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Diffusion Coefficient Formula:
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The diffusion coefficient (D) quantifies how quickly particles spread through a medium due to random thermal motion. It's a fundamental parameter in physics, chemistry, and biology that describes the rate of diffusion in various materials and systems.
The calculator uses the 1D random walk diffusion equation:
Where:
Explanation: This equation derives from Einstein's relation for Brownian motion, where the mean square displacement is proportional to time for diffusion processes.
Details: The diffusion coefficient is crucial for understanding mass transport phenomena, predicting reaction rates, designing separation processes, and modeling biological systems where molecular diffusion plays a key role.
Tips: Enter displacement in meters and time in seconds. Both values must be positive numbers. The calculator will compute the diffusion coefficient in square meters per second.
Q1: What is the physical significance of the diffusion coefficient?
A: The diffusion coefficient measures how rapidly particles or molecules spread through a medium. Higher values indicate faster diffusion, while lower values suggest slower spreading.
Q2: How does temperature affect the diffusion coefficient?
A: Diffusion coefficients generally increase with temperature according to the Arrhenius equation, as higher thermal energy increases molecular motion.
Q3: What are typical values for diffusion coefficients?
A: Diffusion coefficients vary widely: gases (~10⁻⁵ m²/s), liquids (~10⁻⁹ m²/s), and solids (~10⁻¹⁴ m²/s) at room temperature.
Q4: Can this equation be used for 2D or 3D diffusion?
A: For higher dimensions, the equation modifies to D = ⟨r²⟩/(2dt), where d is the dimensionality (2 for 2D, 3 for 3D).
Q5: What are the limitations of this simple model?
A: This model assumes ideal conditions: infinite dilution, no external forces, homogeneous medium, and Fickian diffusion behavior.