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Combining Two Separate Laminar Flows

  1. May 17, 2012 #1

    I was wondering, if I have two different liquid in two separate branches, and then the two branch lead to a single branch such that the two flows now go together in one branch, I was wondering what are the factors (qualitatively) affecting the degree of mixing of the two liquid? What about if it's a gas?

  2. jcsd
  3. May 17, 2012 #2


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    Two laminar flows will continue flowing side-by-side almost indefinitely unless the turn turbulent through either boundary-layer processes or an interfacial instability (e.g. Kelvin-Helmholtz or Rayleigh-Taylor).
  4. May 18, 2012 #3

    So even two miscible liquid like water and ethanol will not mix? Can you explain why because I initially thought that miscibility, density, or diffusion coefficient had a role in this?

    Also what about for very low Re (i.e Re< 1), where the velocity is very small?

  5. May 18, 2012 #4
    what boneh3ad said is not entirely correct. Mixing can happen by diffusion or by convection. Turbulence is a very good way of mixing and in laminar flows mixing is extremely slow. The main mixing then is the diffusion over the interface between the two fluids - governing parameter is the binary diffusion coefficient. You can enhance the mixing by stirring it - this will increase the interface surface area. If the velocity difference between the streams is large (but still laminar), you will get first small disturbance waves and then vortex shedding. Again, the effective surface for diffusion is increased.
  6. May 19, 2012 #5


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    And yet, the spatial distance over which this diffusion occurs is very large in a lamianr flow. Diffusion is rarely a fast process. Look at the confluence of the Ohio and Mississippi Rivers near Southern Illinois. The two merge and continue downstream for miles as two nearly separate flows.
  7. May 22, 2012 #6

    Thanks for the responses

    So basically the depth in which the diffusion occurs at some point in the pipe (from a fixed reference) from an engineering standpoint is very small to begin with and decreases with increasing velocity (but still laminar, and both fluid still moving with same velocity)?

    Does the fact that the fluid is moving affect diffusion at all? i.e. if I pick a reference that moves with the same velocity as both fluid, can I model the diffusion as if both fluids are not moving?

    Lastly, I was wondering how gravity plays a role in the case where I have two miscible fluid (like water and ethanol) and the heavier one comes into the pipe on top of the lighter one? What about two non miscible fluid? Does the flow just become turbulent due to the instability of the flow?

  8. May 25, 2012 #7
    What we are saying is that when the velocity difference between two streams increases, the importance of molecular diffusion becomes smaller and the effect of mixing due to convection and, in the end, turbulence, becomes dominant. The dimensionless parameter describing this is the Reynolds number. If Re is small, molecular diffusion is dominant, even if it is a small effect.

    When you are considering the 1D convection-diffusion equation of a single stream, you can transform the equation into a diffusion equation - this shows that diffusion is not affected by the fluid moving.

    gravity is a different matter. The buoyancy effect due to gravity can be important, but again (like for molecular diffusion), only when the mean velocities are low; cigarette smoke is a well-known example.
    Like you already show with your simple example of water and ethanol, the effect of buoyancy on mixing depends very much on your initial conditions, e.g. heavy fluid on top or not. A fluid can become turbulent due to buoyancy, but viscous effects can be too strong and the fluid motion will die out. The dimensionless parameter to look at is the Grashof number.
  9. May 28, 2012 #8

    Thanks for your insights.

    If neglecting the instabilities that boneh3ad discussed, I'm wondering, if the two streams are both liquids or both gas, how do I find the convective mass transfer coefficient hmass (i.e. is it the same as in the case of air/gas blowing over water/liquid?) as well as the boundary conditions at either side of the boundary layer at the interface of the two fluid. (I guess for simplicity). I can't seem to find anything on liquid-liquid diffusion and gas-gas diffusion.

    When you say low, do you mean that the flow must be in the laminar range?

    If I have a heavier fluid on top but only one of the fluid have high viscosity, then the buoyant effect may create turbulence? Is there a Gr range for which this would occur (I'm guessing given how specific this case is that there isn't)?

    So the only way to maintain stability and no turbulence (such that diffusion is the main process in any mixing) is for the less dense fluid on top, for velocity to be the same for both fluid and Re in laminar region? Any other conditions chances are the fluid will be unstable, turbulence results and diffusion is basically negligible?

    Also I'm curious, what about two fluids that are injected side by side, there would be a varying pressure profile w.r.t. depth due to differing densities, would that also be unstable?

    Thanks very much
    Last edited: May 29, 2012
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