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create cell model

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James McClure
2023-01-16 07:19:20 -05:00
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81
docs/source/userGuide/models/GaussLaw/GaussLaw.rst → docs/source/userGuide/models/cell/cell.rst
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=============================================
Cell model
=============================================
LBPM includes a whole-cell simulator based on a coupled solution of the Nernst-Planck equations with Gauss's law.
*********************
Nernst-Planck model
*********************
The Nernst-Planck model is designed to model ion transport based on the
Nernst-Planck equation.
.. math::
:nowrap:
$$
\frac{\partial C_k}{\partial t} + \nabla \cdot \mathbf{j}_k = 0
$$
where
.. math::
:nowrap:
$$
\mathbf{j}_k = C_k \mathbf{u} - D_k \Big( \nabla C_k + \frac{z_k C_k}{V_T} \nabla \psi\Big)
$$
A LBM solution is developed using a three-dimensional, seven velocity (D3Q7) lattice structure for each species. Each distribution is associated with a particular discrete velocity, such that the concentration is given by their sum,
.. math::
:nowrap:
$$
C_k = \sum_{q=0}^{6} f^k_q \;.
$$
Lattice Boltzmann equations (LBEs) are defined to determine the evolution of the distributions
.. math::
:nowrap:
$$
f^{k}_q (\mathbf{x}_n + \bm{\xi}_q \Delta t, t+ \Delta t)-
f^{k}_q (\mathbf{x}_n, t) = \frac{1}{\lambda_k}
\Big( f^{k}_q - f^{eq}_q \Big)\;,
$$
where the relaxation time :math:`\lambda_k` controls the bulk diffusion coefficient,
.. math::
:nowrap:
$$
D_k = c_s^2\Big( \lambda_k - \frac 12\Big)\;.
$$
The speed of sound for the D3Q7 lattice model is :math:`c_s^2 = \frac 14` and the weights are :math:`W_0 = 1/4` and :math:`W_1,\ldots, W_6 = 1/8`.
Equilibrium distributions are established from the fact that molecular velocity distribution follows a Gaussian distribution within the bulk fluids,
.. math::
:nowrap:
$$
f^{eq}_q = W_q C_k \Big[ 1 + \frac{\bm{\xi_q}\cdot \mathbf{u}^\prime}{c_s^2} \Big]\;.
$$
The velocity is given by
.. math::
:nowrap:
$$
\mathbf{u}^\prime = \mathbf{u} - \frac{z_k D_k}{V_T} \nabla \psi \;.
$$
*********************
Gauss's Law Model
=============================================
*********************
The LBPM Gauss's law solver is designed to solve for the electric field in an ionic fluid.

165
docs/source/userGuide/models/nernstPlanck/nerstPlanck.rst
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=============================================
Nernst-Planck model
=============================================
The Nernst-Planck model is designed to model ion transport based on the
Nernst-Planck equation.
.. math::
:nowrap:
$$
\frac{\partial C_k}{\partial t} + \nabla \cdot \mathbf{j}_k = 0
$$
where
.. math::
:nowrap:
$$
\mathbf{j}_k = C_k \mathbf{u} - D_k \Big( \nabla C_k + \frac{z_k C_k}{V_T} \nabla \psi\Big)
$$
A LBM solution is developed using a three-dimensional, seven velocity (D3Q7) lattice structure for each species. Each distribution is associated with a particular discrete velocity, such that the concentration is given by their sum,
.. math::
:nowrap:
$$
C_k = \sum_{q=0}^{6} f^k_q \;.
$$
Lattice Boltzmann equations (LBEs) are defined to determine the evolution of the distributions
.. math::
:nowrap:
$$
f^{k}_q (\mathbf{x}_n + \bm{\xi}_q \Delta t, t+ \Delta t)-
f^{k}_q (\mathbf{x}_n, t) = \frac{1}{\lambda_k}
\Big( f^{k}_q - f^{eq}_q \Big)\;,
$$
where the relaxation time :math:`\lambda_k` controls the bulk diffusion coefficient,
.. math::
:nowrap:
$$
D_k = c_s^2\Big( \lambda_k - \frac 12\Big)\;.
$$
The speed of sound for the D3Q7 lattice model is :math:`c_s^2 = \frac 14` and the weights are :math:`W_0 = 1/4` and :math:`W_1,\ldots, W_6 = 1/8`.
Equilibrium distributions are established from the fact that molecular velocity distribution follows a Gaussian distribution within the bulk fluids,
.. math::
:nowrap:
$$
f^{eq}_q = W_q C_k \Big[ 1 + \frac{\bm{\xi_q}\cdot \mathbf{u}^\prime}{c_s^2} \Big]\;.
$$
The velocity is given by
.. math::
:nowrap:
$$
\mathbf{u}^\prime = \mathbf{u} - \frac{z_k D_k}{V_T} \nabla \psi \;.
$$
****************************
Example Input File
****************************
.. code-block:: c
MultiphysController {
timestepMax = 25000
num_iter_Ion_List = 4
analysis_interval = 100
tolerance = 1.0e-9
visualization_interval = 1000 // Frequency to write visualization data
}
Stokes {
tau = 1.0
F = 0, 0, 0
ElectricField = 0, 0, 0 //body electric field; user-input unit: [V/m]
nu_phys = 0.889e-6 //fluid kinematic viscosity; user-input unit: [m^2/sec]
}
Ions {
MembraneIonConcentrationList = 150.0e-3, 10.0e-3, 15.0e-3, 155.0e-3 //user-input unit: [mol/m^3]
temperature = 293.15 //unit [K]
number_ion_species = 4 //number of ions
tauList = 1.0, 1.0, 1.0, 1.0
IonDiffusivityList = 1.0e-9, 1.0e-9, 1.0e-9, 1.0e-9 //user-input unit: [m^2/sec]
IonValenceList = 1, -1, 1, -1 //valence charge of ions; dimensionless; positive/negative integer
IonConcentrationList = 4.0e-3, 20.0e-3, 16.0e-3, 0.0e-3 //user-input unit: [mol/m^3]
BC_Solid = 0 //solid boundary condition; 0=non-flux BC; 1=surface ion concentration
//SolidLabels = 0 //solid labels for assigning solid boundary condition; ONLY for BC_Solid=1
//SolidValues = 1.0e-5 // user-input surface ion concentration unit: [mol/m^2]; ONLY for BC_Solid=1
FluidVelDummy = 0.0, 0.0, 0.0 // dummy fluid velocity for debugging
BC_InletList = 0, 0, 0, 0
BC_OutletList = 0, 0, 0, 0
}
Poisson {
lattice_scheme = "D3Q19"
epsilonR = 78.5 //fluid dielectric constant [dimensionless]
BC_Inlet = 0 // ->1: fixed electric potential; ->2: sine/cosine periodic electric potential
BC_Outlet = 0 // ->1: fixed electric potential; ->2: sine/cosine periodic electric potential
//--------------------------------------------------------------------------
//--------------------------------------------------------------------------
BC_Solid = 2 //solid boundary condition; 1=surface potential; 2=surface charge density
SolidLabels = 0 //solid labels for assigning solid boundary condition
SolidValues = 0 //if surface potential, unit=[V]; if surface charge density, unit=[C/m^2]
WriteLog = true //write convergence log for LB-Poisson solver
// ------------------------------- Testing Utilities ----------------------------------------
// ONLY for code debugging; the followings test sine/cosine voltage BCs; disabled by default
TestPeriodic = false
TestPeriodicTime = 1.0 //unit:[sec]
TestPeriodicTimeConv = 0.01 //unit:[sec]
TestPeriodicSaveInterval = 0.2 //unit:[sec]
//------------------------------ advanced setting ------------------------------------
timestepMax = 4000 //max timestep for obtaining steady-state electrical potential
analysis_interval = 25 //timestep checking steady-state convergence
tolerance = 1.0e-10 //stopping criterion for steady-state solution
InitialValueLabels = 1, 2
InitialValues = 0.0, 0.0
}
Domain {
Filename = "Bacterium.swc"
nproc = 2, 1, 1 // Number of processors (Npx,Npy,Npz)
n = 64, 64, 64 // Size of local domain (Nx,Ny,Nz)
N = 128, 64, 64 // size of the input image
voxel_length = 0.01 //resolution; user-input unit: [um]
BC = 0 // Boundary condition type
ReadType = "swc"
ReadValues = 0, 1, 2
WriteValues = 0, 1, 2
}
Analysis {
analysis_interval = 100
subphase_analysis_interval = 50 // Frequency to perform analysis
restart_interval = 5000 // Frequency to write restart data
restart_file = "Restart" // Filename to use for restart file (will append rank)
N_threads = 4 // Number of threads to use
load_balance = "independent" // Load balance method to use: "none", "default", "independent"
}
Visualization {
save_electric_potential = true
save_concentration = true
save_velocity = false
}
Membrane {
MembraneLabels = 2
VoltageThreshold = 0.0, 0.0, 0.0, 0.0
MassFractionIn = 1e-1, 1.0, 5e-3, 0.0
MassFractionOut = 1e-1, 1.0, 5e-3, 0.0
ThresholdMassFractionIn = 1e-1, 1.0, 5e-3, 0.0
ThresholdMassFractionOut = 1e-1, 1.0, 5e-3, 0.0
}