Ball-Melrose lubrication terms via the formulas in :ref:`(Ball and Melrose) <Ball>`
.. image:: Eqs/pair_lubricate.jpg
:align: center
which represents the dissipation W between two nearby particles due to
their relative velocities in the presence of a background solvent with
viscosity *mu*. Note that this is dynamic viscosity which has units of
mass/distance/time, not kinematic viscosity.
The Asq (squeeze) term is the strongest and is included as long as
*flagHI* 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 *flaglog* is set to 1. They
are the next strongest interactions, and the only other singular
interaction, and scale as log(gap). Note that *flaglog* = 1 and
*flagHI* = 0 is invalid, and will result in a warning message, after
which *flagHI* will be set to 1. The Atw (twist) term is currently not
included. It is typically a very small contribution to the lubrication
forces.
The *flagHI* and *flagVF* settings are optional. Neither should be
used, or both must be defined.
*Cutinner* sets the minimum center-to-center separation that will be
used in calculations irrespective of the actual separation. *Cutoff*
is the maximum center-to-center separation at which an interaction is
computed. Using a *cutoff* less than 3 radii is recommended if
*flaglog* is set to 1.
The other component is due to the Fast Lubrication Dynamics (FLD)
approximation, described in :ref:`(Kumar) <Kumar>`. The equation being
solved to balance the forces and torques is
.. image:: Eqs/fld2.jpg
:align: center
where U represents the velocities and angular velocities of the
particles, U^*infty* represents the velocities and the angular
velocities of the undisturbed fluid, and E^*infty* represents the rate
of strain tensor of the undisturbed fluid flow with viscosity
*mu*. 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 *flagVF* is set to 1 (default).
F*rest* 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.
.. 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 :doc:`fix nve/noforce <fix_nve_noforce>` should
be used for spherical particles defined via :doc:`atom_style sphere <atom_style>` or :doc:`fix nve/asphere/noforce <fix_nve_asphere_noforce>` should be used for
spherical particles defined via :doc:`atom_style ellipsoid <atom_style>`. This is because the velocity and angular
momentum of each particle is set by the pair style, and should not be
