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### gran cohesion washino/capillary/viscous

Syntax:

    cohesion washino/capillary/viscous

Description:

This model can be used as part of pair gran It adds a liquid bridge force, caused by a surface liquid film on the particles, to a pair of particles, which consists of a capilary and a viscous part. Furthermore, it solves for the transfer of surface liquid from one particle to the other as the bridge breaks up. The model uses a parameter, maxSeparationDistanceRatio, to apply a cut-off to the liquid bridge force, i.e. radius*maxSeparationDistanceRatio is the effective contact radius of the particles.

The model parameter maxLiquidContent allows to limit the maximum per particle liquid content.

Bridge formation and break-up, surface liquid transfer:

Vbond, the volume of surface liquid involved in the bridge, is given by

    Vbond = 0.05*(surfaceLiquidVolI+surfaceLiquidVolJ)

where surfaceLiquidVolI/J is the surface liquid volume attached to particle i/j. This model assumes that both formation distance and rupture distance are given as follows by (Lian)

    dist0 = (1+contactAngleEff/2)*Vbond^(1/3)

When the bridge breaks, it is assumed that the surface liquid volume distributes evenly to the two particles.

Capilary force:

The capilary force is given by (Rabinovitch) as

    Fcapilary = 2*pi*rEff*surfaceTension* (cos(contactAngleEff) / (1. + dist/(2.*dSpSp)) + sin(alpha)*sin(alpha+contactAngleEff))

where

    prefactor = -1+sqrt(1+2*volBond/(pi*rEff*dist^2))
    dSpSp = 0.5*dist*prefactor
    alpha = sqrt(dist/rEff*prefactor)
    contactAngleEff = 0.5*(contactAngleI+contactAngleJ)

dist is the distance between the particles' surfaces, surfaceTension is the surface tension of the fluid, contactAngleI/J are the contact angles for particle i/j and the fluid.

Viscous force:

the normal and tangential parts of the viscous force are calculated as given by (Nase)

    rEff = radi*radj/(radi+radj)
    stokesPreFactor = 6*pi*fluidViscosity*rEff
    FviscN = stokesPreFactor*vn*rEff/dist
    FviscT = stokesPreFactor*vt*(8/15*log(rEff/dist)+0.9588)

where vn and vt are the normal and tangential relative velocities of the particles at the contact point, fluidViscosity is the viscosity of the fluid and ri and rj are the particle radii. An additional parameter, minSeparationDistanceRatio, is used to prevent the value of the viscous force from becoming too large, i.e. radius*minSeparationDistanceRatio is assumed to be the minimum separation distance.

Computation of liquid transport and effect of liquid content on other particle properties:

Per default, this model automatically instatiates a scalar transport equation that solved for the surface liquid content of each particles, expressed in volume % of solid volume (4/3 pi * radius ^3). The surface liquid volume is assumed to be small, i.e. it is assumed to have no effect on the particle mass, diameter and density.

The user can override the default behavior by explicity specifing a fix that solves for the surface liquid transport between particles. Such fixes are fix liquidtransport/porous or fix liquidtransport/sponge

Intialization:

    If you are using the this model model, you must define the following properties:
    fix id all property/global minSeparationDistanceRatio scalar value
        (value=value for the minimum separation distance, recommended as 1.01)
    fix id all property/global maxSeparationDistanceRatio scalar value
        (value=value for the maximum separation distance, recommended as 1.1)
    fix id all property/global surfaceLiquidContentInitial scalar value
        (value=value for the initial surface liquid volume in % of the solid volume)
    fix id all property/global surfaceTension scalar value
        (value=value for the surface tension of liquid (SI units N/m))
    fix id all property/global fluidViscosity scalar value
        (value=value for the fluidViscosity (SI units Pas))
    fix id all property/global contactAngle peratomtype value_1 value_2 ...
        (value_i=value for contact angle of atom type i and fluid)
    fix id all property/global maxLiquidContent peratomtype value_1 value_2 ...
        (value_i=value for contact angle of atom type i and fluid)

Output:

This gran model stores a couple of per-particle properties, for access by various output commands.

You can access the property surfaceLiquidContent by f_surfaceLiquidContent[0] (units % of solid particle volume), liquidFlux (units % of solid particle volume/time) by accessing f_liquidFlux[0] and liquidSource (units % of solid particle volume/time) by accessing f_liquidSource[0]. The latter can be used to manually set a surface liquid source via the set command.

Currently, there is a restriction that these properties can only be accessed after a run 0 command.

Restrictions:

This model can ONLY be used as part of pair gran, not as part of a fix wall/gran.

The cohesion model is not available for atom_style superquadric

References:

(Lian) Lian, Thornton, Adams, Journal of Colloid and Interface Science, p134, 161 (1993).

(Nase) S. T. Nase, W. L. Vargas, A. A. Abatan, and J. J. Mc-carthy, Powder Technol 116, 214 (2001).

(Rabinovitch) Rabinovitch, Esayanur, Moudil, Langmuir, p10992, 21 (2005)