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<div class="section" id="gran-cohesion-easo-capillary-viscous-model">
<span id="index-0"></span><h1>gran cohesion easo/capillary/viscous model<a class="headerlink" href="#gran-cohesion-easo-capillary-viscous-model" title="Permalink to this headline">¶</a></h1>
<div class="section" id="syntax">
<h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
<div class="highlight-python"><div class="highlight"><pre>cohesion easo/capillary/viscous
</pre></div>
</div>
<ul class="simple">
<li>zero or more keyword/value pairs may be appended to the end (after all models are specified)</li>
</ul>
<pre class="literal-block">
<em>tangential_reduce</em> values = 'on' or 'off'
on = tangential model does not see normal force computed by this model
off = tangential model does see normal force computed by this model
</pre>
</div>
<div class="section" id="description">
<h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
<p>This model can be used as part of <a class="reference internal" href="pair_gran.html"><em>pair gran</em></a>
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, <em>maxSeparationDistanceRatio</em>, to apply a cut-off
to the liquid bridge force, i.e. <em>radius***maxSeparationDistanceRatio</em> is
the effective contact radius of the particles. The model follows a composition
of models suggested by <a class="reference internal" href="#easo"><span>(Easo)</span></a></p>
<hr class="docutils" />
<p>Bridge formation and break-up, surface liquid transfer:</p>
<p><em>Vbond</em>, the volume of surface liquid involved in the bridge, is given by</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">Vbond</span> <span class="o">=</span> <span class="mf">0.05</span><span class="o">*</span><span class="p">(</span><span class="n">surfaceLiquidVolI</span><span class="o">+</span><span class="n">surfaceLiquidVolJ</span><span class="p">)</span>
</pre></div>
</div>
<p>where <em>surfaceLiquidVolI/J</em> is the surface liquid volume attached to particle i/j.
This model assumes that bridge formation occurs upon contact and
the rupture distance is given as follows by <a class="reference internal" href="gran_cohesion_washino_capillary_viscous.html#lian"><span>(Lian)</span></a> :</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">dist0</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">contactAngleEff</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span><span class="o">*</span><span class="n">Vbond</span><span class="o">^</span><span class="p">(</span><span class="mi">1</span><span class="o">/</span><span class="mi">3</span><span class="p">)</span>
</pre></div>
</div>
<p>When the bridge breaks, it is assumed that the surface liquid volume
distributes evenly to the two particles.</p>
<hr class="docutils" />
<p>Capilary force:</p>
<p>The capilary force is given by <a class="reference internal" href="#soulie"><span>(Soulie)</span></a> as:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">Fcapilary</span> <span class="o">=</span> <span class="o">-</span> <span class="n">pi</span><span class="o">*</span><span class="n">surfaceTension</span><span class="o">*</span><span class="n">sqrt</span><span class="p">(</span><span class="n">radi</span><span class="o">*</span><span class="n">radj</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="n">exp</span><span class="p">(</span><span class="n">A</span><span class="o">*</span><span class="n">dist</span><span class="o">/</span><span class="n">R2</span><span class="o">+</span><span class="n">B</span><span class="p">)</span><span class="o">+</span><span class="n">C</span><span class="p">)</span>
</pre></div>
</div>
<p>where</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">volBondScaled</span> <span class="o">=</span> <span class="n">volBond</span><span class="o">/</span><span class="n">R2</span><span class="o">^</span><span class="mi">3</span>
<span class="n">A</span> <span class="o">=</span> <span class="o">-</span><span class="mf">1.1</span><span class="o">*</span><span class="n">volBondScaled</span><span class="o">^</span><span class="p">(</span><span class="o">-</span><span class="mf">0.53</span><span class="p">)</span>
<span class="n">B</span> <span class="o">=</span> <span class="p">(</span><span class="o">-</span><span class="mf">0.148</span><span class="o">*</span><span class="n">log</span><span class="p">(</span><span class="n">volBondScaled</span><span class="p">)</span><span class="o">-</span><span class="mf">0.96</span><span class="p">)</span><span class="o">*</span><span class="n">contactAngleEff</span><span class="o">*</span><span class="n">contactAngleEff</span> <span class="o">-</span> <span class="mf">0.0082</span><span class="o">*</span><span class="n">log</span><span class="p">(</span><span class="n">volBondScaled</span><span class="p">)</span> <span class="o">+</span> <span class="mf">0.48</span>
<span class="n">C</span> <span class="o">=</span> <span class="mf">0.0018</span><span class="o">*</span><span class="n">log</span><span class="p">(</span><span class="n">volBondScaled</span><span class="p">)</span><span class="o">+</span><span class="mf">0.078</span><span class="p">;</span>
<span class="n">contactAngleEff</span> <span class="o">=</span> <span class="mf">0.5</span><span class="o">*</span><span class="p">(</span><span class="n">contactAngleI</span><span class="o">+</span><span class="n">contactAngleJ</span><span class="p">)</span>
</pre></div>
</div>
<p><em>dist</em> is the distance between the particles’ surfaces, <em>surfaceTension</em> is the surface tension
of the fluid, <em>contactAngleI/J</em> are the contact angles for particle i/j and the fluid. <em>R2</em> is the
radius of the larger of the two particles in contact.</p>
<hr class="docutils" />
<p>Viscous force:</p>
<p>the normal and tangential parts of the viscous force are calculated as given by <a class="reference internal" href="gran_cohesion_washino_capillary_viscous.html#nase"><span>(Nase)</span></a> :</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">rEff</span> <span class="o">=</span> <span class="n">radi</span><span class="o">*</span><span class="n">radj</span><span class="o">/</span><span class="p">(</span><span class="n">radi</span><span class="o">+</span><span class="n">radj</span><span class="p">)</span>
<span class="n">stokesPreFactor</span> <span class="o">=</span> <span class="mi">6</span><span class="o">*</span><span class="n">pi</span><span class="o">*</span><span class="n">fluidViscosity</span><span class="o">*</span><span class="n">rEff</span>
<span class="n">FviscN</span> <span class="o">=</span> <span class="n">stokesPreFactor</span><span class="o">*</span><span class="n">vn</span><span class="o">*</span><span class="n">rEff</span><span class="o">/</span><span class="n">dist</span>
<span class="n">FviscT</span> <span class="o">=</span> <span class="n">stokesPreFactor</span><span class="o">*</span><span class="n">vt</span><span class="o">*</span><span class="p">(</span><span class="mi">8</span><span class="o">/</span><span class="mi">15</span><span class="o">*</span><span class="n">log</span><span class="p">(</span><span class="n">rEff</span><span class="o">/</span><span class="n">dist</span><span class="p">)</span><span class="o">+</span><span class="mf">0.9588</span><span class="p">)</span>
</pre></div>
</div>
<p>where <em>vn</em> and <em>vt</em> are the normal and tangential relative velocities of the
particles at the contact point, <em>fluidViscosity</em> is the viscosity of the fluid
and <em>ri</em> and <em>rj</em> are the particle radii. An additional parameter,
<em>minSeparationDistanceRatio</em>, is used to prevent the value of the viscous force from
becoming too large, i.e. <em>radius***minSeparationDistanceRatio</em> is assumed to be
the minimum separation distance.</p>
<hr class="docutils" />
<p>Computation of liquid transport and effect of liquid content on other particle properties:</p>
<p>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.</p>
<p>The user can override the default behavior by explicity specifing a fix that solves
for the surface liquid transport between particles. Such fixes are
<code class="xref doc docutils literal"><span class="pre">fix</span> <span class="pre">liquidtransport/porous</span></code> or
<code class="xref doc docutils literal"><span class="pre">fix</span> <span class="pre">liquidtransport/sponge</span></code></p>
<hr class="docutils" />
<p>Initialization:</p>
<div class="highlight-python"><div class="highlight"><pre>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)
</pre></div>
</div>
<p>The optional keyword <em>tangential_reduce</em> defines if the tangential force model should
“see” the additional normal force excerted by this model. If it is ‘off’ (which is default)
then the tangential force model will be able to transmit a larger amount of tangential force
If <em>tangential_reduce</em> = ‘on’ then the tangential model will not take the normal force
from this model into account, typically leading to a lower value of tangential force
(via the Coulomb friction limit)</p>
<p><strong>Output:</strong></p>
<p>This gran model stores a couple of per-particle properties, for access
by various <span class="xref std std-ref">output commands</span>.</p>
<p>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 <a class="reference internal" href="set.html"><em>set</em></a> command.</p>
<p>Currently, there is a restriction that these properties can only be accessed
after a <a class="reference internal" href="run.html"><em>run 0</em></a> command.</p>
</div>
<div class="section" id="restrictions">
<h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
<p>This model can ONLY be used as part of <a class="reference internal" href="pair_gran.html"><em>pair gran</em></a>, not as part
of a <a class="reference internal" href="fix_wall_gran.html"><em>fix wall/gran</em></a>.</p>
<p>The cohesion model is not available for <a class="reference internal" href="atom_style.html"><em>atom_style</em></a> superquadric</p>
<p><strong>References:</strong></p>
<p id="easo"><strong>(Easo)</strong> Easo, Wassgreen, Comparison of Liquid Bridge Volume Models in DEM Simulations, AIChE Annual Conference (2013).</p>
<p id="lian"><strong>(Lian)</strong> Lian, Thornton, Adams, Journal of Colloid and Interface Science, p134, 161 (1993).</p>
<p id="nase"><strong>(Nase)</strong> S. T. Nase, W. L. Vargas, A. A. Abatan, and J. J. Mc-carthy, Powder Technol 116, 214 (2001).</p>
<p id="shi"><strong>(Shi)</strong> Shi, McCarthy, PowderTechnology, p64, 184 (2008)</p>
<p id="soulie"><strong>(Soulie)</strong> Soulie, Cherblanc, Youssoufi, Saix, Intl. J Numerical and Analytical Methods in Geomechanics, p213, 30 (2006)</p>
<p><strong>Coarse-graining information:</strong></p>
<p>Using <code class="xref doc docutils literal"><span class="pre">coarsegraining</span></code> in
combination with this command might lead to
different dynamics or system state and thus to
inconsistancies.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last"><code class="xref doc docutils literal"><span class="pre">Coarsegraining</span></code> may or
may not be available in LIGGGHTS(R)-PUBLIC.</p>
</div>
</div>
<div class="section" id="default">
<h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
<p><em>tangential_reduce</em> = ‘off’</p>
</div>
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