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I am learning about chromatography and there are two terms that confuse me a lot: linear velocity and volume flow rate. These terms are defined in Daniel Harris's Qualitative Chemical Analysis:

  • Linear velocity: the distance per unit time traveled by the mobile phase. (Unit is cm/s)
  • Volume flow rate: the volume of mobile phase per unit time eluted from the column. (Unit is mL/min)

The van Deemter equation is $H = A + \dfrac{B}{u} + C \cdot u$, in which $u$ is linear velocity.
Here it is applied for gas chromatography:

A graph of flow rate vs. plate height in chromatography.

So I wonder why the van Deemter equation is in fact dependent upon the linear velocity but the graph indicates that the plate height depends on the flow rate? Is there any relation between these two terms? If there is, what is the formula to support that relation?

Further, I want to ask in reality, which of the parameters could we alter to achieve the best resolution?

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    $\begingroup$ With a constant cross-sectional area of the column, these parameters are linearly related. If you hook up two columns in parallel and keep the linear flow rate, the flow rate will double. $\endgroup$
    – Karsten ♦
    Commented May 12 at 12:05
  • $\begingroup$ PH = f(u) = f(g(v)), where PH is plate height, u is linear velocity and v is volume flow. // dV/dt = A . dL/dt $\endgroup$
    – Poutnik
    Commented May 12 at 12:16

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Linear velocity and volumetric flow rate are easy to understand, both indicate how fast things are moving in a separation column, but I have to agree that the term "linear" velocity can be confusing in the chromatography literature because when people say flow rate and "linear velocity" are related by a constant, they are talking about superficial linear velocity $u_{sp}$, which is $$ u_{sp}=\frac{\text {Flow rate}}{\text {Cross section Area}}$$ in consistent units. This is the linear gas or mobile phase velocity based on the cross section of an empty column.

Chromatographers also use average linear velocity $u_{avg}$ is defined as $$u_{avg}=\frac{L}{t_0}$$, where $L$ is the length of the column, and $t_0$ is the dead time. Dead time is the time it takes for an unretained compound to travel an entire column (which can be empty or packed bed). It is assumed that the analyte can traveled every nook and corner of the packed bed. I prefer this one when I make van Deemter curves.

In practice you will see all three types of van Deemter curves with their x-axes labeled different. Basically, it can be plate heights (H) vs. flow rate or average linear velocity or superficial linear velocity. They all tell the same story, how fast the mobile phase is moving in the separation column and how it is affecting the peak width during a separation.

The axis of the figure in the Harris book is off, numerically. Conceptually, it should have been linear velocity $u$. We can rarely have flow rates up to 100 mL/min in normal columns. This could be average linear velocity in cm/min.

Update: The figure is correct as presented in the old edition textbook. They were using a huge column! 5 foot x 1/8 inch i.d. packed gas chromatography column using helium. In the new edition, this van Deemter figure has been replaced with one of my works.

You have to be aware of what the text/author is using. The key question is now what should we use for theoretical work, or what did van Deemter use himself? He used superficial linear velocity because he was studying gas chromatography columns. Do a dimensional analysis and you will see that the two linear velocities have the same units.

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