2011-10-27 00:59:49 +08:00
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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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<HR>
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<H3>pair_style lubricateU command
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</H3>
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<H3>pair_style lubricateU/poly 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 cutinner cutoff gdot flagHI flagVF
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</PRE>
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<UL><LI>style = <I>lubricateU</I> or <I>lubricateU/poly</I>
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<LI>mu = dynamic viscosity (dynamic viscosity units)
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<LI>flaglog = 0/1 log terms in the lubrication approximation on/off
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<LI>cutinner = inner cut off distance (distance units)
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<LI>cutoff = outer cutoff for interactions (distance units)
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<LI>gdot = shear rate (1/time units)
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<LI>flagHI (optional) = 0/1 to include/exclude 1/r hydrodynamic interactions
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<LI>flagVF (optional) = 0/1 to include/exclude 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 lubricateU 1.5 1 2.01 2.5 0.01 1 1
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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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<P><B>Description:</B>
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</P>
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<P>Styles <I>lubricateU</I> and <I>lubricateU/poly</I> compute velocities and
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angular velocities such that the hydrodynamic interaction balances the
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force and torque due to all other types of interactions.
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</P>
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<P>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 as long as
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<I>flagHI</I> is set to 1 (default). It scales as 1/gap where gap is the
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separation between the surfaces of the 2 particles. The Ash (shear)
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and Apu (pump) terms are only included if <I>flaglog</I> is set to 1. They
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are the next strongest interactions, and the only other singular
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interaction, and scale as log(gap). Note that <I>flaglog</I> = 1 and
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<I>flagHI</I> = 0 is invalid, and will result in a warning message, after
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which <I>flagHI</I> will be set to 1. The Atw (twist) term is currently not
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included. It is typically a very small contribution to the lubrication
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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>. The equation being
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solved to balance the forces and torques is
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</P>
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<CENTER><IMG SRC = "Eqs/fld2.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 velocities and the angular
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velocities of the undisturbed fluid, and E^<I>infty</I> represents the rate
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of strain tensor of the undisturbed fluid flow with viscosity
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<I>mu</I>. Again, note that this is dynamic viscosity which has units of
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mass/distance/time, not kinematic viscosity. Volume fraction
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corrections to R_FU are included if <I>flagVF</I> is set to 1 (default).
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</P>
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<P>F<I>rest</I> represents the forces and torques due to all other types of
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interactions, e.g. Brownian, electrostatic etc. Note that this
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algorithm neglects the inertial terms, thereby removing the
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restriction of resolving the small interial time scale, which may not
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be of interest for colloidal particles. This pair style solves for
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the velocity such that the hydrodynamic force balances all other types
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of forces, thereby resulting in a net zero force (zero inertia limit).
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When defining this pair style, it must be defined last so that when
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this style is invoked all other types of forces have already been
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computed. For the same reason, it won't work if additional non-pair
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styles are defined (such as bond or Kspace forces) as they are
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calculated in LAMMPS after the pairwise interactions have been
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computed.
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</P>
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<P>IMPORTANT NOTE: When using these styles, the these pair styles are
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designed to be used with implicit time integration and a
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correspondingly larger timestep. Thus either <A HREF = "fix_nve_noforce.html">fix
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nve/noforce</A> should be used for spherical
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particles defined via <A HREF = "atom_style.html">atom_style sphere</A> or <A HREF = "fix_nve_asphere_noforce.html">fix
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nve/asphere/noforce</A> should be used for
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spherical particles defined via <A HREF = "atom_style.html">atom_style
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ellipsoid</A>. This is because the velocity and angular
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momentum of each particle is set by the pair style, and should not be
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reset by the time integration fix.
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</P>
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<P>Style <I>lubricateU</I> requires monodisperse spherical particles; style
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<I>lubricateU/poly</I> allows for polydisperse spherical particles.
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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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"wall/harmonic_fix_wall.html". 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. To use these wall styles with pair_style <I>lubricateU</I>
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or <I>lubricateU/poly</I>, the <I>fld yes</I> option must be specified in the
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fix wall command.
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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><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>Currently, these pair styles assume that all other types of
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forces/torques on the particles have been already been computed when
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it is invoked. This requires this style to be defined as the last of
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the pair styles, and that no fixes apply additional constraint forces.
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One exception is the <A HREF = "fix_wall.html">fix wall/colloid</A> commands, which
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has an "fld" option to apply their wall forces correctly.
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</P>
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<P>Only spherical monodisperse particles are allowed for pair_style
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lubricateU.
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</P>
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<P>Only spherical particles are allowed for pair_style lubricateU/poly.
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</P>
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<P>For sheared suspensions, it is assumed that the shearing is done in
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the xy plane, with x being the velocity direction and y being the
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velocity-gradient direction. In this case, one must use <A HREF = "fix_deform.html">fix
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deform</A> with the same rate of shear (erate).
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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_lubricate.html">pair_style
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lubricate</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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2011-10-27 00:59:49 +08:00
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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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2011-10-27 01:21:47 +08:00
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<A NAME = "Kumar"></A>
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2011-10-27 00:59:49 +08:00
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2011-10-27 01:21:47 +08:00
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<P><B>(Kumar)</B> Kumar and Higdon, Phys Rev E, 82, 051401 (2010).
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</P>
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</HTML>
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