Stokes Number

Definition

The Stokes number is a dimensionless number that characterizes the behavior of particles suspended in a fluid flow, quantifying the ratio of inertial forces to viscous forces. This value is crucial for understanding how particles interact with the fluid around them, particularly during interphase momentum transfer, where the movement of particles can significantly affect the overall flow characteristics and particle distribution within the fluid.

5 Must Know Facts For Your Next Test

1. The Stokes number (St) is defined as St = \frac{\rho_p d_p^2 U}{18 \mu L} where \rho_p is the particle density, d_p is the particle diameter, U is the characteristic flow velocity, \mu is the dynamic viscosity of the fluid, and L is a characteristic length scale.
2. A low Stokes number (St << 1) indicates that particles closely follow the fluid flow, while a high Stokes number (St >> 1) suggests that particles have significant inertia and may not respond immediately to changes in the fluid flow.
3. In interphase momentum transfer, understanding the Stokes number helps predict how well particles will mix with or separate from the fluid, affecting processes like sedimentation and dispersion.
4. The Stokes number can help identify regimes of flow behavior; for instance, it plays a role in determining whether particle-laden flows are laminar or turbulent.
5. In applications like aerosol science or chemical reactors, controlling the Stokes number is important for optimizing particle transport and reaction rates.

Review Questions

• How does the Stokes number influence particle behavior in a fluid flow?
  • The Stokes number significantly influences how particles behave within a fluid. A low Stokes number indicates that particles are well-coupled to the fluid flow, meaning they tend to follow the motion of the fluid closely. Conversely, a high Stokes number suggests that particles have enough inertia to resist changes in flow direction, causing them to lag behind or separate from the fluid stream. Understanding this relationship is essential for predicting how particles will disperse or settle in various applications.
• Discuss the implications of varying Stokes numbers on interphase momentum transfer in multiphase flows.
  • Varying Stokes numbers can have profound implications for interphase momentum transfer in multiphase flows. For instance, in systems with low Stokes numbers, efficient momentum transfer occurs as particles easily follow the fluid motion. In contrast, high Stokes numbers may result in poor mixing and uneven distribution of particles due to their tendency to lag behind. This can impact processes like sedimentation rates and reaction efficiencies in chemical reactors. Thus, understanding and controlling Stokes numbers can help optimize performance in various multiphase systems.
• Evaluate how knowledge of the Stokes number can be applied to enhance industrial processes involving multiphase flows.
  • Knowledge of the Stokes number allows engineers to fine-tune industrial processes involving multiphase flows for improved efficiency and performance. By understanding how particles behave based on their Stokes number, operators can design reactors or separators that optimize particle dispersion or settling rates. For instance, controlling flow velocities and fluid properties can help maintain low Stokes numbers for better mixing in chemical reactors or achieve desired settling velocities in sedimentation tanks. This optimization leads to more effective process control and can significantly reduce costs associated with inefficient designs.

Related terms

Drag Force: The force exerted by a fluid on a particle moving through it, which opposes the particle's motion and is influenced by the particle's size, shape, and velocity.

Reynolds Number: A dimensionless number used to predict flow patterns in different fluid flow situations, representing the ratio of inertial forces to viscous forces in the fluid.

Settling Velocity: The velocity at which a particle falls through a fluid under the influence of gravity and drag force, often influenced by the Stokes number and other factors.