What is stokes law?

Stokes' Law

Stokes' Law describes the relationship between the viscous drag force experienced by a small spherical object moving through a viscous fluid. It is a fundamental concept in fluid dynamics, particularly useful for understanding the motion of particles in liquids and gases.

• Definition: Stokes' Law states that the drag force (F_d) on a sphere moving slowly through a viscous fluid is directly proportional to the sphere's radius (r), the fluid's viscosity (η), and the sphere's velocity (v).

• Equation: The mathematical expression for Stokes' Law is:

  • F_d = 6π η r v

• Assumptions and Limitations: Stokes' Law is based on several assumptions that limit its applicability:

  • Spherical Shape: The object must be a perfect sphere. Deviations from sphericity can introduce significant errors.
  • Laminar Flow: The flow around the sphere must be laminar (smooth and orderly), characterized by a low Reynolds Number (typically Re < 0.1). Higher Reynolds numbers indicate turbulent flow, where Stokes' Law is no longer valid.
  • Homogeneous Fluid: The fluid must be homogeneous and isotropic (having the same properties in all directions).
  • No Wall Effects: The sphere must be far enough from any boundaries (e.g., the walls of a container) that the walls do not affect the flow around the sphere.
  • Steady Velocity: The sphere's velocity must be constant.
  • No Slip Condition: The fluid in immediate contact with the sphere's surface has zero velocity relative to the sphere.

• Applications: Stokes' Law has numerous applications in various fields, including:

  • Sedimentation: Determining the settling velocity of particles in fluids, such as in sedimentation processes in water treatment.
  • Viscometry: Measuring the viscosity of fluids by observing the motion of a sphere through them.
  • Aerodynamics: Estimating the drag force on small particles in air.
  • Colloid Science: Studying the behavior of colloidal suspensions.

• Key Parameters:

  • F_d: Drag force (N)
  • η: Dynamic Viscosity of the fluid (Pa·s or N·s/m²)
  • r: Radius of the spherical object (m)
  • v: Velocity of the sphere relative to the fluid (m/s)