+Syntax: +
+pair_style style mu flaglog flagfld cutinner cutoff t_target seed ++
Examples: +
+pair_style brownian 1.5 1 1 2.01 2.5 2.0 5878567 (assuming radius=1) +pair_coeff 1 1 2.05 2.8 +pair_coeff * * ++
Description: +
+Styles brownian and brownain/poly compute Brownian forces and +torques on finite-size particles. The former requires monodisperse +spherical particles; the latter allows for polydisperse spherical +particles. +
+These pair styles are designed to be used with either the pair_style +lubricate or pair_style +lubricateU commands to provide thermostatting +when dissipative lubrication forces are acting. Thus the parameters +mu, flaglog, flagfld, cutinner, and cutoff should be +specified consistent with the settings in the lubrication pair styles. +For details, refer to either of the lubrication pair styles. +
+The t_target setting is used to specify the target temperature of +the system. The random number seed is used to generate random +numbers for the thermostatting procedure. +
+The following coefficients must be defined for each pair of atoms +types via the pair_coeff command as in the examples +above, or in the data file or restart files read by the +read_data or read_restart +commands, or by mixing as described below: +
+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. +
+Mixing, shift, table, tail correction, restart, rRESPA info: +
+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 geometric. See +the "pair_modify" command for details. +
+This pair style does not support the pair_modify +shift option for the energy of the pair interaction. +
+The pair_modify table option is not relevant +for this pair style. +
+This pair style does not support the pair_modify +tail option for adding long-range tail corrections to energy and +pressure. +
+This pair style writes its information to binary restart +files, so pair_style and pair_coeff commands do not need +to be specified in an input script that reads a restart file. +
+This pair style can only be used via the pair keyword of the +run_style respa command. It does not support the +inner, middle, outer keywords. +
+Restrictions: +
+These styles are part of the FLD package. They are only enabled if +LAMMPS was built with that package. See the Making +LAMMPS section for more info. +
+Only spherical monodisperse particles are allowed for pair_style +brownian. +
+Only spherical particles are allowed for pair_style brownian/poly. +
+Related commands: +
+pair_coeff, pair_style +lubricate, pair_style +lubricateU +
+Default: none +
+ diff --git a/doc/pair_brownian.txt b/doc/pair_brownian.txt new file mode 100644 index 0000000000..665118db7c --- /dev/null +++ b/doc/pair_brownian.txt @@ -0,0 +1,108 @@ +"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c + +:link(lws,http://lammps.sandia.gov) +:link(ld,Manual.html) +:link(lc,Section_commands.html#comm) + +:line + +pair_style brownian command :h3 +pair_style brownian/poly command :h3 + +[Syntax:] + +pair_style style mu flaglog flagfld cutinner cutoff t_target seed :pre + +style = {brownian} or {brownian/poly} +mu = dynamic viscosity (dynamic viscosity units) +flaglog = 0/1 log terms in the lubrication approximation on/off +flagfld = 0/1 to include/exclude Fast Lubrication Dynamics effects +cutinner = inner cutoff distance (distance units) +cutoff = outer cutoff for interactions (distance units) +t_target = target temp of the system (temperature units) +seed = seed for the random number generator (positive integer) :ul + +[Examples:] + +pair_style brownian 1.5 1 1 2.01 2.5 2.0 5878567 (assuming radius=1) +pair_coeff 1 1 2.05 2.8 +pair_coeff * * :pre + +[Description:] + +Styles {brownian} and {brownain/poly} compute Brownian forces and +torques on finite-size particles. The former requires monodisperse +spherical particles; the latter allows for polydisperse spherical +particles. + +These pair styles are designed to be used with either the "pair_style +lubricate"_pair_lubricate.html or "pair_style +lubricateU"_pair_lubricateU.html commands to provide thermostatting +when dissipative lubrication forces are acting. Thus the parameters +{mu}, {flaglog}, {flagfld}, {cutinner}, and {cutoff} should be +specified consistent with the settings in the lubrication pair styles. +For details, refer to either of the lubrication pair styles. + +The {t_target} setting is used to specify the target temperature of +the system. The random number {seed} is used to generate random +numbers for the thermostatting procedure. + +The following coefficients must be defined for each pair of atoms +types via the "pair_coeff"_pair_coeff.html command as in the examples +above, or in the data file or restart files read by the +"read_data"_read_data.html or "read_restart"_read_restart.html +commands, or by mixing as described below: + +cutinner (distance units) +cutoff (distance units) :ul + +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. + +:line + +[Mixing, shift, table, tail correction, restart, rRESPA info]: + +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 {geometric}. See +the "pair_modify" command for details. + +This pair style does not support the "pair_modify"_pair_modify.html +shift option for the energy of the pair interaction. + +The "pair_modify"_pair_modify.html table option is not relevant +for this pair style. + +This pair style does not support the "pair_modify"_pair_modify.html +tail option for adding long-range tail corrections to energy and +pressure. + +This pair style writes its information to "binary restart +files"_restart.html, so pair_style and pair_coeff commands do not need +to be specified in an input script that reads a restart file. + +This pair style can only be used via the {pair} keyword of the +"run_style respa"_run_style.html command. It does not support the +{inner}, {middle}, {outer} keywords. + +:line + +[Restrictions:] + +These styles are part of the FLD package. They are only enabled if +LAMMPS was built with that package. See the "Making +LAMMPS"_Section_start.html#2_3 section for more info. + +Only spherical monodisperse particles are allowed for pair_style +brownian. + +Only spherical particles are allowed for pair_style brownian/poly. + +[Related commands:] + +"pair_coeff"_pair_coeff.html, "pair_style +lubricate"_pair_lubricate.html, "pair_style +lubricateU"_pair_lubricateU.html + +[Default:] none diff --git a/doc/pair_lubricate.html b/doc/pair_lubricate.html new file mode 100644 index 0000000000..41d0ed3298 --- /dev/null +++ b/doc/pair_lubricate.html @@ -0,0 +1,178 @@ + +Syntax: +
+pair_style style mu flaglog flagfld cutinner cutoff ++
Examples: (all assume radius = 1) +
+pair_style lubricate 1.5 1 1 2.01 2.5 +pair_coeff 1 1 2.05 2.8 +pair_coeff * * ++
pair_style lubricate 1.5 1 1 2.01 2.5 +pair_coeff * * +variable mu equal ramp(1,2) +fix 1 all adapt 1 pair lubricate mu * * v_mu ++
Description: +
+Styles lubricate and lubricate/poly compute hydrodynamic +interactions between mono-disperse spherical particles in a pairwise +fashion. The interactions have 2 components. The first is +Ball-Melrose lubrication terms via the formulas in (Ball and +Melrose) +
+
+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 always included. 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 +include if flaglog is set to 1. Thy are the next strongest +interactions, and the only other singular interaction, and scale as +log(gap). The Atw (twist) term is currently not included. It is +typically a very small contribution to the lubrication forces. +
+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 (Higdon), which can be +represented by the following equation +
+
+where U represents the velocities and angular velocities of the +particles, U^infty represents the velocity and the angular velocity +of the undisturbed fluid, and E^infty represents the rate of strain +tensor of the undisturbed fluid with viscosity mu. Again, note that +this is dynamic viscosity which has units of mass/distance/time, not +kinematic viscosity. +
+IMPORTANT NOTE: When using the FLD terms, these pair styles are +designed to be used with explicit time integration and a +correspondingly small timestep. Thus either fix +nve/sphere or fix +nve/asphere should be used for time integration. +To perform implicit FLD, see the pair_style +lubricateU command. +
+Style lubricate requires monodisperse spherical particles; style +lubricate/poly allows for polydisperse spherical particles. +
+The viscosity mu can be varied in a time-dependent manner over the +course of a simluation, in which case in which case the pair_style +setting for mu will be overridden. See the fix adapt +command for details. +
+If the suspension is sheared via the fix deform +command then the pair style uses the shear rate to adjust the +hydrodynamic interactions accordingly. +
+Since lubrication forces are dissipative, it is usually desirable to +thermostat the system at a constant temperature. If Brownian motion +(at a constant temperature) is desired, it can be set using the +pair_style brownian command. These pair styles +and the brownian style should use consistent parameters for mu, +flaglog, flagfld, cutinner, and cutoff. +
+The following coefficients must be defined for each pair of atoms +types via the pair_coeff command as in the examples +above, or in the data file or restart files read by the +read_data or read_restart +commands, or by mixing as described below: +
+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. +
+Mixing, shift, table, tail correction, restart, rRESPA info: +
+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 geometric. See +the "pair_modify" command for details. +
+This pair style does not support the pair_modify +shift option for the energy of the pair interaction. +
+The pair_modify table option is not relevant +for this pair style. +
+This pair style does not support the pair_modify +tail option for adding long-range tail corrections to energy and +pressure. +
+This pair style writes its information to binary restart +files, so pair_style and pair_coeff commands do not need +to be specified in an input script that reads a restart file. +
+This pair style can only be used via the pair keyword of the +run_style respa command. It does not support the +inner, middle, outer keywords. +
+Restrictions: +
+These styles are part of the FLD package. They are only enabled if +LAMMPS was built with that package. See the Making +LAMMPS section for more info. +
+Only spherical monodisperse particles are allowed for pair_style +lubricate. +
+Only spherical particles are allowed for pair_style lubricate/poly. +
+Related commands: +
+pair_coeff, pair_style +lubricateU +
+Default: none +
+(Ball) Ball and Melrose, Physica A, 247, 444-472 (1997). +
+ + +(Higdon) Amit and Higdon, Phys Rev E (2010). +
+ diff --git a/doc/pair_lubricate.txt b/doc/pair_lubricate.txt new file mode 100644 index 0000000000..d22f459b96 --- /dev/null +++ b/doc/pair_lubricate.txt @@ -0,0 +1,170 @@ +"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c + +:link(lws,http://lammps.sandia.gov) +:link(ld,Manual.html) +:link(lc,Section_commands.html#comm) + +:line + +pair_style lubricate command :h3 +pair_style lubricate/poly command :h3 + +[Syntax:] + +pair_style style mu flaglog flagfld cutinner cutoff :pre + +style = {lubricate} or {lubricate/poly} +mu = dynamic viscosity (dynamic viscosity units) +flaglog = 0/1 log terms in the lubrication approximation off/on +flagfld = 0/1 to include/exclude Fast Lubrication Dynamics effects +cutinner = inner cutoff distance (distance units) +cutoff = outer cutoff for interactions (distance units) :ul + +[Examples:] (all assume radius = 1) + +pair_style lubricate 1.5 1 1 2.01 2.5 +pair_coeff 1 1 2.05 2.8 +pair_coeff * * :pre + +pair_style lubricate 1.5 1 1 2.01 2.5 +pair_coeff * * +variable mu equal ramp(1,2) +fix 1 all adapt 1 pair lubricate mu * * v_mu :pre + +[Description:] + +Styles {lubricate} and {lubricate/poly} compute hydrodynamic +interactions between mono-disperse spherical particles in a pairwise +fashion. The interactions have 2 components. The first is +Ball-Melrose lubrication terms via the formulas in "(Ball and +Melrose)"_#Ball + +:c,image(Eqs/pair_lubricate.jpg) + +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 always included. 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 +include if {flaglog} is set to 1. Thy are the next strongest +interactions, and the only other singular interaction, and scale as +log(gap). The Atw (twist) term is currently not included. It is +typically a very small contribution to the lubrication forces. + +{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 "(Higdon)"_#Higdon, which can be +represented by the following equation + +:c,image(Eqs/fld.jpg) + +where U represents the velocities and angular velocities of the +particles, U^{infty} represents the velocity and the angular velocity +of the undisturbed fluid, and E^{infty} represents the rate of strain +tensor of the undisturbed fluid with viscosity mu. Again, note that +this is dynamic viscosity which has units of mass/distance/time, not +kinematic viscosity. + +IMPORTANT NOTE: When using the FLD terms, these pair styles are +designed to be used with explicit time integration and a +correspondingly small timestep. Thus either "fix +nve/sphere"_fix_nve_sphere.html or "fix +nve/asphere"_fix_nve_asphere.html should be used for time integration. +To perform implicit FLD, see the "pair_style +lubricateU"_pair_lubricateU.html command. + +Style {lubricate} requires monodisperse spherical particles; style +{lubricate/poly} allows for polydisperse spherical particles. + +The viscosity mu can be varied in a time-dependent manner over the +course of a simluation, in which case in which case the pair_style +setting for mu will be overridden. See the "fix adapt"_fix_adapt.html +command for details. + +If the suspension is sheared via the "fix deform"_fix_deform.html +command then the pair style uses the shear rate to adjust the +hydrodynamic interactions accordingly. + +Since lubrication forces are dissipative, it is usually desirable to +thermostat the system at a constant temperature. If Brownian motion +(at a constant temperature) is desired, it can be set using the +"pair_style brownian"_pair_brownian.html command. These pair styles +and the {brownian} style should use consistent parameters for {mu}, +{flaglog}, {flagfld}, {cutinner}, and {cutoff}. + +:line + +The following coefficients must be defined for each pair of atoms +types via the "pair_coeff"_pair_coeff.html command as in the examples +above, or in the data file or restart files read by the +"read_data"_read_data.html or "read_restart"_read_restart.html +commands, or by mixing as described below: + +cutinner (distance units) +cutoff (distance units) :ul + +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. + +:line + +[Mixing, shift, table, tail correction, restart, rRESPA info]: + +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 {geometric}. See +the "pair_modify" command for details. + +This pair style does not support the "pair_modify"_pair_modify.html +shift option for the energy of the pair interaction. + +The "pair_modify"_pair_modify.html table option is not relevant +for this pair style. + +This pair style does not support the "pair_modify"_pair_modify.html +tail option for adding long-range tail corrections to energy and +pressure. + +This pair style writes its information to "binary restart +files"_restart.html, so pair_style and pair_coeff commands do not need +to be specified in an input script that reads a restart file. + +This pair style can only be used via the {pair} keyword of the +"run_style respa"_run_style.html command. It does not support the +{inner}, {middle}, {outer} keywords. + +:line + +[Restrictions:] + +These styles are part of the FLD package. They are only enabled if +LAMMPS was built with that package. See the "Making +LAMMPS"_Section_start.html#2_3 section for more info. + +Only spherical monodisperse particles are allowed for pair_style +lubricate. + +Only spherical particles are allowed for pair_style lubricate/poly. + +[Related commands:] + +"pair_coeff"_pair_coeff.html, "pair_style +lubricateU"_pair_lubricateU.html + +[Default:] none + +:line + +:link(Ball) +[(Ball)] Ball and Melrose, Physica A, 247, 444-472 (1997). + +:link(Higdon) +[(Higdon)] Amit and Higdon, Phys Rev E (2010). diff --git a/doc/pair_lubricateU.html b/doc/pair_lubricateU.html new file mode 100644 index 0000000000..f3e0763898 --- /dev/null +++ b/doc/pair_lubricateU.html @@ -0,0 +1,199 @@ + +Syntax: +
+pair_style style mu flaglog cutinner cutoff gdot ++
Examples: (all assume radius = 1) +
+pair_style lubricateU 1.5 1 2.01 2.5 0.01 +pair_coeff 1 1 2.05 2.8 +pair_coeff * * ++
Description: +
+Styles lubricateU and lubricateU/poly compute velocities and +angular velocities such that the hydrodynamic interaction balances the +force and torque due to all other types of interactions. +
+The interactions have 2 components. The first is +Ball-Melrose lubrication terms via the formulas in (Ball and +Melrose) +
+
+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 always included. 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 +include if flaglog is set to 1. Thy are the next strongest +interactions, and the only other singular interaction, and scale as +log(gap). The Atw (twist) term is currently not included. It is +typically a very small contribution to the lubrication forces. +
+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 (Higdon). The equation being +solved to balance the forces and torques is +
+
+where U represents the velocities and angular velocities of the +particles, Uinfty represents the velocities and the angular +velocities of the undisturbed fluid, and Einfty 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. +
+Frest 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. +
+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 fix +nve/noforce should be used for spherical +particles defined via atom_style sphere or fix +nve/asphere/noforce should be used for +spherical particles defined via atom_style +ellipsoid. 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. +
+Style lubricateU requires monodisperse spherical particles; style +lubricateU/poly allows for polydisperse spherical particles. +
+If the suspension is sheared via the fix deform +command then the pair style uses the shear rate to adjust the +hydrodynamic interactions accordingly. +
+Since lubrication forces are dissipative, it is usually desirable to +thermostat the system at a constant temperature. If Brownian motion +(at a constant temperature) is desired, it can be set using the +pair_style brownian command. These pair styles +and the brownian style should use consistent parameters for mu, +flaglog, flagfld = 1, cutinner, and cutoff. +
+The following coefficients must be defined for each pair of atoms +types via the pair_coeff command as in the examples +above, or in the data file or restart files read by the +read_data or read_restart +commands, or by mixing as described below: +
+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. +
+Mixing, shift, table, tail correction, restart, rRESPA info: +
+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 geometric. See +the "pair_modify" command for details. +
+This pair style does not support the pair_modify +shift option for the energy of the pair interaction. +
+The pair_modify table option is not relevant +for this pair style. +
+This pair style does not support the pair_modify +tail option for adding long-range tail corrections to energy and +pressure. +
+This pair style writes its information to binary restart +files, so pair_style and pair_coeff commands do not need +to be specified in an input script that reads a restart file. +
+This pair style can only be used via the pair keyword of the +run_style respa command. It does not support the +inner, middle, outer keywords. +
+Restrictions: +
+These styles are part of the FLD package. They are only enabled if +LAMMPS was built with that package. See the Making +LAMMPS section for more info. +
+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 fix wall/colloid command, which +has an "fld" option to apply its wall forces correctly. +
+Only spherical monodisperse particles are allowed for pair_style +lubricateU. +
+Only spherical particles are allowed for pair_style lubricateU/poly. +
+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 fix +deform with the same rate of shear (erate). +
+Related commands: +
+pair_coeff, pair_style +lubricate +
+Default: none +
+(Ball) Ball and Melrose, Physica A, 247, 444-472 (1997). +
+ + +(Higdon) Amit and Higdon, Phys Rev E (2010). +
+ diff --git a/doc/pair_lubricateU.txt b/doc/pair_lubricateU.txt new file mode 100644 index 0000000000..8f01aabd4e --- /dev/null +++ b/doc/pair_lubricateU.txt @@ -0,0 +1,191 @@ +"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c + +:link(lws,http://lammps.sandia.gov) +:link(ld,Manual.html) +:link(lc,Section_commands.html#comm) + +:line + +pair_style lubricateU command :h3 +pair_style lubricateU/poly command :h3 + +[Syntax:] + +pair_style style mu flaglog cutinner cutoff gdot :pre + +style = {lubricateU} or {lubricateU/poly} +mu = dynamic viscosity (dynamic viscosity units) +flaglog = 0/1 log terms in the lubrication approximation on/off +cutinner = inner cut off distance (distance units) +cutoff = outer cutoff for interactions (distance units) +gdot = shear rate (1/time units) :ul + +[Examples:] (all assume radius = 1) + +pair_style lubricateU 1.5 1 2.01 2.5 0.01 +pair_coeff 1 1 2.05 2.8 +pair_coeff * * :pre + +[Description:] + +Styles {lubricateU} and {lubricateU/poly} compute velocities and +angular velocities such that the hydrodynamic interaction balances the +force and torque due to all other types of interactions. + +The interactions have 2 components. The first is +Ball-Melrose lubrication terms via the formulas in "(Ball and +Melrose)"_#Ball + +:c,image(Eqs/pair_lubricate.jpg) + +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 always included. 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 +include if {flaglog} is set to 1. Thy are the next strongest +interactions, and the only other singular interaction, and scale as +log(gap). The Atw (twist) term is currently not included. It is +typically a very small contribution to the lubrication forces. + +{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 "(Higdon)"_#Higdon. The equation being +solved to balance the forces and torques is + +:c,image(Eqs/fld2.jpg) + +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. + +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. + +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 "fix +nve/noforce"_fix_nve_noforce.html should be used for spherical +particles defined via "atom_style sphere"_atom_style.html or "fix +nve/asphere/noforce"_fix_nve_asphere_noforce.html should be used for +spherical particles defined via "atom_style +ellipsoid"_atom_style.html. 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. + +Style {lubricateU} requires monodisperse spherical particles; style +{lubricateU/poly} allows for polydisperse spherical particles. + +If the suspension is sheared via the "fix deform"_fix_deform.html +command then the pair style uses the shear rate to adjust the +hydrodynamic interactions accordingly. + +Since lubrication forces are dissipative, it is usually desirable to +thermostat the system at a constant temperature. If Brownian motion +(at a constant temperature) is desired, it can be set using the +"pair_style brownian"_pair_brownian.html command. These pair styles +and the {brownian} style should use consistent parameters for {mu}, +{flaglog}, {flagfld = 1}, {cutinner}, and {cutoff}. + +:line + +The following coefficients must be defined for each pair of atoms +types via the "pair_coeff"_pair_coeff.html command as in the examples +above, or in the data file or restart files read by the +"read_data"_read_data.html or "read_restart"_read_restart.html +commands, or by mixing as described below: + +cutinner (distance units) +cutoff (distance units) :ul + +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. + +:line + +[Mixing, shift, table, tail correction, restart, rRESPA info]: + +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 {geometric}. See +the "pair_modify" command for details. + +This pair style does not support the "pair_modify"_pair_modify.html +shift option for the energy of the pair interaction. + +The "pair_modify"_pair_modify.html table option is not relevant +for this pair style. + +This pair style does not support the "pair_modify"_pair_modify.html +tail option for adding long-range tail corrections to energy and +pressure. + +This pair style writes its information to "binary restart +files"_restart.html, so pair_style and pair_coeff commands do not need +to be specified in an input script that reads a restart file. + +This pair style can only be used via the {pair} keyword of the +"run_style respa"_run_style.html command. It does not support the +{inner}, {middle}, {outer} keywords. + +:line + +[Restrictions:] + +These styles are part of the FLD package. They are only enabled if +LAMMPS was built with that package. See the "Making +LAMMPS"_Section_start.html#2_3 section for more info. + +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 "fix wall/colloid"_fix_wall.html command, which +has an "fld" option to apply its wall forces correctly. + +Only spherical monodisperse particles are allowed for pair_style +lubricateU. + +Only spherical particles are allowed for pair_style lubricateU/poly. + +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 "fix +deform"_fix_deform.html with the same rate of shear (erate). + +[Related commands:] + +"pair_coeff"_pair_coeff.html, "pair_style +lubricate"_pair_lubricate.html + +[Default:] none + +:line + +:link(Ball) +[(Ball)] Ball and Melrose, Physica A, 247, 444-472 (1997). + +:link(Higdon) +[(Higdon)] Amit and Higdon, Phys Rev E (2010).