Step 1: Recall the rheological behaviors relevant to drilling fluids:
Drilling fluids are non-Newtonian fluids. The behaviors of interest here are dilatant (shear thickening, apparent viscosity increases with shear rate), pseudoplastic (shear thinning, apparent viscosity decreases with shear rate), thixotropic (a time dependent structure that gels at rest and thins under shear, then rebuilds again when shearing stops) and rheopectic (a time dependent structure where viscosity builds up under continued shear, the opposite of thixotropic).
Step 2: Analyze option (A) Dilatant:
A dilatant fluid becomes thicker as shear rate increases. This is undesirable for a drilling fluid because the fluid needs to flow easily through the bit nozzles where shear rates are very high. Conventional drilling fluids are not dilatant, so option (A) is incorrect.
Step 3: Analyze option (B) Pseudoplastic:
A pseudoplastic fluid becomes thinner as shear rate increases. This is exactly what a drilling fluid needs, low viscosity at the high shear rates near the bit for efficient hydraulics and good rate of penetration, and higher viscosity at the low shear rates in the annulus for good cuttings transport. Conventional water base and oil base muds show this behavior, so option (B) is correct.
Step 4: Analyze option (C) Thixotropic:
A thixotropic fluid forms a gel structure when left static and breaks down into a more fluid state once shearing resumes. Drilling fluids are deliberately formulated to be thixotropic so that when circulation is stopped, the fluid gels and holds cuttings and weighting agents in suspension, preventing settling, and then thins again once pumping restarts. So option (C) is correct.
Step 5: Analyze option (D) Rheopectic:
A rheopectic fluid thickens under continued shearing, which is the reverse of thixotropic behavior and is a rare property not associated with conventional drilling fluids. So option (D) is incorrect.
Final Answer:
\[ \boxed{\text{(B) Pseudoplastic and (C) Thixotropic}} \]