ARF

Examples using this class are:

Acoustofluidics 2022: ARF Comparison

Frontiers: Air Bubble in Water

Frontiers: HFE Droplet in Water

Frontiers: PS Particle in Water

Yosioka and Kawasima (1955) Figure 2

Multicore ARF Computation

class osaft.solutions.yosioka1955.arf.ARF(f, R_0, rho_s, c_s, rho_f, c_f, p_0, wave_type, position=None, N_max=5, small_particle=False, bubble_solution=False)[source]

Bases: ScatteringField, BaseARF

ARF class for Yosioka & Kawasima (1955)

Parameters:

f (Union[Frequency, float, int]) – Frequency [Hz]
R_0 (Union[Sphere, float, int]) – Radius of the sphere [m]
rho_s (float) – Density of the fluid-like sphere [kg/m^3]
c_s (float) – Speed of sound of the particle [m/s]
rho_f (float) – Density of the fluid [kg/m^3]
c_f (float) – Speed of sound of the fluid [m/s]
p_0 (float) – Pressure amplitude of the field [Pa]
position (Optional[float], optional) – Position in the standing wave field [rad]
Default: None
wave_type (WaveType) – either standing or progressive wave
N_max (int, optional) –
Default: 5
small_particle (bool, optional) –
Default: False
bubble_solution (bool, optional) –
Default: False

Public Data Attributes:

`small_particle`	Small particle limit option.
`bubble_solution`	Bubble solution option.
`F`	Density-compressibility factor \(F\) [-]

Inherited from BaseYosioka

`supported_wavetypes`
`sigma`	ratio of speeds of sound [-].
`lambda_rho`	ratio of densities [-]
`x_f`	dimensionless wavenumber in the fluid [-]
`x_s`	dimensionless wavenumber in the particle
`position`	Wraps to `osaft.core.backgroundfields.BackgroundField.position`
`p_0`	Wraps to `osaft.core.backgroundfields.BackgroundField.p_0`
`wave_type`	Wraps to `osaft.core.backgroundfields.BackgroundField.wave_type`
`rho_s`	Wraps to `osaft.core.fluids.InviscidFluid.rho_f`
`c_s`	Wraps to `osaft.core.fluids.InviscidFluid.c_f`
`rho_f`	Wraps to `osaft.core.fluids.InviscidFluid.rho_f`
`c_f`	Wraps to `osaft.core.fluids.InviscidFluid.c_f`
`kappa_f`	Wraps to `osaft.core.fluids.InviscidFluid.kappa_f`
`k_f`	Wraps to `osaft.core.fluids.InviscidFluid.k_f`
`k_s`	Wraps to `osaft.core.fluids.InviscidFluid.k_f`
`I_ac`	Wraps to `osaft.core.backgroundfields.BackgroundField.I_ac`
`E_ac`	Wraps to `osaft.core.backgroundfields.BackgroundField.E_ac`

Inherited from BaseSphereFrequencyComposite

`R_0`	Wrapper for `osaft.core.geometries.Sphere.R_0`
`area`	Wrapper for `osaft.core.geometries.Sphere.area`
`volume`	Wrapper for `osaft.core.geometries.Sphere.volume`

Inherited from BaseFrequencyComposite

`f`	wrapper for `osaft.core.frequency.Frequency.f`
`omega`	wrapper for `osaft.core.frequency.Frequency.omega`

Inherited from BaseSolution

`supported_wavetypes`
`wave_type`	returns the wave type of the solution

Inherited from BaseScattering

`N_max`	Cutoff mode number for infinite sums
`field`
`omega`
`R_0`
`rho_f`
`k_f`

Public Methods:

`compute_arf`()	Acoustic radiation force [N]
`K_n`(n)	Coefficient \(K_n\) [m^2/s]
`M_n`(n)	Coefficient \(M_n\) [m^2/s]

Inherited from ScatteringField

`radial_particle_velocity`(r, theta, t[, mode])	Radial particle velocity [m/s]
`tangential_particle_velocity`(r, theta, t[, mode])	Tangential particle velocity [m/s]
`potential_coefficient`(n)	Wrapper to the fluid scattering coefficients for an inviscid fluid
`Phi_1`(r, theta, t[, mode])	Fluid velocity potential \(\Phi_1\) [m^2/s]
`Phi_i`(r, theta, t[, mode])	Fluid velocity potential of the incident field \(\Phi_i\) [m^2/s]
`Phi_s`(r, theta, t[, mode])	Fluid velocity potential of the scattered field \(\Phi_s\) [m^2/s]
`Phi_star`(r, theta, t[, mode])	Particle velocity potential \(\Phi^*\) [m^2/s]
`V_r_sc`(n, r)	Radial scattering field velocity term of mode n without Legendre coefficients
`V_theta_sc`(n, r)	Tangential scattering field velocity term of mode n without Legendre coefficients
`A_n`(n)	Coefficient \(A_n\) [m^2/s]
`B_n`(n)	Coefficient \(B_n\) [m^2/s]

Inherited from BaseYosioka

A_in(n)

Wraps to osaft.core.backgroundfields.BackgroundField.A_in

Inherited from BaseFrequencyComposite

input_variables()

Returns all properties that are settable.

Inherited from BaseSolution

`copy`()	Returns a copy of the object
`check_wave_type`()	Checks if `wave_type` is in `supported_wavetypes`

Inherited from BaseScattering

`radial_acoustic_fluid_velocity`(r, theta, t, ...)	Returns the value for the radial acoustic velocity in [m/s].
`tangential_acoustic_fluid_velocity`(r, theta, ...)	Returns the value for the tangential acoustic velocity in [m/s].
`pressure`(r, theta, t, scattered, incident[, ...])	Returns the acoustic pressure [Pa].
`potential_coefficient`(n)	Wrapper to the fluid scattering coefficients for an inviscid fluid
`velocity_potential`(r, theta, t, scattered, ...)	Returns the velocity potential of the fluid in [m^2/s].
`radial_particle_velocity`(r, theta, t[, mode])	Returns the value for the radial particle velocity in [m/s].
`tangential_particle_velocity`(r, theta, t[, mode])	Returns the value for the tangential particle velocity in [m/s].
`radial_particle_displacement`(r, theta, t[, mode])	Particle displacement in radial direction
`tangential_particle_displacement`(r, theta, t)	Particle displacement in tangential direction
`radial_mode_superposition`(radial_func, r, ...)	Returns either a single mode (`mode=int`) or a the sum until `N_max` (`mode=None`).
`tangential_mode_superposition`(...)	Returns either a single mode (`mode=int`) or a the sum until `N_max` (`mode=None`).
`V_r_i`(n, r)	Radial incident field velocity term of mode n without Legendre coefficients
`V_theta_i`(n, r)	Tangential incident field velocity term of mode n without Legendre coefficients
`V_r_sc`(n, r)	Radial scattering field velocity term of mode n without Legendre coefficients
`V_theta_sc`(n, r)	Tangential scattering field velocity term of mode n without Legendre coefficients
`V_r`(n, r, scattered, incident)	Superposition of `V_r_sc()` and `V_r_i()` depending on `scattered` and `incident`
`V_theta`(n, r, scattered, incident)	Superposition of `V_theta_sc()` and `V_theta_i()` depending on `scattered` and `incident`

Inherited from BaseARF

compute_arf()

Returns the value for the ARF in Newton [N].

A_in(n)

Wraps to osaft.core.backgroundfields.BackgroundField.A_in

Return type:: complex

A_n(n)

Coefficient \(A_n\) [m^2/s]

(Eq. 22)

Parameters:: n (int) – mode [-]
Return type:: complex

B_n(n)

Coefficient \(B_n\) [m^2/s]

(Eq. 23)

Parameters:: n (int) – mode [-]
Return type:: complex

K_n(n)[source]

Coefficient \(K_n\) [m^2/s]

(Eq. 43)

Parameters:: n (int) – mode [-]
Return type:: complex
Returns:: coefficient [m^2/s]

M_n(n)[source]

Coefficient \(M_n\) [m^2/s]

(Eq. 42)

Parameters:: n (int) – mode [-]
Return type:: complex
Returns:: coefficient [m^2/s]

Phi_1(r, theta, t, mode=None)

Fluid velocity potential \(\Phi_1\) [m^2/s]

(Eq. 17)

Parameters:

r (float) – radial coordinate [m]
theta (float) – tangential coordinate [rad]
t (float) – time [s]
mode (Optional[int], optional) – mode
Default: None

Return type:

complex

Phi_i(r, theta, t, mode=None)

Fluid velocity potential of the incident field \(\Phi_i\) [m^2/s]

(Eq. 16, 27)

Parameters:

r (float) – radial coordinate [m]
theta (float) – tangential coordinate [rad]
t (float) – time [s]
mode (Optional[int], optional) – mode
Default: None

Return type:

complex

Phi_s(r, theta, t, mode=None)

Fluid velocity potential of the scattered field \(\Phi_s\) [m^2/s]

(Eq. 18, 29)

Parameters:

r (float) – radial coordinate [m]
theta (float) – tangential coordinate [rad]
t (float) – time [s]
mode (Optional[int], optional) – mode
Default: None

Return type:

complex

Phi_star(r, theta, t, mode=None)

Particle velocity potential \(\Phi^*\) [m^2/s]

Parameters:

r (float) – radial coordinate [m]
theta (float) – tangential coordinate [rad]
t (float) – time [s]
mode (Optional[int], optional) – mode
Default: None

Return type:

complex

V_r(n, r, scattered, incident)

Superposition of V_r_sc() and V_r_i() depending on scattered and incident

At least one of the two must be True.

Parameters:

n (int) – mode
r (float) – radial coordinate [m]
scattered (bool) – add scattered field
incident (bool) – add incident

Return type:

complex

V_r_i(n, r)

Radial incident field velocity term of mode n without Legendre coefficients

Returns radial incident field velocity in [m/s]

Parameters:

n (int) – mode
r (Union[float, Sequence]) – radial coordinate [m]

Return type:

complex

V_r_sc(n, r)

Radial scattering field velocity term of mode n without Legendre coefficients

Returns radial scattering field velocity in [m/s]

Parameters:

n (int) – mode
r (Union[float, Sequence[float]]) – radial coordinate [m]

Return type:

Union[complex, Sequence[complex]]

V_theta(n, r, scattered, incident)

Superposition of V_theta_sc() and V_theta_i() depending on scattered and incident

At least one of the two must be True.

Parameters:

n (int) – mode
r (float) – radial coordinate [m]
scattered (bool) – add scattered field
incident (bool) – add incident

Return type:

complex

V_theta_i(n, r)

Tangential incident field velocity term of mode n without Legendre coefficients

Returns tangential incident field velocity in [m/s]

Parameters:

n (int) – mode
r (Union[float, Sequence]) – radial coordinate [m]

Return type:

complex

V_theta_sc(n, r)

Tangential scattering field velocity term of mode n without Legendre coefficients

Returns tangential scattering field velocity in [m/s]

Parameters:

n (int) – mode
r (Union[float, Sequence[float]]) – radial coordinate [m]

Return type:

Union[complex, Sequence[complex]]

check_wave_type()

Checks if wave_type is in supported_wavetypes

Raises:: WrongWaveTypeError – If wave_type is not supported
Return type:: None

compute_arf()[source]

Acoustic radiation force [N]

Computes the ARF, based on the general solution (Eq. 44), or the approximation for either small particles (Eq. 59, 62) or small bubbles (Eq. 68, 73), if the respective options are selected.

Raises:

WrongWaveTypeError – if wrong wave_type
AssumptionWarning – if the used parameters might not be valid for the chosen limiting case

Return type:

float

copy()

Returns a copy of the object

Return type:: BaseSolution

classmethod input_variables()

Returns all properties that are settable.

Returns a list of the names of all properties that are settable, i.e. all properties that wrap a PassiveVariable.

Return type:: list[str]

potential_coefficient(n)

Wrapper to the fluid scattering coefficients for an inviscid fluid

This method must be implemented by every theory to have a common interface for other modules.

Parameters:: n (int) – mode
Return type:: complex

pressure(r, theta, t, scattered, incident, mode=None)

Returns the acoustic pressure [Pa].

Parameters:

r (Union[float, Sequence]) – radial coordinate [m]
theta (Union[float, Sequence]) – tangential coordinate [rad]
t (Union[float, Sequence]) – time [s]
scattered (bool) – add scattered field
incident (bool) – add incident
mode (Optional[int], optional) – specific mode number of interest; if None then all modes until N_max
Default: None

Return type:

complex

radial_acoustic_fluid_velocity(r, theta, t, scattered, incident, mode=None)

Returns the value for the radial acoustic velocity in [m/s].

This method must be implemented by every theory to have a common interface for other modules.

Parameters:

r (Union[float, Sequence]) – radial coordinate [m]
theta (Union[float, Sequence]) – tangential coordinate [rad]
t (Union[float, Sequence]) – time [s]
scattered (bool) – scattered field contribution
incident (bool) – incident field contribution
mode (Optional[int], optional) – specific mode number of interest; if None then all modes until N_max
Default: None

Return type:

Union[complex, ndarray]

radial_mode_superposition(radial_func, r, theta, t, mode=None)

Returns either a single mode (mode=int) or a the sum until N_max (mode=None).

If mode=int the formula is

\[e^{-i\omega t}\, f_{\text{mode}}(r) \,P_{\text{mode}}(\cos\theta)\]

If mode=None the formula is

\[e^{-i\omega t} \sum_{n=0}^{\text{N}_{\text{max}}} \,f_n(r) \,P_n(\cos\theta)\]

where \(f_\text{n}(r)\) is the radial_func(n, r) passed to the method.

Parameters:

radial_func (Callable[[int, float], complex]) – radial function dependent on r
r (Union[float, Sequence]) – radial coordinate [m]
theta (Union[float, Sequence]) – tangential coordinate [rad]
t (Union[float, Sequence]) – time [s]
mode (Optional[int], optional) – specific mode number of interest; if None then all modes until N_max
Default: None

Return type:

Union[complex, ndarray]

radial_particle_displacement(r, theta, t, mode=None)

Particle displacement in radial direction

Returns the value of the particle displacement in radial direction in [m]

Parameters:

r (Union[float, Sequence]) – radial coordinate [m]
theta (Union[float, Sequence]) – tangential coordinate [rad]
t (Union[float, Sequence]) – time [s]
mode (Optional[int], optional) – specific mode number of interest; if None that all modes until N_max
Default: None

Return type:

Union[complex, ndarray]

radial_particle_velocity(r, theta, t, mode=None)

Radial particle velocity [m/s]

Parameters:

r (Union[float, Sequence[float]]) – radial coordinate [m]
theta (Union[float, Sequence[float]]) – tangential coordinate [rad]
t (Union[float, Sequence[float]]) – time [s]
mode (Optional[int], optional) – mode
Default: None

Return type:

Union[float, Sequence[float]]

tangential_acoustic_fluid_velocity(r, theta, t, scattered, incident, mode=None)

Returns the value for the tangential acoustic velocity in [m/s].

This method must be implemented by every theory to have a common interface for other modules.

Parameters:

r (Union[float, Sequence]) – radial coordinate [m]
theta (Union[float, Sequence]) – tangential coordinate [rad]
t (Union[float, Sequence]) – time [s]
scattered (bool) – scattered field contribution
incident (bool) – incident field contribution
mode (Optional[int], optional) – specific mode number of interest; if None then all modes until N_max
Default: None

Return type:

Union[complex, ndarray]

tangential_mode_superposition(tangential_func, r, theta, t, mode)

Returns either a single mode (mode=int) or a the sum until N_max (mode=None).

If mode=int the formula is

\[e^{-i\omega t}\, f_\text{mode}(r) \,P^1_{\text{mode}}(\cos\theta)\]

If mode=None the formula is

\[e^{-i\omega t}\sum_{n=0}^{\text{N}_{\text{max}}} \,f_n(r) \,P^1_n(\cos\theta)\]

where \(f_n(r)\) is the tangential_func(n, r) passed to the method.

Parameters:

tangential_func (Callable[[int, float], complex]) – tangential function dependent on r
r (Union[float, Sequence]) – radial coordinate [m]
theta (Union[float, Sequence]) – tangential coordinate [rad]
t (Union[float, Sequence]) – time [s]
mode (int) – specific mode number of interest; if None then all modes until N_max

Return type:

Union[complex, ndarray]

tangential_particle_displacement(r, theta, t, mode=None)

Particle displacement in tangential direction

Returns the value of the particle displacement in tangential direction in [m]

Parameters:

r (Union[float, Sequence]) – radial coordinate [m]
theta (Union[float, Sequence]) – tangential coordinate [rad]
t (Union[float, Sequence]) – time [s]
mode (Optional[int], optional) – specific mode number of interest; if None that all modes until N_max
Default: None

Return type:

Union[complex, ndarray]

tangential_particle_velocity(r, theta, t, mode=None)

Tangential particle velocity [m/s]

Parameters:

r (Union[float, Sequence[float]]) – radial coordinate [m]
theta (Union[float, Sequence[float]]) – tangential coordinate [rad]
t (Union[float, Sequence[float]]) – time [s]
mode (Optional[int], optional) – mode
Default: None

Return type:

Union[float, Sequence[float]]

velocity_potential(r, theta, t, scattered, incident, mode=None)

Returns the velocity potential of the fluid in [m^2/s].

Parameters:

r (Union[float, Sequence]) – radial coordinate [m]
theta (Union[float, Sequence]) – tangential coordinate [rad]
t (Union[float, Sequence]) – time [s]
scattered (bool) – add scattered field
incident (bool) – add incident
mode (Optional[int], optional) – specific mode number of interest; if None then all modes until N_max
Default: None

Return type:

complex

property E_ac: float: Wraps to osaft.core.backgroundfields.BackgroundField.E_ac

property F: float

Density-compressibility factor \(F\) [-]

(Eq. 60, 63, 75)

Acoustic contrast factor for small particle solutions. The error from the article in the factor for a bubble in standing wave has been corrected. :return: contrast factor [-]