Stokes Number

Definition

The Stokes number is a dimensionless number that characterizes the behavior of particles suspended in a fluid flow, defined as the ratio of the particle's inertia to the viscous forces acting on it. This number helps determine how effectively a particle can follow the fluid motion, indicating whether it is likely to settle or remain suspended. The Stokes number is crucial in analyzing particle-laden flows, as it influences the dispersion, sedimentation, and interactions of particles within the fluid medium.

5 Must Know Facts For Your Next Test

1. The Stokes number (St) is calculated using the formula: $$St = \frac{\tau_p}{\tau_f}$$ where $$\tau_p$$ is the characteristic time scale for the particle's response and $$\tau_f$$ is the characteristic time scale of the fluid flow.
2. A Stokes number less than 1 indicates that particles closely follow the flow of the fluid, while a Stokes number greater than 1 suggests that particles are more influenced by inertia and may not follow the flow as closely.
3. In applications such as aerosol dynamics and sediment transport, understanding the Stokes number helps predict how particles will behave under different flow conditions.
4. The Stokes number can be affected by factors such as particle size, shape, and density, as well as the viscosity and density of the fluid.
5. In turbulent flows, the Stokes number plays a critical role in determining how particles disperse and interact with each other, affecting processes like mixing and reaction kinetics.

Review Questions

• How does the Stokes number relate to the behavior of particles in different flow regimes?
  • The Stokes number directly relates to particle behavior in various flow regimes by indicating whether particles will closely follow fluid motion or exhibit inertial effects. In low Reynolds number flows (laminar), a Stokes number less than 1 shows that particles can effectively track the fluid streamlines. Conversely, in high Reynolds number flows (turbulent), a Stokes number greater than 1 means that particles are more likely to deviate from fluid paths due to their inertia.
• Discuss how changes in particle size influence the Stokes number and its implications for particle-laden flows.
  • Changes in particle size significantly impact the Stokes number since larger particles tend to have higher inertial effects compared to smaller ones. As particle size increases, their response time to changes in flow conditions (represented by $$\tau_p$$) also increases, leading to a higher Stokes number. This higher Stokes number indicates that larger particles may settle out of suspension more readily or fail to follow rapid changes in fluid velocity, thus influencing overall dispersion patterns and sedimentation rates in particle-laden flows.
• Evaluate how understanding the Stokes number can improve industrial applications involving particulate matter in fluids.
  • Understanding the Stokes number can greatly enhance industrial applications involving particulate matter, such as in chemical engineering processes, air pollution control, and wastewater treatment. By accurately predicting how particles behave based on their Stokes numbers, engineers can optimize designs for reactors, separators, and filters to enhance efficiency and effectiveness. Moreover, knowledge of how particles interact with their surrounding fluid allows for better management of processes such as mixing and sedimentation, ultimately leading to improved product quality and reduced environmental impact.

Related terms

Drag Force: The resistance force experienced by a particle moving through a fluid, which depends on the particle's velocity and shape, as well as the properties of the fluid.

Particle Reynolds Number: A dimensionless quantity used to predict flow patterns around particles in a fluid, determined by the ratio of inertial forces to viscous forces acting on the particle.

Sedimentation: The process by which particles settle out of a fluid due to gravitational forces, often influenced by the Stokes number.