DOC: distributionModels: improve header file documentation

src/lagrangian/distributionModels/RosinRammler/RosinRammler.H

@@ -28,13 +28,107 @@ Class
     Foam::distributionModels::RosinRammler
 
 Description
-    Rosin-Rammler distributionModel
+    Particle-size distribution model wherein random samples are drawn
+    from the doubly-truncated two-parameter Rosin-Rammler (Weibull)
+    probability density function:
 
-   \f[
+    \f[
-       CDF(x) =
+        f(x; \lambda, n, A, B) =
-            (1 - exp(-(x/d)^n + (d_0/d)^n)
+            \frac{
-           /(1 - exp(-(d_1/d)^n + (d_0/d)^n)
+                \frac{n}{\lambda}
-   \f]
+                \left( \frac{x}{\lambda} \right)^{n-1}
+                \exp\{ -(\frac{x}{\lambda})^n \}
+            }{
+                \exp\{- (\frac{A}{\lambda})^n \}
+              - \exp\{- (\frac{B}{\lambda})^n \}
+            }
+    \f]
+    where
+
+    \vartable
+        f(x; \lambda, n, A, B) | Rosin-Rammler probability density function
+        \lambda   | Scale parameter
+        n         | Shape parameter
+        x         | Sample
+        A         | Minimum of the distribution
+        B         | Maximum of the distribution
+    \endvartable
+
+    Constraints:
+    - \f$ \infty > B > A > 0\f$
+    - \f$ x \in [B,A] \f$
+    - \f$ \lambda > 0 \f$
+    - \f$ n > 0 \f$
+
+    Random samples are generated by the inverse transform sampling technique
+    by using the quantile function of the doubly-truncated two-parameter
+    Rosin-Rammler (Weibull) probability density function:
+
+    \f[
+        x = \lambda \left( q_{min} - \ln (1 - u r) \right)^{1/n}
+    \f]
+    with
+
+    \f[
+        r = 1 - \exp(-q_{max} + q_{min})
+    \f]
+
+    \f[
+        q_{min} = \left(\frac{A}{\lambda}\right)^n
+    \f]
+
+    \f[
+        q_{max} = \left(\frac{B}{\lambda}\right)^n
+    \f]
+    where \f$ u \f$ is sample drawn from the uniform probability
+    density function on the unit interval \f$ (0, 1) \f$.
+
+    Reference:
+    \verbatim
+    Doubly-truncated two-parameter Weibull distribution and its moments (tag:C):
+        Crénin, F. (2015).
+        Truncated Weibull Distribution Functions and Moments.
+        SSRN 2690255.
+        DOI:10.2139/ssrn.2690255
+    \endverbatim
+
+Usage
+    Minimal example by using \c constant/\<CloudProperties\>:
+    \verbatim
+    subModels
+    {
+        injectionModels
+        {
+            <name>
+            {
+                ...
+
+                sizeDistribution
+                {
+                    type        RosinRammler;
+                    RosinRammlerDistribution
+                    {
+                        lambda      <scaleParameterValue>;
+                        n           <shapeParameterValue>;
+                        minValue    <minValue>;
+                        maxValue    <maxValue>;
+                    }
+                }
+            }
+        }
+    }
+    \endverbatim
+
+    where the entries mean:
+    \table
+      Property     | Description                       | Type | Reqd | Deflt
+      type         | Type name: RosinRammler           | word | yes  | -
+      RosinRammlerDistribution | Distribution settings | dict | yes  | -
+      lambda       | Scale parameter                   | scalar | yes  | -
+      n            | Shape parameter                   | scalar | yes  | -
+      minValue     | Minimum of the distribution       | scalar | yes  | -
+      maxValue     | Maximum of the distribution       | scalar | yes  | -
+    \endtable
 
 SourceFiles
     RosinRammler.C

src/lagrangian/distributionModels/binned/binned.H

@@ -27,8 +27,57 @@ Class
     Foam::distributionModels::binned
 
 Description
-    A binned distribution model where the random sample is taken from a
+    Particle-size distribution model wherein random samples are
-    discrete set of bins
+    drawn from a given discrete set of (\c bin, \c probability) pairs,
+    where in terms of its meaning, \c bins correspond to particle sizes
+    and \c probabilities correspond to (relative) probability of occurrences.
+
+    The second column (i.e. \c probability) are normalised by the sum of all
+    its values, resulting in a normalised column in the domain of [0,1].
+    To generate a sample, first a sample drawn from the uniform probability
+    density function on the unit interval (i.e. \c u), and then, the \c bin
+    corresponding to the first \c probability larger than \c u is fetched
+    as the particle size to be further processed.
+
+Usage
+    Minimal example by using \c constant/\<CloudProperties\>:
+    \verbatim
+    subModels
+    {
+        injectionModels
+        {
+            <name>
+            {
+                ...
+
+                sizeDistribution
+                {
+                    type        binned;
+                    binnedDistribution
+                    {
+                        distribution
+                        (
+                            (<bin1>    <probability1>)
+                            (<bin2>    <probability2>)
+                            ...
+                            (<binN>    <probabilityN>)
+                        );
+                    }
+                }
+            }
+        }
+    }
+    \endverbatim
+
+    where the entries mean:
+    \table
+      Property     | Description                       | Type | Reqd | Deflt
+      type         | Type name: binned                 | word | yes  | -
+      binnedDistribution | Distribution settings       | dict | yes  | -
+      distribution | \<bin\>-\<probability\> pairs     | dict | yes  | -
+      \<bin\>      | Particle size                     | scalar | yes | -
+      \<probability\> | Probability of occurrence      | scalar | yes | -
+    \endtable
 
 SourceFiles
     binned.C

src/lagrangian/distributionModels/distributionModel/distributionModel.H

@@ -24,15 +24,21 @@ License
     You should have received a copy of the GNU General Public License
     along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
 
+Namespace
+    Foam::distributionModels
+
+Description
+    A namespace for various probability distribution model implementations.
+
 Class
     Foam::distributionModel
 
 Description
-    A library of runtime-selectable distribution models.
+    A library of runtime-selectable doubly-truncated probability distribution
+    models. Returns random samples based on given distribution parameters.
 
-    Returns a sampled value given the expectation (nu) and variance (sigma^2)
+    Available distribution models include:
-
+    - binned
-    Current distribution models include:
     - exponential
     - fixedValue
     - general
@@ -42,11 +48,6 @@ Description
     - Mass-based Rosin-Rammler
     - uniform
 
-    The distributionModel is tabulated in equidistant nPoints, in an interval.
-    These values are integrated to obtain the cumulated distribution model,
-    which is then used to change the distribution from unifrom to
-    the actual distributionModel.
-
 SourceFiles
     distributionModel.C
     distributionModelNew.C

src/lagrangian/distributionModels/exponential/exponential.H

@@ -28,7 +28,87 @@ Class
     Foam::distributionModels::exponential
 
 Description
-    exponential distribution model
+    Particle-size distribution model wherein random samples are drawn
+    from the doubly-truncated exponential probability density function:
+
+    \f[
+        f(x; \lambda, A, B) =
+            \lambda \frac{\exp(-\lambda (x - A))}{1 - \exp(-\lambda(B-A))}
+    \f]
+    where
+
+    \vartable
+        f(x; \lambda, A, B) | Exponential probability density function
+        \lambda   | Rate parameter
+        x         | Sample
+        A         | Minimum of the distribution
+        B         | Maximum of the distribution
+    \endvartable
+
+    Constraints:
+    - \f$ \infty > B > A > 0 \f$
+    - \f$ x \in [B,A] \f$
+    - \f$ \lambda > 0 \f$
+
+    Random samples are generated by the inverse transform sampling technique
+    by using the quantile function of the doubly-truncated exponential
+    probability density function:
+
+    \f[
+        x = - \frac{1}{\lambda} \ln (r)
+    \f]
+
+    with
+
+    \f[
+        r = q_{min} + u (q_{max} - q_{min})
+    \f]
+
+    \f[
+        q_{min} = \exp(-\lambda A)
+    \f]
+
+    \f[
+        q_{max} = \exp(-\lambda B)
+    \f]
+    where \f$ u \f$ is a sample drawn from the uniform probability
+    density function on the unit interval \f$ (0, 1) \f$.
+
+Usage
+    Minimal example by using \c constant/\<CloudProperties\>:
+    \verbatim
+    subModels
+    {
+        injectionModels
+        {
+            <name>
+            {
+                ...
+
+                sizeDistribution
+                {
+                    type        exponential;
+                    exponentialDistribution
+                    {
+                        lambda      <lambdaValue>;
+                        minValue    <minValue>;
+                        maxValue    <maxValue>;
+                    }
+                }
+            }
+        }
+    }
+    \endverbatim
+
+    where the entries mean:
+    \table
+      Property     | Description                       | Type | Reqd | Deflt
+      type         | Type name: exponential            | word | yes  | -
+      exponentialDistribution | Distribution settings  | dict | yes  | -
+      lambda       | Rate parameter                    | scalar | yes  | -
+      minValue     | Minimum of the distribution       | scalar | yes  | -
+      maxValue     | Maximum of the distribution       | scalar | yes  | -
+    \endtable
 
 SourceFiles
     exponential.C

src/lagrangian/distributionModels/fixedValue/fixedValue.H

@@ -6,6 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
+    Copyright (C) 2021 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -27,7 +28,39 @@ Class
     Foam::distributionModels::fixedValue
 
 Description
-    Returns a fixed value
+    Particle-size distribution model wherein samples are given fixed values.
+
+Usage
+    Minimal example by using \c constant/\<CloudProperties\>:
+    \verbatim
+    subModels
+    {
+        injectionModels
+        {
+            <name>
+            {
+                ...
+
+                sizeDistribution
+                {
+                    type        fixedValue;
+                    fixedValueDistribution
+                    {
+                        value   <value>;
+                    }
+                }
+            }
+        }
+    }
+    \endverbatim
+
+    where the entries mean:
+    \table
+      Property     | Description                       | Type | Reqd | Deflt
+      type         | Type name: fixedValue             | word | yes  | -
+      fixedValueDistribution | Distribution settings   | dict | yes  | -
+      value        | Fixed value for size              | scalar | yes | -
+    \endtable
 
 SourceFiles
     fixedValue.C

src/lagrangian/distributionModels/general/general.H

@@ -28,7 +28,66 @@ Class
     Foam::distributionModels::general
 
 Description
-    general distribution model
+    Particle-size distribution model wherein random samples are
+    drawn from a given arbitrary probability density function
+    or cumulative distribution function. Input distributions are
+    specified as pairs of (size, probability) (i.e. (point, value) ).
+
+Usage
+    Minimal example by using \c constant/\<CloudProperties\>:
+    \verbatim
+    subModels
+    {
+        injectionModels
+        {
+            <name>
+            {
+                ...
+
+                sizeDistribution
+                {
+                    type        general;
+                    generalDistribution
+                    {
+                        cumulative      false;
+
+                        distribution
+                        (
+                            (<size1>    <probability1>)
+                            (<size2>    <probability2>)
+                            ...
+                            (<sizeN>    <probabilityN>)
+                        );
+                    }
+                }
+            }
+        }
+    }
+    \endverbatim
+
+    where the entries mean:
+    \table
+      Property     | Description                       | Type | Reqd | Deflt
+      type         | Type name: general                | word | yes  | -
+      generalDistribution | Distribution settings      | dict | yes  | -
+      distribution | \<size\>-\<probability\> pairs    | dict | yes  | -
+      \<size\>     | Particle size                     | scalar | yes | -
+      \<probability\> | Volume fraction/probability    | scalar | yes | -
+      cumulative   | Flag to determine if input distribution is specified <!--
+                   --> as cumulative or as density     | bool | no   | false
+    \endtable
+
+Note
+  - An example for a pair within \c distribution subdictionary
+  can be given as follows: "(1e-07 1.3)" means 1.3\% of particles
+  are modelled with a particle diameter of "1e-7" [m], and so on.
+  - Variation between input pairs is assumed to be linear.
+  - Elements in the second column (i.e. probability) are normalised.
+  - Elements in the second column for cumulative distribution
+  functions must start from zero and must be non-decreasing (i.e. monotonic).
+  - Elements in the first column (i.e. size) must be specified
+  in an ascending order.
+  - Input pairs cannot contain any negative element.
 
 SourceFiles
     general.C

src/lagrangian/distributionModels/massRosinRammler/massRosinRammler.H

@@ -25,27 +25,141 @@ License
     along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
 
 Class
-    Foam::massRosinRammler
+    Foam::distributionModels::massRosinRammler
 
 Description
-    Mass-based Rosin-Rammler distributionModel.
+    Particle-size distribution model wherein random samples are drawn
+    from the two-parameter Rosin-Rammler (Weibull) probability density
+    function corrected to take into account varying number of particles
+    per parcels for fixed-mass parcels.
 
-    Corrected form of the Rosin-Rammler distribution taking into account the
+    "There is a factor of \f$x^3\f$ difference between the size distribution
-    varying number of particels per parces for for fixed-mass parcels.  This
+    probability density function of individual particles and modeled parcels
-    distribution should be used when
+    of particles, \f$ f_{parcels}(D) = x^3 f_{particles}(D) \f$, because the
+    submodel parameter, \f$ PPP \f$ (number of particles per parcel) is based
+    on a fixed mass per parcel which weights the droplet distribution by
+    a factor proportional to \f$ 1/x^3 \f$ (i.e. \f$ PPP = \dot{m}_{total}
+    \Delta_{t_{inj(per-parcel)}} / {m}_{particle}  \f$)." (YHD:p. 1374-1375).
+
+    \c massRosinRammler should be preferred over \c RosinRammler
+    when \c parcelBasisType is based on \c mass:
     \verbatim
         parcelBasisType mass;
     \endverbatim
 
-    See equation 10 in reference:
+    The doubly-truncated mass-corrected
+    Rosin-Rammler probability density function:
+
+    \f[
+        f(x; \lambda, n, A, B) =
+                x^3
+                \frac{n}{\lambda}
+                \left( \frac{x}{\lambda} \right)^{n-1}
+                \frac{
+                    \exp\{ -(\frac{x}{\lambda})^n \}
+                }
+                {
+                    \exp\{ -(\frac{A}{\lambda})^n \}
+                  - \exp\{ -(\frac{B}{\lambda})^n \}
+                }
+    \f]
+    where
+
+    \vartable
+        f(x; \lambda, n, A, B) | Rosin-Rammler probability density function
+        \lambda   | Scale parameter
+        n         | Shape parameter
+        x         | Sample
+        A         | Minimum of the distribution
+        B         | Maximum of the distribution
+    \endvartable
+
+    Constraints:
+    - \f$ \lambda > 0 \f$
+    - \f$ n > 0 \f$
+
+    Random samples are generated by the inverse transform sampling technique
+    by using the quantile function of the doubly-truncated two-parameter
+    mass-corrected Rosin-Rammler (Weibull) probability density function:
+
+    \f[
+        d = \lambda \, Q(a, u)^{1/n}
+    \f]
+    with
+
+    \f[
+        a = \frac{3}{n} + 1
+    \f]
+    where \f$ Q(z_1, z_2) \f$ is the inverse of regularised lower incomplete
+    gamma function, and \f$ u \f$ is a sample drawn from the uniform
+    probability density function on the interval \f$ (x, y) \f$:
+
+    \f[
+        x = \gamma \left( a, \frac{A}{\lambda}^n \right)
+    \f]
+
+    \f[
+        y = \gamma \left( a, \frac{B}{\lambda}^n \right)
+    \f]
+    where \f$ \gamma(z_1, z_2) \f$ is the lower incomplete gamma function.
+
+    Reference:
     \verbatim
-        Yoon, S. S., Hewson, J. C., DesJardin, P. E., Glaze, D. J.,
+        Standard model (tag:YHD):
-        Black, A. R., & Skaggs, R. R. (2004).
+            Yoon, S. S., Hewson, J. C., DesJardin, P. E.,
-        Numerical modeling and experimental measurements of a high speed
+            Glaze, D. J., Black, A. R., & Skaggs, R. R. (2004).
-        solid-cone water spray for use in fire suppression applications.
+            Numerical modeling and experimental measurements of a high speed
-        International Journal of Multiphase Flow, 30(11), 1369-1388.
+            solid-cone water spray for use in fire suppression applications.
+            International Journal of Multiphase Flow, 30(11), 1369-1388.
+            DOI:10.1016/j.ijmultiphaseflow.2004.07.006
     \endverbatim
 
+Usage
+    Minimal example by using \c constant/\<CloudProperties\>:
+    \verbatim
+    subModels
+    {
+        injectionModels
+        {
+            <name>
+            {
+                ...
+                parcelBasisType  mass;
+                ...
+
+                sizeDistribution
+                {
+                    type        massRosinRammler;
+                    massRosinRammlerDistribution
+                    {
+                        lambda      <scaleParameterValue>;
+                        n           <shapeParameterValue>;
+                        minValue    <minValue>;
+                        maxValue    <maxValue>;
+                    }
+                }
+            }
+        }
+    }
+    \endverbatim
+
+    where the entries mean:
+    \table
+      Property     | Description                       | Type | Reqd | Deflt
+      type         | Type name: massRosinRammler       | word | yes  | -
+      massRosinRammlerDistribution | Distribution settings | dict | yes  | -
+      lambda       | Scale parameter                   | scalar | yes  | -
+      n            | Shape parameter                   | scalar | yes  | -
+      minValue     | Minimum of the distribution       | scalar | yes  | -
+      maxValue     | Maximum of the distribution       | scalar | yes  | -
+    \endtable
+
+Note
+  - In the current context, \c lambda (or \c d) is called "characteristic
+    droplet size", and \c n "empirical dimensionless constant to specify
+    the distribution width, sometimes referred to as the dispersion
+    coefficient." (YHD:p. 1374).
+
 SourceFiles
     massRosinRammler.C
 

src/lagrangian/distributionModels/multiNormal/multiNormal.H

@@ -28,12 +28,149 @@ Class
     Foam::distributionModels::multiNormal
 
 Description
-    A multiNormal distribution model
+    Particle-size distribution model wherein random samples are drawn
+    from a mixture of a finite set of doubly-truncated univariate normal
+    probability density functions:
 
+    \f[
+        g (\mathbf{x}; \mathbf{\mu}, \mathbf{\sigma}, A, B) =
+            \sum_i w_i f(x_i; \mu_i, \sigma_i, A, B)
+    \f]
+    with for any distribution:
+
+    \f[
+        f(x; \mu, \sigma, A, B) =
+            \frac{1}{\sigma}
+            \frac{
+                \phi \left( \frac{x - \mu}{\sigma} \right)
+            }{
+                \Phi \left( \frac{B - \mu}{\sigma} \right)
+              - \Phi \left( \frac{A - \mu}{\sigma} \right)
+            }
+    \f]
+    where
+
+    \vartable
+      f(x; \mu, \sigma, A, B) | Doubly-truncated univariate normal distribution
+      \mu         | Mean of the parent general normal distribution
+      \sigma      | Standard deviation of the parent general normal distribution
+      \phi(\cdot) | General normal probability density function
+      \Phi(\cdot) | General normal cumulative distribution function
+      x           | Sample
+      A           | Minimum of the distribution (the same for each distribution)
+      B           | Maximum of the distribution (the same for each distribution)
+      w_i         | Weighting factor
+    \endvartable
+
+    Constraints:
+    - \f$ \infty > B > A > 0 \f$
+    - \f$ x \in [B,A] \f$
+    - \f$ \sigma^2 > 0 \f$
+    - \f$ w_i >= 0 \f$
+
+    Random samples are generated by a combination of the inverse transform
+    sampling technique and categorical sampling in three steps:
+    - Draw a sample from the uniform probability density function
+    on the unit interval \f$u = (0, 1)\f$
+    - Find the interval among normalised cumulative weight intervals
+    wherein \f$ u \f$ resides
+    - Draw a sample from the distribution corresponding to the interval by
+    using the quantile function of the doubly-truncated univariate normal
+    probability density function by the following expressions (similar to
+    \c distributionModels::normal):
+
+    \f[
+        x = \mu + \sigma \sqrt{2} \, {erf}^{-1} \left( 2 p - 1 \right)
+    \f]
+    with
+
+    \f[
+        p = u \,
+            \left(
+                \Phi\left(
+                    \frac{B - \mu}{\sigma}
+                    \right)
+              - \Phi\left(
+                    \frac{A - \mu}{\sigma}
+                    \right)
+            \right)
+          + \Phi\left( \frac{A - \mu}{\sigma} \right)
+    \f]
+
+    \f[
+        \Phi(\xi) =
+            \frac{1}{2}
+            \left(
+                1 + {erf}\left(\frac{\xi - \mu}{\sigma \sqrt{2} }\right)
+            \right)
+    \f]
+    where \f$ u \f$ is another sample drawn from the uniform probability
+    density function on the unit interval \f$ (0, 1) \f$.
+
+Usage
+    Minimal example by using \c constant/\<CloudProperties\>:
     \verbatim
-        model = sum_i strength_i * exp(-0.5*((x - expectation_i)/variance_i)^2 )
+    subModels
+    {
+        injectionModels
+        {
+            <name>
+            {
+                ...
+
+                sizeDistribution
+                {
+                    type        multiNormal;
+                    multiNormalDistribution
+                    {
+                        minValue  <min>;
+                        maxValue  <max>;
+                        mu
+                        (
+                            <mean1>
+                            <mean2>
+                            ...
+                        );
+                        sigma
+                        (
+                            <standard deviation1>
+                            <standard deviation2>
+                            ...
+                        );
+                        weight
+                        (
+                            <weight1>
+                            <weight2>
+                            ...
+                        );
+                    }
+                }
+            }
+        }
+    }
     \endverbatim
 
+    where the entries mean:
+    \table
+      Property   | Description                       | Type | Reqd   | Deflt
+      type       | Type name: multiNormal            | word | yes    | -
+      multiNormalDistribution | Distribution settings  | dict | yes  | -
+      minValue   | Minimum of the distribution       | scalar | yes  | -
+      maxValue   | Maximum of the distribution       | scalar | yes  | -
+      mu         | List of means of parent general normal <!--
+                 --> distributions                | scalarList | yes | -
+      sigma      | List of standard deviations of parent  <!--
+                 --> general normal distributions | scalarList | yes | -
+      weight   | List of weights of a given distribution in <!--
+                 --> the distribution mixture     | scalarList | yes | -
+    \endtable
+
+Notes
+  - The sum of normal distributions (i.e. a mixture distribution) should not
+  be confused with the sum of normally-distributed random variables.
+  - \c minValue and \c maxValue are the same for all distributions
+  in the distribution mixture.
+  - \c weight should always be input in a non-decreasing (i.e. monotonic) order.
 
 SourceFiles
     multiNormal.C

src/lagrangian/distributionModels/normal/normal.H

@@ -28,13 +28,124 @@ Class
     Foam::distributionModels::normal
 
 Description
-    A normal distribution model
+    Particle-size distribution model wherein random samples are drawn
+    from the doubly-truncated univariate normal probability density function:
 
+    \f[
+        f(x; \mu, \sigma, A, B) =
+            \frac{1}{\sigma}
+            \frac{
+                \phi \left( \frac{x - \mu}{\sigma} \right)
+            }{
+                \Phi \left( \frac{B - \mu}{\sigma} \right)
+              - \Phi \left( \frac{A - \mu}{\sigma} \right)
+            }
+    \f]
+    where
+
+    \vartable
+      f(x; \mu, \sigma, A, B) | Doubly-truncated univariate normal distribution
+      \mu         | Mean of the parent general normal distribution
+      \sigma      | Standard deviation of the parent general normal distribution
+      \phi(\cdot) | General normal probability density function
+      \Phi(\cdot) | General normal cumulative distribution function
+      x           | Sample
+      A           | Minimum of the distribution
+      B           | Maximum of the distribution
+    \endvartable
+
+    Constraints:
+    - \f$ \infty > B > A > 0 \f$
+    - \f$ x \in [B,A] \f$
+    - \f$ \sigma^2 > 0 \f$
+
+    Random samples are generated by the inverse transform sampling technique
+    by using the quantile function of the doubly-truncated univariate normal
+    probability density function:
+
+    \f[
+        x = \mu + \sigma \sqrt{2} \, {erf}^{-1} \left( 2 p - 1 \right)
+    \f]
+    with
+
+    \f[
+        p = u \,
+            \left(
+                \Phi\left(
+                    \frac{B - \mu}{\sigma}
+                    \right)
+              - \Phi\left(
+                    \frac{A - \mu}{\sigma}
+                    \right)
+            \right)
+          + \Phi\left( \frac{A - \mu}{\sigma} \right)
+    \f]
+
+    \f[
+        \Phi(\xi) =
+            \frac{1}{2}
+            \left(
+                1 + {erf}\left(\frac{\xi - \mu}{\sigma \sqrt{2} }\right)
+            \right)
+    \f]
+    where \f$ u \f$ is sample drawn from the uniform probability
+    density function on the unit interval \f$ (0, 1) \f$.
+
+    Reference:
     \verbatim
-        model = strength * exp(-0.5*((x - expectation)/variance)^2 )
+        Governing expressions (tag:B):
+            Burkardt, J. (2014).
+            The truncated normal distribution.
+            Department of Scientific Computing Website,
+            Florida State University, 1-35.
+            URL:people.sc.fsu.edu/~jburkardt/presentations/truncated_normal.pdf
+            (Retrieved on: 19 Feb 2021)
     \endverbatim
 
-    strength only has meaning if there's more than one distribution model
+Usage
+    Minimal example by using \c constant/\<CloudProperties\>:
+    \verbatim
+    subModels
+    {
+        injectionModels
+        {
+            <name>
+            {
+                ...
+
+                sizeDistribution
+                {
+                    type        normal;
+                    normalDistribution
+                    {
+                        mu        <mean>;
+                        sigma     <stardard deviation>;
+                        minValue  <min>;
+                        maxValue  <max>;
+                    }
+                }
+            }
+        }
+    }
+    \endverbatim
+
+    where the entries mean:
+    \table
+      Property   | Description                       | Type | Reqd   | Deflt
+      type       | Type name: normal                 | word | yes    | -
+      normalDistribution | Distribution settings     | dict | yes    | -
+      mu         | Mean of the parent general normal distribution <!--
+                 -->                                 | scalar | yes  | -
+      sigma      | Standard deviation of the parent general normal <!--
+                 --> distribution                    | scalar | yes  | -
+      minValue   | Minimum of the distribution       | scalar | yes  | -
+      maxValue   | Maximum of the distribution       | scalar | yes  | -
+    \endtable
+
+Note
+  - The mean and standard deviation of the parent general normal probability
+  distribution function (i.e. input) are not the same with those of the
+  truncated probability distribution function.
 
 SourceFiles
     normal.C

src/lagrangian/distributionModels/uniform/uniform.H

@@ -28,7 +28,69 @@ Class
     Foam::distributionModels::uniform
 
 Description
-    Uniform/equally-weighted distribution model
+    Particle-size distribution model wherein random samples are drawn
+    from the doubly-truncated uniform probability density function:
+
+    \f[
+        f(x; A, B) = \frac{1}{B - A}
+    \f]
+    where
+
+    \vartable
+      f(x; A, B)  | Doubly-truncated uniform distribution
+      x           | Sample
+      A           | Minimum of the distribution
+      B           | Maximum of the distribution
+    \endvartable
+
+    Constraints:
+    - \f$ \infty > B > A > 0 \f$
+    - \f$ x \in [B,A] \f$
+    - \f$ \sigma^2 > 0 \f$
+
+    Random samples are generated by the inverse transform sampling technique
+    by using the quantile function of the uniform probability density function:
+
+    \f[
+        x = u \, (B - A) + A
+    \f]
+
+    where \f$ u \f$ is sample drawn from the uniform probability
+    density function on the unit interval \f$ (0, 1) \f$.
+
+Usage
+    Minimal example by using \c constant/\<CloudProperties\>:
+    \verbatim
+    subModels
+    {
+        injectionModels
+        {
+            <name>
+            {
+                ...
+
+                sizeDistribution
+                {
+                    type        uniform;
+                    uniformDistribution
+                    {
+                        minValue  <min>;
+                        maxValue  <max>;
+                    }
+                }
+            }
+        }
+    }
+    \endverbatim
+
+    where the entries mean:
+    \table
+      Property   | Description                       | Type | Reqd   | Deflt
+      type       | Type name: uniform                | word | yes    | -
+      uniformDistribution | Distribution settings    | dict | yes    | -
+      minValue   | Minimum of the distribution       | scalar | yes  | -
+      maxValue   | Maximum of the distribution       | scalar | yes  | -
+    \endtable
 
 SourceFiles
     uniform.C