🎬how the Neumann boundary condition dictates the behavior of a sealed system

The animation visually confirms that diffusion in a closed environment is fundamentally a mass-conserving process. Even as the initial, non-uniform concentration profile spreads out and smooths over time, the average concentration of the substance remains constant (as verified by the "Avg. Concentration" display). The zero slope (zero gradient) at the boundaries physically represents the zero flux condition, ensuring that no substance enters or leaves the system. The final state is a uniform concentration profile where the concentration everywhere equals the initial average concentration, signifying thermal or chemical equilibrium within the sealed volume.

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how the Neumann boundary condition dictates the behavior of a sealed system | Animated Resultsviadean on Notion