for this pair style.
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</P>
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<P>This pair style does not support the <A HREF = "pair_modify.html">pair_modify</A>
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tail option for adding long-range tail corrections to energy and
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pressure.
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</P>
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<P>This pair style writes its information to <A HREF = "restart.html">binary restart
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files</A>, so pair_style and pair_coeff commands do not need
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to be specified in an input script that reads a restart file.
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</P>
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<P>This pair style can only be used via the <I>pair</I> keyword of the
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<A HREF = "run_style.html">run_style respa</A> command. It does not support the
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<I>inner</I>, <I>middle</I>, <I>outer</I> keywords.
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</P>
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<HR>
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<P><B>Restrictions:</B>
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</P>
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<P>These styles are part of the FLD package. They are only enabled if
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LAMMPS was built with that package. See the <A HREF = "Section_start.html#2_3">Making
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LAMMPS</A> section for more info.
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</P>
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<P>Only spherical monodisperse particles are allowed for pair_style
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lubricate.
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</P>
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<P>Only spherical particles are allowed for pair_style lubricate/poly.
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</P>
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<P>These pair styles will not restart exactly when using the
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<A HREF = "read_restart.html">read_restart</A> command, though they should provide
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statistically similar results. This is because the forces they
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compute depend on atom velocities. See the
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<A HREF = "read_restart.html">read_restart</A> command for more details.
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</P>
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<P><B>Related commands:</B>
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</P>
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<P><A HREF = "pair_coeff.html">pair_coeff</A>, <A HREF = "pair_lubricateU.html">pair_style
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lubricateU</A>
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</P>
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<P><B>Default:</B>
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</P>
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<P>The default settings for the optional args are flagHI = 1 and flagVF =
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1.
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</P>
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<HR>
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<A NAME = "Ball"></A>
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<P><B>(Ball)</B> Ball and Melrose, Physica A, 247, 444-472 (1997).
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</P>
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<A NAME = "Kumar"></A>
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<P><B>(Kumar)</B> Kumar and Higdon, Phys Rev E, 82, 051401 (2010). See also
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his thesis for more details: A. Kumar, "Microscale Dynamics in
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Suspensions of Non-spherical Particles", Thesis, University of
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Illinois Urbana-Champaign,
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(2010). (<A HREF = "https://www.ideals.illinois.edu/handle/2142/16032">https://www.ideals.illinois.edu/handle/2142/16032</A>)
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</P>
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</HTML>
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