Plastic Flow (Bingham Plastic)

Definition of Plastic Flow (Bingham Plastic):

• A plastic fluid (Bingham Plastic) behaves as a solid until a certain yield stress is exceeded.
• Beyond this point, it flows like a Newtonian fluid with a constant viscosity.

Rheological Behavior:

• Requires minimum force (yield value) to initiate flow.
• Once flow starts, shear stress and shear rate are linearly related.
• Does not pass through the origin on a shear stress vs. shear rate graph.

Equation:

• $\boldsymbol{\tau} = \boldsymbol{\tau}_{0} + \eta_{p} \cdot \dot{\boldsymbol{\gamma}}$
• Where:
  • τ: shear stress
  • τ₀​: yield stress
  • η_p​: plastic viscosity
  • γ˙​: shear rate

Examples:

• Toothpaste
• Ointments
• Concentrated suspensions
• Some emulsions
• Here’s the graph replicating the concept in your image: a Bingham plastic fluid that shows no flow until a yield stress (τ₀) is exceeded, after which it flows linearly.

Pharmaceutical Relevance:

• Holds its shape until used (ideal for topicals)
• Easy to handle and fill after yield stress is surpassed

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