Stokes flow in a Hele-Shaw cell

Stokesian hydrodynamic in a Hele-Shaw cell

RBM (Rigid Body Motion: Velocity and Angular Velocity)

class pystokes.twoWalls.Rbm

Rigid body motion (RBM)

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particles: int

Number of particles (N)

viscosity: float

Viscosity of the fluid (eta)

mobilityTT(v, r, F, H)

Compute velocity due to body forces using \(v=\mu^{TT}\cdot F\) …

Parameters:

  • v (np.array) – An array of velocities An array of size 3*N,

  • r (np.array) – An array of positions An array of size 3*N,

  • F (np.array) – An array of forces An array of size 3*N,

  • H (float) – Height of the Hele-Shaw cell

propulsionT2s(v, r, S, H)

Compute velocity due to 2s mode of the slip …

Parameters:

  • v (np.array) – An array of velocities An array of size 3*N,

  • r (np.array) – An array of positions An array of size 3*N,

  • S (np.array) – An array of forces An array of size 5*N,

  • H (float) – Height of the Hele-Shaw cell

propulsionT3t(v, r, D, H)

Compute velocity due to 3t mode of the slip …

Parameters:

  • v (np.array) – An array of velocities An array of size 3*N,

  • r (np.array) – An array of positions An array of size 3*N,

  • D (np.array) – An array of forces An array of size 3*N,

  • H (float) – Height of the Hele-Shaw cell

Flow

class pystokes.twoWalls.Flow

Flow at given points

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Parameters:

  • radius (float) – Radius of the particles.

  • particles (int) – Number of particles

  • viscosity (viscosity of the fluid) –

  • gridpoints (int) – Number of grid points

flowField1s(vv, rt, r, F, H)

Compute flow field at field points due body forces …

Parameters:

  • vv (np.array) – An array of flow at field points An array of size 3*Nt,

  • rt (np.array) – An array of field points An array of size 3*Nt,

  • r (np.array) – An array of positions An array of size 3*N,

  • F (np.array) – An array of body force An array of size 3*N,

  • H (float) – Height of the Hele-Shaw cell

flowField2s(vv, rt, r, S, H)

Compute flow field at field points due to 2s mode of th slip …

Parameters:

  • vv (np.array) – An array of flow at field points An array of size 3*Nt,

  • rt (np.array) – An array of field points An array of size 3*Nt,

  • r (np.array) – An array of positions An array of size 3*N,

  • S (np.array) – An array of 2s mode of the slip An array of size 5*N,

  • H (float) – Height of the Hele-Shaw cell

flowField3t(vv, rt, r, D, H)

Compute flow field at field points due to 3t mode of th slip …

Parameters:

  • vv (np.array) – An array of flow at field points An array of size 3*Nt,

  • rt (np.array) – An array of field points An array of size 3*Nt,

  • r (np.array) – An array of positions An array of size 3*N,

  • D (np.array) – An array of 2s mode of the slip An array of size r*N,

  • H (float) – Height of the Hele-Shaw cell