How piston velocity can be calculated from the flux into the diffusion chamber over a waterbody?
The piston velocity can be calculated from the flux into the diffusion chamber over a waterbody by using Fick's first law of diffusion, which relates the flux of a substance to its concentration gradient. The diffusion chamber is typically used to measure the concentration of a substance in the waterbody, and the flux is the rate at which the substance diffuses across the interface between the water and the air above it.
Assuming that the diffusion process is one-dimensional and that the concentration gradient is constant across the interface, Fick's first law can be expressed as:
J = -D * dC/dx
where J is the flux, D is the diffusion coefficient of the substance, C is its concentration, and x is the distance across the interface. The negative sign indicates that the flux is directed from high concentration to low concentration.
To calculate the piston velocity from the flux, we can use the following relationship:
J = ρ * u * A
where ρ is the density of the air, u is the piston velocity, and A is the cross-sectional area of the diffusion chamber. This equation relates the flux of the substance to the mass flow rate of air across the diffusion chamber, which is equal to the product of the air density, piston velocity, and cross-sectional area.
By equating the two expressions for J, we can obtain an equation for the piston velocity:
u = -D * dC/dx / (ρ * A)
Therefore, to calculate the piston velocity, we need to measure the concentration of the substance in the waterbody, its diffusion coefficient, and the cross-sectional area of the diffusion chamber. We can then use these values to calculate the concentration gradient across the interface and the piston velocity.
Thank you Kristaq Hazizi Sir for answering my question. Could we use the theoretical diffusion coefficient and air density value from literature? And is dC/dx the rate of change of dissolved concentration over different depth ?
Yes, you can use theoretical diffusion coefficient and air density values from literature as long as they are relevant to the specific substance and conditions you are working with. The diffusion coefficient is a property that depends on the substance being measured and the medium in which it is diffusing, so it can be determined experimentally or estimated based on published data.
Regarding the term dC/dx, it represents the rate of change of dissolved concentration (C) with respect to the distance across the interface (x). In the context of the diffusion chamber over a waterbody, x would typically represent the vertical depth or height within the diffusion chamber. The concentration gradient is the change in concentration per unit distance. Therefore, dC/dx is the derivative of the concentration profile with respect to depth.
To calculate dC/dx, you would need to measure or estimate the dissolved concentration of the substance at different depths within the waterbody or diffusion chamber and then calculate the concentration gradient using those values.
It's worth noting that the assumption of a constant concentration gradient across the interface may not always hold true in real-world scenarios. In some cases, the concentration gradient may vary with depth due to various factors such as stratification or mixing processes in the waterbody. Therefore, it's important to consider the specific conditions and characteristics of the system you are working with when calculating the piston velocity.