Theoretical Concepts and Applications of Turbulent Flow Chromatography

Mar 01, 2012

Turbulent flow chromatography is often used for on-line sample cleanup of biological matrices in liquid chromatography–mass spectrometry applications. However, the general mechanisms are not well represented in the literature and there is a lot of misunderstanding of turbulent flow chromatography's basic principles. This column installment will explore the technique's theoretical concepts, explain how they can be applied, and discuss common practice through examples in the literature.

Turbulent flow was first defined over 100 years ago by British physicist Osborne Reynolds (1). Reynolds discovered that the flow of a fluid through a conduit becomes turbulent when the momentum of the fluid exceeds its resistance to flow by a factor of 2000–3000. The ratio of these opposing forces, known as the Reynolds number (R e), is expressed in equation 1:

The momentum, which is a certain amount of mass moving at a certain velocity (v), takes into account the fluid's density (ρ) and the diameter of the tube (D f). We can increase the fluid's momentum by increasing its velocity or by increasing the diameter of the tube, or both. The resistance to flow is expressed as the absolute or dynamic viscosity of the fluid (η), which is in units of grams per centimeter-second, or centipoise (cP). The transition from laminar to turbulent flow occurs as R e increases past a critical value between 2000 and 3000 in a straight tube with a smooth internal surface.

In the case of a tube packed with particles, such as a chromatographic column, the diameters of all of the flow paths cannot be measured, but the average diameter of the packing particles (d p) can be measured. The spaces between particles are proportional to the average size of the particles. Therefore, columns packed with large particles hold a greater mass of mobile phase than those packed with small particles. Equation 2 describes a special case (R e') of the Reynolds number for columns packed with particles:

where ε0 is the external porosity.

According to equation 2, turbulence occurs more readily in columns packed with large particles — 35–75 µm — than those packed with small particles — 3–10 µm. Experimental observations of solute band broadening relative to column retention have indicated that the transition from laminar to turbulent flow occurs as R e' increases beyond a value greater than 1 and that virtually all of the flow paths within a column become turbulent as R e' exceeds a value of 10 (2).

Solute band broadening relative to column retention is measured as the height equivalent to a theoretical plate (H). Typically, H increases from a minimum as the mobile phase velocity increases as long as the flow remains laminar. As the flow becomes turbulent through more and more channels in the packed column, H begins to decrease and reaches a minimum when all of the flow paths in the column become turbulent. Compared to flow through a straight hollow tube, transition from laminar to turbulent flow is much more gradual in a packed column as the flow rate increases.