Write the diffusion equation for moisture uptake in a laminate (Fick's law) and describe the meaning of D and M_inf.

Write the diffusion equation for moisture uptake in a laminate (Fick's law) and describe the meaning of D and M_inf.

• A. ∂C/∂t = D ∂^2C/∂x^2; D is density; M_inf is maximum moisture.
• B. ∂C/∂t = D ∂^2M/∂x^2; D is the diffusion coefficient; M_inf is equilibrium moisture content.
• C. ∂C/∂t = k ∂^2C/∂x^2; k is thermal conductivity; M_inf is equilibrium moisture.
• D. ∂C/∂t = D ∂^2C/∂x^2; D is the diffusion coefficient; C is concentration; M_inf is the equilibrium moisture content.

Answer: (D)

Moisture diffusion in a laminate is described by Fick’s second law in one dimension, showing how the moisture concentration changes with time due to the curvature of its spatial profile: ∂C/∂t = D ∂^2C/∂x^2. Here, D is the diffusion coefficient, a material property (with units of m^2/s) that controls how fast moisture spreads through the material. C represents the moisture concentration inside the laminate (the amount of water per unit volume or per solid, depending on the chosen definition). M_inf denotes the equilibrium moisture content—the moisture level the material approaches at long times under a given environmental condition. This form and these meanings align with the standard interpretation of Fickian diffusion for moisture uptake.

Moisture diffusion in a laminate is described by Fick’s second law in one dimension, showing how the moisture concentration changes with time due to the curvature of its spatial profile: ∂C/∂t = D ∂^2C/∂x^2. Here, D is the diffusion coefficient, a material property (with units of m^2/s) that controls how fast moisture spreads through the material. C represents the moisture concentration inside the laminate (the amount of water per unit volume or per solid, depending on the chosen definition). M_inf denotes the equilibrium moisture content—the moisture level the material approaches at long times under a given environmental condition. This form and these meanings align with the standard interpretation of Fickian diffusion for moisture uptake.