# Average Mass Transfer Coefficient and Evaporation Time of Solvent from Coating

What is the average mass transfer coefficient, k, for the given system? How long will it take for the solvent to completely evaporate from the coating?

The average mass transfer coefficient, k, can be determined using the equation: **k = (Nu * D) / δ**. In this problem, **Nu = 2** is given. To find the time for complete solvent evaporation, we can use the concept of mass transfer rate and calculate it using the equation: **m_dot = k * A * (C_s - C_inf)**.

## Average Mass Transfer Coefficient, k

**k = (Nu * D) / δ**. In this case, the Nusselt number,

**Nu = 2**, is given. The Nusselt number characterizes the convection heat transfer between the coating and the surrounding air. The diffusion coefficient,

**D**, is dependent on the properties of the solvent and air at the given conditions. Given a coating thickness of

**0.1 mm (δ)**, we can substitute these values into the equation to calculate the average mass transfer coefficient,

**k**.

## Time for Complete Evaporation

To determine the time it will take for the solvent to completely evaporate from the coating, we need to calculate the mass transfer rate using the equation**m_dot = k * A * (C_s - C_inf)**. The mass transfer rate is influenced by the mass transfer coefficient,

**k**, the surface area of the coating,

**A**, the concentration of the solvent at the surface,

**C_s**, and the concentration of the solvent in the surrounding air,

**C_inf**. We can assume that as the solvent evaporates, the concentration at the surface remains constant at the vapor pressure of the solvent at 40 °C, which is given as

**0.05 atm (C_s)**. The concentration in the surrounding air is negligible as it acts as an "infinite sink" for mass transfer. By rearranging the equation, we can solve for the time it takes for the solvent to completely evaporate:

**t = (m / m_dot)**, where

**m**is the initial mass of the solvent in the coating. In conclusion, the average mass transfer coefficient,

**k**, and the time for complete solvent evaporation can be calculated using the provided equations and values. These parameters play a crucial role in understanding the evaporation process of the solvent from the coating.