12+13 - Flow Simulation - Potential Flow

Question 1

Biomaterial flow

Answer 1

• cement simulation for osteoporosis treatment
  — stab°, mobility
  — /!\ leakage, new fractures
• interventional treatment planning
• 3D Darcy flow model q = k/mu . nabla(p)
  k intrinsic permeability
  pore network model from image processing + mathcl model
• simulate vertebroplasty patient-specific + outcome

Question 2

Joint lubrication

Answer 2

• intra-articular flow: squeezed film + weeping
• fluid flow model
  — root mean square roughness = important factor
  — contact of asperities -> rough = slower, peak contact = increased resistance
  => self-limiting surface sealing
• /!\ degeneration = inflammation
• HA important role in mechanoregulation of cartilage metabolism

Question 3

Potential flow

Answer 3

• assumption
  — frictionless, incompressible
  — continuity: div(u) = 0 = du/dx + dv/dy
  — irrotational: rot(u) = 0 = du/dy - dv/dx
• stream fct u = ∂psi/∂y, v = -∂psi/∂x
  irrot => nabla2(psi) = 0
• potential fct u = ∂phi/∂x, v = ∂phi/∂y
  continuity => nabla2(phi) = 0
• define BCs and use symmetry