Rheology formulation

• Rheology


  Study of the flow and deformation properties of matter
• Viscosity


  Resistance of a fluid to flow or movement
• Coefficient of dynamic viscosity is proportional to the ratio of shear stress (σ) and shear rate (γ)
• Shear stress (σ)


  • Force applied (N) per unit of surface (m2) parallel to the fluid layers (i.e. force per LATERAL area). Not the same as a pressure (a force per NORMAL area)
• Shear rate (γ)


  • Rate at which the velocity of flow (m/s) decreases depending on the distance (m) from the point in which the force is applied
• Newtonian fluids


  Fluids with constant viscosity, which have zero shear rate at zero shear stress. Shear rate is directly proportional to shear stress.
• Newtonian fluids


  • Pure gases
  • Pure liquids
  • Solutions of low MW molecules
• Non-Newtonian fluids


  • Majority of pharmaceutical systems
• Plastic or Bingham flow

  • Rheogram does not pass through the origin, intersects y-axis at yield value (σy), fluid does not flow until minimum stress of σy is applied
• Plastic or Bingham flow


  • Concentrated suspensions
  • Dispersions with flocculated particles
  • Mayonnaise
• Pseudoplastic flow


  • Material flows as soon as shear stress is applied, relationship between shear stress and shear rate is not linear, "shear thinning" fluids, viscosity changes with shear stress so we talk about APPARENT VISCOSITY
• Pseudoplastic flow


  • Solutions of natural or chemically modified hydrocolloids (tragacanth, methylcellulose) and synthetic polymers (polyacrylic acid, PVP)
• Dilatant flow


  • Viscosity increases with increase in shear stress, "shear thickening" liquids
• Dilatant flow


  • Dispersions of highly concentrated small deflocculated particles, mainly during dispersions preparation (e.g. wet sand)
• Newton's law states that the flow rate is proportional to the stress applied
• Shear stress is expressed in N/m2 or Pa, shear rate in s-1, dynamic viscosity in Pa·s
• Plotting shear rate vs shear stress for a Newtonian fluid

  Calculate the dynamic viscosity from the slope of the line
• The power law can be used to describe different behaviours: n<1 pseudoplastic flow, n=1 Newtonian flow, n>1 dilatant flow