Stokes Flow Equations
The Stokes flow equations, also known as creeping flow equations, are a simplified form of the Navier-Stokes equations that describe the motion of viscous fluids at very low Reynolds numbers, where inertial forces are negligible compared to viscous forces. They consist of the Stokes equation (a linearized momentum equation) and the continuity equation, used to model slow, steady flows such as those in microfluidics, sedimentation, or lubrication. This approximation is fundamental in fluid dynamics for analyzing scenarios where fluid motion is dominated by viscosity, such as in biological systems or small-scale industrial processes.
Developers should learn Stokes flow equations when working in computational fluid dynamics (CFD), biomedical engineering, or microfluidics, as they provide an efficient mathematical model for simulating low-speed fluid flows without the complexity of full Navier-Stokes equations. For example, in designing lab-on-a-chip devices or modeling blood flow in capillaries, Stokes equations enable accurate predictions of pressure and velocity fields with reduced computational cost. They are also essential for understanding fundamental fluid mechanics concepts and applying them to real-world problems in fields like chemical engineering or geophysics.