Which law is commonly used to predict the sedimentation rate of particles in a suspension?

• A. Stokes' law
• B. Newton's law
• C. Fick's law
• D. Ohm's law

Answer: (A)

When a particle settles in a viscous fluid, its downward pull due to gravity (minus buoyancy) is balanced by the viscous drag from the fluid. For small spherical particles in creeping (laminar) flow, that drag is described by Stokes’ law: F_drag = 6πμr v. Setting (ρ_p − ρ_f) (4/3)πr^3 g equal to F_drag and solving for the terminal velocity v gives v = (2/9) [r^2 g (ρ_p − ρ_f)] / μ, or in terms of diameter d: v = (g d^2 (ρ_p − ρ_f)) / (18 μ). This velocity is the sedimentation rate under the assumed conditions. Stokes’ law is widely used because it directly relates particle size, density difference, fluid viscosity, and gravity to the settling speed, provided the flow is laminar (low Reynolds number), the particle is spherical, and interactions between particles are negligible (dilute suspension). If these conditions aren’t met, corrections are needed (e.g., for non-spherical particles or higher Reynolds numbers). Other laws mentioned describe different phenomena (diffusion or electrical behavior) and aren’t used to predict sedimentation rates.