Understanding Fluid Dynamics in Snow Globes

What is Fluid Dynamics?

Fluid dynamics is the study of fluids (liquids and gases) and their motion. It encompasses both theoretical analysis and experimental methods to understand how forces affect fluid behavior, including pressure, viscosity, and turbulence.

In a snow globe, fluid dynamics plays out through the interactions between the viscous liquid and the glitter particles suspended within it.

The Role of Viscosity

Viscosity is a measure of a fluid’s resistance to gradual deformation by shear or tensile stress. In a snow globe, higher viscosity results in slower movement and more pronounced vortices due to the increased internal friction between particles.

By adjusting the viscosity slider, you can observe how it affects the settling rate of glitter particles and the decay rate of vortex structures.

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Stokes' Law and Terminal Velocity

Stokes’ law describes the drag force exerted on a spherical object moving through a fluid. In a snow globe, this law explains why glitter particles settle at specific terminal velocities, which are determined by their size, density, and the properties of the surrounding liquid.

The terminal velocity can be calculated using the formula: v = (2/9) * (r^2 * (ρ_p - ρ_f) * g) / η, where r is the particle radius, ρ_p is the particle density, ρ_f is the fluid density, g is the acceleration due to gravity, and η is the dynamic viscosity of the fluid.

Lamb-Oseen Vortex Decay

A Lamb-Oseen vortex is a type of vortex that decays over time. In a snow globe, shaking introduces these vortices into the liquid, which then dissipate due to viscous forces and particle interactions.

The decay rate of these vortices can be observed by adjusting the shake intensity slider or using the gesture to inject new vortices, noting how they diminish over time.

Frequently asked questions

How does shaking affect the snow globe's fluid dynamics?

Shaking introduces initial conditions that create Lamb-Oseen vortices in the liquid. These vortices decay over time due to viscous forces and particle interactions, illustrating the principles of fluid dynamics.

What is terminal velocity, and how does it relate to the particles in a snow globe?

Terminal velocity is the constant speed at which an object moves through a fluid when the sum of its drag force and buoyancy equals its gravitational force. In a snow globe, each particle settles at its own terminal velocity based on its size, density, and the properties of the liquid.

Why do glitter particles settle sideways in the snow globe?

Glitter particles settle sideways due to their shape and the Stokes-drag force acting upon them. This sideways settling is a result of the fluid dynamics at play, where particles experience both vertical gravitational pull and horizontal drag forces from the liquid.

Can I use what I learn from a snow globe to understand real-world phenomena?

Absolutely! The principles observed in a snow globe apply to many real-world scenarios, such as sedimentation in rivers, air pollution dispersion, and even blood flow in the human body. Understanding these dynamics helps in fields like environmental science, engineering, and medicine.

Try it live

Everything above runs in your browser — open Snow Globe Fluid Dynamics and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.

▶ Open Snow Globe Fluid Dynamics simulation