We examine flow and transport through an orifice in a flat wall separating semi-infinite atmospheres of two dissimilar gases. The analysis assumes steady conditions and order-unity values of the Schmidt number $\mathit{\text{Sc}}$ and Péclet number $\mathit{\text{Pe}}$, such that advection and diffusion contribute comparably to mass and momentum transport. Mixing between the two gases induces order-unity variations in viscosity and density, resulting in coupled concentration and velocity fields. The solution yields the mass transfer rates of both gases, expressed in terms of an appropriately defined Sherwood number, as well as the overpressure required to sustain the flow, all as functions of $\mathit{\text{Sc}}$ and $\mathit{\text{Pe}}$. An explicit analytical solution is obtained in the limit of small $\mathit{\text{Pe}}$, while numerical integration is used to describe flows with $\mathit{\text{Pe}}=O\left(1\right)$. The mixing of hydrogen and air is used as an illustrative example that serves to highlight the influence of large gas-molecular-weight differences on the flow structure and associated mixing rate, with additional selected results given for the case of hydrogen and water vapor.

Close

PrevNext

View figure in article

• Flow boundary effects
• Laminar flows
• Low Reynolds number flows
• Microfluidics