API¶

Particle Models¶

FluidizedBedND¶

class aldsim.core.particle.fluidizedbed.FluidizedBedND(Da=None)[source]¶

Bases: object

Model for batch fluidized bed reactor under plug flow approximations.

Implementation of a non-dimensional model for particle coating by atomic layer deposition. It assumes a well mixed approximation for particle mixing and plug flow approximation for precursor transport.

The model assumes a first-order irreversible Langmuir kinetics with the sticking probability value contained in the Damkohler number.

The normalized time in the model refers to the normalized dose time during the precursor exposure step.

Parameters¶

Dafloat: Damkohler number, a dimensionless parameter representing the ratio of reaction rate to transport rate. Higher values indicate faster surface reactions relative to mass transport. Must be non-negative.

Attributes¶

Dafloat: The Damkohler number for the system.

Examples¶

Create a FluidizedBedND model with a Damkohler number of 2.0:

>>> model = FluidizedBedND(Da=2.0)
>>> coverage = model.calc_coverage(t=1.0)
>>> print(f"Coverage: {coverage:.3f}")
Coverage: 0.797

Calculate saturation curve over normalized dose time:

>>> t, coverage = model.saturation_curve(tmax=3.0, dt=0.1)
>>> max_coverage = coverage[-1]
>>> print(f"Maximum coverage: {max_coverage:.3f}")
Maximum coverage: 0.950

Notes¶

The Damkohler number (Da) is defined as:

Da = k * τ

where k is the first-order reaction rate constant and τ is the characteristic time scale for precursor dosing.

calc_coverage(t=1, Da=None)[source]¶

Calculate the surface coverage at a given normalized dose time

Computes the fractional surface coverage θ of particles by precursor molecules in the batch fluidized bed reactor at a specified normalized dose time. The calculation uses analytical solutions for the well-mixed particle model with plug flow precursor transport and first-order Langmuir kinetics.

Parameters¶

tfloat, optional: Normalized dose time (dimensionless), defined as the ratio of actual dose time to the characteristic dosing time. Default is 1.0 (dose duration equals the characteristic time). Must be non-negative.
Dafloat, optional: Damkohler number. If provided, updates the model’s Da attribute and uses this value for the calculation. If None (default), uses the current model’s Da value.

Returns¶

float: Surface coverage θ (dimensionless), bounded between 0 and 1. A value of 0 indicates no coverage, while 1 indicates complete monolayer saturation.

Examples¶

Calculate coverage at the end of dosing (t=1):

>>> model = FluidizedBedND(Da=2.0)
>>> coverage = model.calc_coverage(t=1.0)
>>> print(f"Coverage: {coverage:.3f}")
Coverage: 0.797

Override the Damkohler number for a specific calculation:

>>> coverage = model.calc_coverage(t=1.0, Da=5.0)
>>> print(f"Coverage with Da=5: {coverage:.3f}")
Coverage with Da=5: 0.959

model_kwd = ['dose', 'nondim']¶

run(tmax=5, dt=0.01)[source]¶

Run complete simulation including coverage and precursor utilization

Executes the fluidized bed model simulation over a range of normalized dose times, computing both surface coverage and precursor utilization at each time step. This method provides comprehensive results for analyzing both coating efficiency and precursor usage in a batch reactor with well-mixed particles and plug flow precursor transport.

Parameters¶

tmaxfloat, optional: Maximum normalized dose time for the simulation. Default is 5.0. Should be greater than 0. Larger values allow observation of near-saturation behavior.
dtfloat, optional: Time step size for the simulation (dimensionless). Default is 0.01. Smaller values provide higher resolution but increase computation time. Must be positive and smaller than tmax.

Returns¶

tndarray: Array of normalized dose times, shape (n,), where n = tmax/dt. Values range from 0 to (tmax - dt).
coveragendarray: Array of surface coverage values θ at each time point, shape (n,). Each value is bounded between 0 and 1, representing fractional monolayer coverage.
precursorndarray: Array of precursor utilization factors at each time point, shape (n,). Each value is bounded between 0 and 1, representing the fraction of precursor that has reacted with particle surfaces. Values closer to 0 indicate less efficient precursor usage.

Examples¶

Run a basic simulation with default parameters:

>>> model = FluidizedBedND(Da=2.0)
>>> t, coverage, precursor = model.run()
>>> print(f"Final coverage: {coverage[-1]:.3f}")
Final coverage: 0.993

Notes¶

This method combines the functionality of calc_coverage() and precursor utilization calculations to provide a complete picture of the fluidized bed ALD process.

Parameters¶

tmaxfloat, optional: Maximum normalized dose time for the curve. Default is 5.0. Determines the extent of the curve. Larger values show near-saturation behavior but may be unnecessary if saturation is reached earlier.
dtfloat, optional: Time step size (dimensionless). Default is 0.01. Smaller values provide smoother curves but increase computation time. Must be positive and smaller than tmax.

Returns¶

tndarray: Array of normalized dose times, shape (n,), where n = tmax/dt. Values range from 0 to (tmax - dt).
coveragendarray: Array of surface coverage values θ at each time point, shape (n,). Each value is bounded between 0 and 1. The coverage increases monotonically, approaching saturation at large dose times.

Examples¶

Generate a saturation curve with default parameters:

>>> model = FluidizedBedND(Da=2.0)
>>> t, coverage = model.saturation_curve()
>>> print(f"Coverage at t=1: {coverage[100]:.3f}")  # dt=0.01, so index 100 is t=1
Coverage at t=1: 0.797

Create a high-resolution saturation curve:

>>> t, coverage = model.saturation_curve(tmax=3.0, dt=0.001)
>>> import matplotlib.pyplot as plt
>>> plt.plot(t, coverage)
>>> plt.xlabel('Normalized dose time')
>>> plt.ylabel('Surface coverage θ')
>>> plt.title(f'Fluidized Bed ALD Saturation Curve (Da={model.Da})')
>>> plt.grid(True)
>>> plt.show()

WellMixedParticleND¶

class aldsim.core.particle.rotatingdrum.WellMixedParticleND(Da=None)[source]¶

Bases: object

Model for batch particle coating under a well mixed reactor approximation.

Implementation of a non-dimensional model for particle coating by atomic layer deposition under a well mixed approximation for particle mixing and well stirred approximation for precursor transport. This model is applicable to rotating drum reactors and other systems where particles are thoroughly mixed and the gas phase is well stirred.

The model assumes a first-order irreversible Langmuir kinetics with the sticking probability value contained in the Damkohler number.

Parameters¶

Dafloat, optional: Damkohler number, a dimensionless parameter representing the ratio of reaction rate to transport rate. Higher values indicate faster surface reactions relative to mass transport. Must be non-negative. If None, must be specified in subsequent method calls.

Attributes¶

Dafloat: The Damkohler number for the system.

Examples¶

Create a WellMixedParticleND model with a Damkohler number of 2.0:

>>> model = WellMixedParticleND(Da=2.0)
>>> coverage = model.calc_coverage(t=1.0)
>>> print(f"Coverage: {coverage:.3f}")
Coverage: 0.757

Calculate saturation curve over normalized dose time:

>>> t, coverage = model.saturation_curve(tmax=3.0, dt=0.1)
>>> max_coverage = coverage[-1]
>>> print(f"Maximum coverage: {max_coverage:.3f}")
Maximum coverage: 0.950

calc_coverage(Da=None, t=1)[source]¶

Calculate the surface coverage at a given normalized dose time

Computes the fractional surface coverage θ of particles by precursor molecules in the well-mixed batch reactor at a specified normalized dose time. The calculation uses an implicit solution solved numerically via bounded Newton’s method, accounting for the coupling between surface coverage and precursor depletion in the batch system.

Parameters¶

Dafloat, optional: Damkohler number. If provided, updates the model’s Da attribute and uses this value for the calculation. If None (default), uses the current model’s Da value.
tfloat, optional: Normalized dose time (dimensionless), defined as the ratio of actual dose time to the characteristic reaction time. Default is 1.0. Must be non-negative.

Returns¶

float: Surface coverage θ (dimensionless), bounded between 0 and 1. A value of 0 indicates no coverage, while 1 indicates complete monolayer saturation.

Examples¶

Calculate coverage at unit dose time:

>>> model = WellMixedParticleND(Da=2.0)
>>> coverage = model.calc_coverage(t=1.0)
>>> print(f"Coverage: {coverage:.3f}")
Coverage: 0.757

Override the Damkohler number for a specific calculation:

>>> coverage = model.calc_coverage(Da=5.0, t=1.0)
>>> print(f"Coverage with Da=5: {coverage:.3f}")
Coverage with Da=5: 0.924

Parameters¶

tmaxfloat, optional: Maximum normalized dose time for the simulation. Default is 5.0. Should be greater than 0. Larger values allow observation of near-saturation behavior in batch operation.
dtfloat, optional: Time step size for output (dimensionless). Default is 0.01. Smaller values provide higher resolution but may increase computation time. Must be positive and smaller than tmax.

Returns¶

tndarray: Array of normalized dose times, shape (n,) where n ≈ tmax/dt. Values range from 0 to approximately tmax.
coveragendarray: Array of surface coverage values θ at each time point, shape (n,). Each value is bounded between 0 and 1, representing fractional monolayer coverage. Coverage increases with time.
precursorndarray: Array of precursor utilization fractions at each time point, shape (n,). Each value is bounded between 0 and 1, representing the fraction of precursor that has been consumed (reacted with particles).

Examples¶

Run a basic simulation with default parameters:

>>> model = WellMixedParticleND(Da=2.0)
>>> t, coverage, precursor = model.run()
>>> print(f"Final coverage: {coverage[-1]:.3f}")
Final coverage: 0.993

Run simulation with custom time range and resolution:

>>> t, coverage, precursor = model.run(tmax=3.0, dt=0.05)

Parameters¶

tmaxfloat, optional: Maximum normalized dose time for the curve. Default is 5.0. Determines the extent of the curve. Larger values show near-saturation behavior but may be unnecessary if saturation is reached earlier in batch operation.
dtfloat, optional: Time step size for output (dimensionless). Default is 0.01. Smaller values provide smoother curves but may increase computation time. Must be positive and smaller than tmax.

Returns¶

tndarray: Array of normalized dose times, shape (n,) where n ≈ tmax/dt. Values range from 0 to approximately tmax.
coveragendarray: Array of surface coverage values θ at each time point, shape (n,). Each value is bounded between 0 and 1. The coverage increases monotonically, approaching saturation as precursor is depleted in batch operation.

Examples¶

Generate a saturation curve with default parameters:

>>> model = WellMixedParticleND(Da=2.0)
>>> t, coverage = model.saturation_curve()
>>> print(f"Coverage at t=1: {coverage[100]:.3f}")  # dt=0.01, index ≈100
Coverage at t=1: 0.757

Create a high-resolution saturation curve:

>>> t, coverage = model.saturation_curve(tmax=3.0, dt=0.001)
>>> import matplotlib.pyplot as plt
>>> plt.plot(t, coverage)
>>> plt.xlabel('Normalized dose time')
>>> plt.ylabel('Surface coverage θ')
>>> plt.title(f'Batch ALD Saturation Curve (Da={model.Da})')
>>> plt.grid(True)
>>> plt.show()

SpatialPlugFlow¶

class aldsim.core.particle.spatialplugflow.SpatialPlugFlow(Da)[source]¶

Bases: object

Plug flow model for particle coating using spatial ALD

Implementation of a non-dimensional model for particle coating by atomic layer deposition for moving particles under stratified mixing (homogeneous mixing only on the plane perpendicular to the direction of movement). Precursor transport is modeled using the plug flow approximation, with both precursor and particles moving along the same direction.

The model assumes a first-order irreversible Langmuir kinetics with the sticking probability value contained in the Damkohler number.

The normalized time in the model refers to the normalized residence time of particles in the reactor.

Parameters¶

Dafloat: Damkohler number, a dimensionless parameter representing the ratio of reaction rate to transport rate. Higher values indicate faster surface reactions relative to mass transport. Must be non-negative.

Attributes¶

Dafloat: The Damkohler number for the system.

Examples¶

Create a SpatialPlugFlow model with a Damkohler number of 2.0:

>>> model = SpatialPlugFlow(Da=2.0)
>>> coverage = model.calc_coverage(t=1.0)
>>> print(f"Coverage: {coverage:.3f}")
Coverage: 0.667

Calculate saturation curve over normalized residence time:

>>> t, coverage = model.saturation_curve(tmax=3.0, dt=0.1)
>>> max_coverage = coverage[-1]
>>> print(f"Maximum coverage: {max_coverage:.3f}")
Maximum coverage: 0.950

calc_coverage(t=1, Da=None)[source]¶

Calculate the surface coverage at a given normalized residence time

Computes the fractional surface coverage θ of particles by precursor molecules in the plug flow reactor at a specified normalized residence time. The calculation uses analytical solutions for the plug flow model with first-order Langmuir kinetics.

Parameters¶

tfloat, optional: Normalized residence time (dimensionless), defined as the ratio of actual residence time to the characteristic reactor time. Default is 1.0 (particles exit at the reactor characteristic time). Must be non-negative.
Dafloat, optional: Damkohler number. If provided, updates the model’s Da attribute and uses this value for the calculation. If None (default), uses the current model’s Da value.

Returns¶

float: Surface coverage θ (dimensionless), bounded between 0 and 1. A value of 0 indicates no coverage, while 1 indicates complete monolayer saturation.

Examples¶

Calculate coverage at the reactor exit (t=1):

>>> model = SpatialPlugFlow(Da=2.0)
>>> coverage = model.calc_coverage(t=1.0)
>>> print(f"Coverage: {coverage:.3f}")
Coverage: 0.667

Override the Damkohler number for a specific calculation:

>>> coverage = model.calc_coverage(t=1.0, Da=5.0)
>>> print(f"Coverage with Da=5: {coverage:.3f}")
Coverage with Da=5: 0.833

calc_precursor(t, Da=None)[source]¶

Calculate the fraction of unused precursor exiting the reactor

Computes the fraction of precursor molecules that pass through the reactor without reacting with particle surfaces. This quantity is important for understanding precursor efficiency and optimizing process economics.

Parameters¶

tfloat: Normalized residence time (dimensionless), defined as the ratio of actual residence time to the characteristic reactor time. Must be non-negative.
Dafloat, optional: Damkohler number. If provided, updates the model’s Da attribute and uses this value for the calculation. If None (default), uses the current model’s Da value.

Returns¶

float: Fraction of unused precursor (dimensionless), bounded between 0 and 1. A value of 0 indicates complete precursor utilization (all precursor reacts), while 1 indicates no precursor consumption.

Examples¶

Calculate unused precursor at reactor exit:

>>> model = SpatialPlugFlow(Da=2.0)
>>> unused = model.calc_precursor(t=1.0)
>>> utilization = 1 - unused
>>> print(f"Precursor utilization: {utilization:.1%}")
Precursor utilization: 66.7%

Parameters¶

tmaxfloat, optional: Maximum normalized residence time for the simulation. Default is 5.0. Should be greater than 0. Larger values allow observation of near-saturation behavior.
dtfloat, optional: Time step size for the simulation (dimensionless). Default is 0.01. Smaller values provide higher resolution but increase computation time. Must be positive and smaller than tmax.

Returns¶

tndarray: Array of normalized residence times, shape (n,), where n = tmax/dt. Values range from 0 to (tmax - dt).
coveragendarray: Array of surface coverage values θ at each time point, shape (n,). Each value is bounded between 0 and 1, representing fractional monolayer coverage.
precursorndarray: Array of unused precursor fractions at each time point, shape (n,). Each value is bounded between 0 and 1, representing the fraction of precursor that exits the reactor without reacting.

Examples¶

Run a basic simulation with default parameters:

>>> model = SpatialPlugFlow(Da=2.0)
>>> t, coverage, precursor = model.run()
>>> print(f"Final coverage: {coverage[-1]:.3f}")
Final coverage: 0.993

Run simulation with custom time range and resolution:

>>> t, coverage, precursor = model.run(tmax=3.0, dt=0.05)
>>> import matplotlib.pyplot as plt
>>> plt.plot(t, coverage, label='Coverage')
>>> plt.plot(t, precursor, label='Unused precursor')
>>> plt.xlabel('Normalized residence time')
>>> plt.ylabel('Fraction')
>>> plt.legend()
>>> plt.show()

Notes¶

This method combines the functionality of calc_coverage() and calc_precursor() to provide a complete picture of the ALD process.

Parameters¶

tmaxfloat, optional: Maximum normalized residence time for the curve. Default is 5.0. Determines the extent of the curve. Larger values show near-saturation behavior but may be unnecessary if saturation is reached earlier.
dtfloat, optional: Time step size (dimensionless). Default is 0.01. Smaller values provide smoother curves but increase computation time. Must be positive and smaller than tmax.

Returns¶

tndarray: Array of normalized residence times, shape (n,), where n = tmax/dt. Values range from 0 to (tmax - dt).
coveragendarray: Array of surface coverage values θ at each time point, shape (n,). Each value is bounded between 0 and 1. The coverage increases monotonically, approaching saturation at large residence times.

Examples¶

Generate a saturation curve with default parameters:

>>> model = SpatialPlugFlow(Da=2.0)
>>> t, coverage = model.saturation_curve()
>>> print(f"Coverage at t=1: {coverage[100]:.3f}")  # dt=0.01, so index 100 is t=1
Coverage at t=1: 0.667

Create a high-resolution saturation curve:

>>> t, coverage = model.saturation_curve(tmax=3.0, dt=0.001)
>>> import matplotlib.pyplot as plt
>>> plt.plot(t, coverage)
>>> plt.xlabel('Normalized residence time')
>>> plt.ylabel('Surface coverage θ')
>>> plt.title(f'ALD Saturation Curve (Da={model.Da})')
>>> plt.grid(True)
>>> plt.show()

SpatialWellMixedND¶

class aldsim.core.particle.spatialwellmixed.SpatialWellMixedND(Da=None)[source]¶

Bases: WellMixedParticleND

Model for continuous particle coating under well stirred approximations.

Implementation of a non-dimensional model for particle coating by atomic layer deposition for moving particles under stratified mixing (homogeneous mixing only on the plane perpendicular to the direction of movement). Precursor transport is modeled using the well stirred approximation. This model is applicable to continuous flow systems where particles move through the reactor while the gas phase is well stirred.

The model assumes a first-order irreversible Langmuir kinetics with the sticking probability value contained in the Damkohler number.

The normalized time in the model refers to the normalized residence time of particles in the reactor.

This model is formally equivalent to a batch particle coating under the well stirred approximation (WellMixedParticleND) in which the normalized residence time is replaced by the normalized dose time. The mathematical formulation is identical, allowing SpatialWellMixed to inherit all methods from WellMixedParticleND.

Parameters¶

Dafloat, optional: Damkohler number, a dimensionless parameter representing the ratio of reaction rate to transport rate. Higher values indicate faster surface reactions relative to mass transport. Must be non-negative. If None, must be specified in subsequent method calls.

Attributes¶

Dafloat: The Damkohler number for the system.

Examples¶

Create a SpatialWellMixed model with a Damkohler number of 2.0:

>>> model = SpatialWellMixedND(Da=2.0)
>>> coverage = model.calc_coverage(t=1.0)
>>> print(f"Coverage: {coverage:.3f}")
Coverage: 0.757

Calculate saturation curve over normalized residence time:

>>> t, coverage = model.saturation_curve(tmax=3.0, dt=0.1)
>>> max_coverage = coverage[-1]
>>> print(f"Maximum coverage: {max_coverage:.3f}")
Maximum coverage: 0.950

ALD in high aspect ratio features¶

DiffusionViaND¶

class aldsim.core.diffusion.DiffusionViaND(AR, p_stick0, p_rec0=0, p_rec1=0)[source]¶

Bases: object

Model for ALD in high aspect ratio circular vias.

Implementation of a non-dimensional model for atomic layer deposition in high-aspect-ratio circular vias. The model uses a Knudsen diffusion transport model and self-limited surface reaction kinetics and surface recombination.

The model assumes a first-order irreversible Langmuir kinetics with the sticking probability value determining the reaction rate. It also supports recombination processes on both bare and reacted surface sites.

Parameters¶

ARfloat: Aspect ratio of the circular via (depth/diameter). Higher values indicate deeper, narrower structures where diffusion limitations become more significant. Must be non-negative.
p_stick0float: Sticking probability for the self-limited ALD process. Represents the probability that a precursor molecule will react when it encounters a surface site.
p_rec0float, optional: Recombination probability on bare (unreacted) surface sites. Default is 0.
p_rec1float, optional: Recombination probability on reacted surface sites. Default is 0.

Attributes¶

ARfloat: The aspect ratio of the via.
p_stick0float: The sticking probability of the ALD process.
p_rec0float: The recombination probability on bare sites.
p_rec1float: The recombination probability on reacted sites.
dzfloat: Size of the discretized elements, normalized to the via diameter. Computed as 1/nsegments.
nsegmentsint: Number of discretized elements per unit aspect ratio. Default is 4.

Examples¶

Create a DiffusionViaND model for a via with aspect ratio 10:

>>> model = DiffusionViaND(AR=10, p_stick0=0.05)
>>> times, coverage = model.run(max_time=2.0)
>>> print(f"Final mean coverage: {coverage[-1].mean():.3f}")

Model with recombination effects:

>>> model = DiffusionViaND(AR=20, p_stick0=0.03, p_rec0=0.01, p_rec1=0.05)
>>> times, coverage = model.run_until_cov(max_cov=0.95)
>>> print(f"Time to reach 95% coverage: {times[-1]:.3f}")

Notes¶

The model uses Knudsen diffusion to describe precursor transport inside the circular via. The governing equations are solved using a finite difference method with banded matrix solver for efficiency.

All time values in the model are normalized by a characteristic diffusion time scale.

property dz¶: size of the elements (normalized to the diameter) used to solve the transport equation

model_kwd = ['dose', 'nondim']¶

property nsegments¶: Number of discretized elements per unit aspect ratio

run(N=None, max_time=1, save_every=0.2, dt=0.05)[source]¶

Run simulation for a specified normalized time period

Executes the diffusion-reaction model for precursor transport and surface coverage evolution inside a high aspect ratio circular via. The simulation runs until the specified maximum normalized time is reached, saving coverage profiles at regular time intervals.

Parameters¶

Nint, optional: Number of discretized segments along the via depth. If None (default), automatically calculated as 4 * AR to ensure adequate spatial resolution. Higher values provide better accuracy but increase computation time.
max_timefloat, optional: Maximum normalized time for the simulation. Default is 1.0. Represents the duration of precursor exposure in normalized units. Must be positive.
save_everyfloat, optional: Normalized time interval at which coverage profiles are saved. Default is 0.2. Smaller values provide more time resolution but increase memory usage. Must be positive and less than max_time.
dtfloat, optional: Time step size for numerical integration (dimensionless). Default is 0.05. Smaller values improve accuracy but increase computation time. Must be positive and smaller than save_every.

Returns¶

timeslist of float: List of normalized times corresponding to saved coverage profiles. Length matches the coverage list.
coveragelist of ndarray: List of coverage arrays at saved time points. Each array has shape (N,) representing the coverage profile along the via depth, from the entrance (index 0) to the bottom (index N-1). Values are bounded between 0 and 1.

Examples¶

Run simulation with default parameters:

>>> model = DiffusionViaND(AR=10, p_stick0=0.05)
>>> times, coverage = model.run()
>>> print(f"Number of saved profiles: {len(coverage)}")
Number of saved profiles: 6

Run with custom time parameters and higher resolution:

>>> model = DiffusionViaND(AR=15, p_stick0=0.03)
>>> times, coverage = model.run(N=100, max_time=3.0, save_every=0.5)
>>> final_coverage = coverage[-1]
>>> print(f"Coverage at bottom: {final_coverage[-1]:.3f}")

Parameters¶

Nint, optional: Number of discretized segments along the via depth. If None (default), automatically calculated as 4 * AR to ensure adequate spatial resolution. Higher values provide better accuracy but increase computation time.
max_covfloat, optional: Target mean coverage at which the simulation stops. Default is 0.99. Represents the spatially-averaged fractional surface coverage. Must be between 0 and 1.
save_everyfloat, optional: Coverage interval at which profiles and times are saved. Default is 0.2. For example, with default value, profiles are saved when mean coverage reaches 0.2, 0.4, 0.6, 0.8, and the final target. Must be positive and less than max_cov.
dtfloat, optional: Time step size for numerical integration (dimensionless). Default is 0.05. Smaller values improve accuracy but increase computation time.

Returns¶

timeslist of float: List of normalized times corresponding to saved coverage profiles. Times increase monotonically. Length matches the coverage list.
coveragelist of ndarray: List of coverage arrays at saved coverage intervals. Each array has shape (N,) representing the coverage profile along the via depth, from the entrance (index 0) to the bottom (index N-1). Values are bounded between 0 and 1.

Examples¶

Run simulation until 90% mean coverage:

>>> model = DiffusionViaND(AR=10, p_stick0=0.5)
>>> times, coverage = model.run_until_cov(max_cov=0.9)
>>> print(f"Time to reach 90% coverage: {times[-1]:.3f}")
Time to reach 90% coverage: 2.345

Save coverage profiles every 10% increment:

>>> model = DiffusionViaND(AR=15, p_stick0=0.3, p_rec0=0.1)
>>> times, coverage = model.run_until_cov(max_cov=0.95, save_every=0.1)

API¶

Particle Models¶

FluidizedBedND¶

Parameters¶

Attributes¶

Examples¶

Notes¶

Parameters¶

Returns¶

Examples¶

Parameters¶

Returns¶

Examples¶

Notes¶

See Also¶

Parameters¶

Returns¶

Examples¶

See Also¶

WellMixedParticleND¶

Parameters¶

Attributes¶

Examples¶

Parameters¶

Returns¶

Examples¶

See Also¶

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Returns¶

Examples¶

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Parameters¶

Returns¶

Examples¶

See Also¶

SpatialPlugFlow¶

Parameters¶

Attributes¶

Examples¶

Parameters¶

Returns¶

Examples¶

Parameters¶

Returns¶

Examples¶

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Parameters¶

Returns¶

Examples¶

Notes¶

See Also¶

Parameters¶

Returns¶

Examples¶

See Also¶

SpatialWellMixedND¶

Parameters¶

Attributes¶

Examples¶

See Also¶

ALD in high aspect ratio features¶

DiffusionViaND¶

Parameters¶

Attributes¶

Examples¶

Notes¶

Parameters¶

Returns¶

Examples¶

See Also¶

Parameters¶

Returns¶

Examples¶

See Also¶