however part of a more general phenomenon associated with how solvents mix. There are some excellent reference works in this field that explains and visualises the mixing process as well as a better understanding of the fluidic motion within a packed bed. [3] [4] [5]

The science of mixing has been extensively studied, and this has resulted in the generation of some very detailed models of fluid flow and how liquids mix. [6] [7] [8] [9] In the case of an injection plug this will describe how the injection plug disperses within the mobile phase. When the injection solvent is the same as the mobile phase the mixing with the mobile phase will not affect the retention of the analytes, however, when the injection solvent is different; the dispersion of the injection solvent, or transfer solvent when considering 2D HPLC, can become very important. The degree of mixing will depend on the nature of the flow, whether the flow is laminar or turbulent. In general, the fluid flow within a typical LC will be flowing under laminar conditions, although it is relatively trivial to determine what the fluid characteristics are by using the Reynolds equation [10], which is a measure of the inertial to viscous forces present within the fluid.

Re = μ0 where;

l – is a characteristic length scale, which for an open tubular system is the diameter of the pipe.

– is the mean linear velocity of the fluid through the column or the superficial velocity.

μ0 η – is the dynamic viscosity of the mobile phase.

It is generally accepted that Re below 10 is laminar and above 2000 the flow is fully developed turbulence. For most HPLC systems the flow will not be fully turbulent, assuming viscosity of water, a flow rate of 1 mL/min and using 5/1000” tubing. It should be noted that the flow within the column uses a different characteristic length scale, which is related to the size of the channels between particles, and in this case enhanced mixing has been observed [11], suggesting that the flow is inertially dominated as opposed to dominated by viscous forces.

Where the flow is predominantly laminar complex morphologies can be created at the interface between the sample plug and the mobile phase. These structures are referred to as viscous fingers. Viscous fingering also referred to as a Saffman–Taylor instability is the formation of patterns, that look like fingers, in an unstable interface between two fluids in a porous medium, described mathematically [12]. It occurs at the interface between two different fluids percolating through a porous bed when the low-viscosity fluid pushes the high-viscosity fluid. In a chromatographic system, these two fluids are the mobile phase and a sample plug. If a high viscosity fluid is displacing a low viscosity fluid then the leading interface remains sharp, however, the trailing interface will exhibit a complex pattern resembling fingers. This phenomenon has been observed in preparative size-exclusion chromatography [13] resulting in severely distorted bands and, in a worst-case scenario, multiple bands are eluted when a single solute component was injected. Viscous fingering is unlikely to occur in analytical separations as the injection bands are too small, the concentration too dilute, and the viscosity tends to be very similar or the same as the mobile phase. For preparative chromatography and for transferring in 2D HPLC this is not always the case.

l η

Figure 2

The impact that altering the transfer solvent composition has on the peak shape; a - 100:0 Methanol:Water

b - 70:30 Methanol:Water c - 50:50 Methanol:Water d - 20:80 Methanol:Water

It is should be noted that fingering can occur even in the absence of a porous medium. If a low-viscosity fluid is injected into a sample loop containing a high-viscosity fluid, the low-viscosity fluid will begin to form fingers as it moves through the fluid, producing fractal structures. [14] [15]

Mayfield [13] investigated a series of different solvents, to simulate the effects that would be observed performing a heart cut between the first and second dimensions. Using a series of test probes, p-cresol, methoxybenzene, and ethoxybenzene, and a series of different mobile phases/injection solvents comprising of different mixtures of water/ acetonitrile and methanol; the researchers demonstrated that significant amounts of distortion could occur because of ineffective mixing due to the formation of viscous fingers. The team went on further to show the morphology of the viscous fingers that were being generated within the chromatographic system. This was achieved using a mixture of dichloromethane, toluene and cyclohexanol which in the correct proportions has the exact refractive index as the C18 silica, allowing for direct visualisation of the mixing phenomenon. Use a series of different amounts of cyclohexanol in the injection plug allowed the pictures to be obtained which clearly demonstrated the effect of viscous fingering and also very nicely explained the peak distortions that were observed.

To address these issues, it is recommended where possible to ensure that there is compatibility with the analytes, injection/transfer solvents and the individual mobile phases that are being used. This may require an extensive series of injections for both the first and second dimensions but it will result in a much more robust methodology. Ideally, in all cases, the peak shape should be investigated as well as the detector linearity response as these are ideal markers to identify if the mixing is proceeding beneficially. However, as with all forms of chromatography, a balance will have to be established between all of the experimental parameters to optimise the chromatographic performance.


Two-dimensional liquid chromatography offers a substantial advantage over one-dimensional chromatography in being able to achieve much

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