Section 1.1.1 Solutions Reserve Problem 1.1.1R “Drilling mud” is used in hydrocarbon drilling operations to carry debris to the surface and to both cool and lubricate the drill bit. It is frequently modeled as a Bingham plastic. Explain why a substance that behaves according to this model does not satisfy the definition of a fluid. SOLUTION: The relationship between the applied shear stress and the strain rate of a Bingham plastic can be obtained from many sources, including Section 1.6 of this text. Although it behaves like a Newtonian fluid for an applied shear stress larger than its yield stress, it exhibits a strain rate of zero (like a solid) if the applied shear stress is lower than the yield stress. From Section 1.1 of this text: “A fluid is defined as a substance that deforms continuously when acted on by a shearing stress of any magnitude.” Because a Bingham plastic has a finite yield stress, its behavior does not satisfy the definition of a fluid. Q.E.D. NOTE: Although the question did not require you to think about the implications of a finite yield stress, they can be significant. Consider the start-up of a drill surrounded by such a fluid. In general terms, what might the flow look like? Would it require more torque to start the drill than it would for a Newtonian fluid?