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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radius: float
Radius of the particles (a).
particles: int
Number of particles (Np)
viscosity: float
Viscosity of the fluid (eta)
mobilityTT()

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*Np,
  • r (np.array) – An array of positions An array of size 3*Np,
  • F (np.array) – An array of forces An array of size 3*Np,
  • H (float) – Height of the Hele-Shaw cell
propulsionT2s()

Compute velocity due to 2s mode of the slip …

Parameters:
  • v (np.array) – An array of velocities An array of size 3*Np,
  • r (np.array) – An array of positions An array of size 3*Np,
  • S (np.array) – An array of forces An array of size 5*Np,
  • H (float) – Height of the Hele-Shaw cell
propulsionT3t()

Compute velocity due to 3t mode of the slip …

Parameters:
  • v (np.array) – An array of velocities An array of size 3*Np,
  • r (np.array) – An array of positions An array of size 3*Np,
  • D (np.array) – An array of forces An array of size 3*Np,
  • 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()

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*Np,
  • F (np.array) – An array of body force An array of size 3*Np,
  • H (float) – Height of the Hele-Shaw cell
flowField2s()

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*Np,
  • S (np.array) – An array of 2s mode of the slip An array of size 5*Np,
  • H (float) – Height of the Hele-Shaw cell
flowField3t()

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*Np,
  • D (np.array) – An array of 2s mode of the slip An array of size r*Np,
  • H (float) – Height of the Hele-Shaw cell