Faxen's 2nd Law is a fundamental principle in fluid mechanics that describes the relationship between viscous torque and the rotation of a spherical particle in a fluid flow.
Faxen's 2nd Law is important because it allows scientists and engineers to calculate the effects of fluid flow on small particles, such as bacteria, in a precise and quantitative manner. This is crucial in understanding various physical and biological processes, such as the transport of nutrients and pollutants in aquatic environments.
To calculate viscous torque using Faxen's 2nd Law, you need to know the fluid viscosity, the size and shape of the particle, and the fluid flow velocity. The formula for calculating viscous torque involves the particle's radius, distance from the center of rotation, and the fluid shear stress at the particle's surface.
Faxen's 2nd Law has numerous applications in various fields, including biology, engineering, and environmental science. It is used to study the behavior of microorganisms in fluid environments, design microfluidic devices, and understand the transport of pollutants in water bodies.
While Faxen's 2nd Law is a valuable tool in fluid mechanics, it does have some limitations. It assumes that the particle is small compared to the fluid flow and that the fluid is Newtonian. In addition, it does not take into account the effects of particle-particle interactions or the presence of other forces, such as gravity, on the particle's motion.