Sherwood number - effective and molecular diffusion

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SUMMARY

The Sherwood number (Sh), which represents the ratio of convective to diffusive mass transfer, is crucial for understanding mass transport mechanisms. In discussions regarding the effective diffusion coefficient (De) versus the molecular diffusion coefficient (D), it is established that the Sherwood number is indeed proportional to the ratio De/D. The effective diffusion coefficient is defined as the value necessary to achieve observed mass flux, factoring in both diffusion and convection. For example, the diffusion of CO2 in water has a molecular diffusion coefficient of approximately 2E-9, while the effective diffusion coefficient measured for observed mass transport is 2E-8.

PREREQUISITES
  • Understanding of the Sherwood number and its significance in mass transfer.
  • Knowledge of molecular diffusion coefficients and their measurement.
  • Familiarity with the concepts of convective and diffusive transport mechanisms.
  • Basic principles of fluid dynamics and mass flux calculations.
NEXT STEPS
  • Research the mathematical derivation of the Sherwood number in various systems.
  • Explore the relationship between molecular diffusion coefficients and effective diffusion coefficients in different fluids.
  • Study the impact of temperature and pressure on diffusion coefficients in chemical systems.
  • Investigate experimental methods for measuring effective diffusion coefficients in real-world applications.
USEFUL FOR

Chemical engineers, researchers in mass transfer phenomena, and professionals involved in fluid dynamics and transport processes will benefit from this discussion.

TboneWalker
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I'm having a little trouble understanding the Sherwood number, (Sh, mass transfer Nusselt number), which gives the ratio of convective to diffusive mass transfer. My question is: given a system that has a molecular diffusion coefficient of D, the effective diffusion coefficient is measured to De because of convective forces that speed up the process. Will the Sherwood number then be proportional to De/D?
 
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If you want my opinion, I'd say yes. But if you want my second opinion, I'd say no. :smile:
 
Thanks, that clears it up :wink:

Any more thoughts anyone?
 
How are you distinguishing the diffusion coefficient and "effective diffusion coefficient"? The diffusion coefficient as typically defined already takes temperature and Brownian motion into account, and thus it is hard to see what distinction you could be drawing there. As I understand it, the Sherwood number is used to express the ratio of transport by convection (diffusion plus advection) to that of transport by diffusion alone. So it is hard to see how you could measure an "effective diffusion coefficient" that is different from the actual one.
 
The "effective diffusion coefficient" that I measure is the value the diffusion coefficient has to have in order to achieve the observed mass flux, assuming that diffusion alone is the driving mechanism.

For instance, I know that the diffusion of CO2 in water in reality is around 2E-9. In order to get the mass transport I'm observing, the diffusivity has to be 2E-8. Thus the "effective diffusion coefficient" is equal to 2E-8. The transport mechanism is off course not purely diffusion, but the effective diffusion coefficient would describe the amount of flux, and the ratio De/D would give you an idea of the ratio of diffusive transport compared to the total transport. I might be totally off here...
 

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