Generally, mixtures of DMSO and water are not used as mobile phase in the separation of essential oils via HPLC.
Methanol is often used in combination with water as a mobile phase in RP separations. Methanol can be used for flushing normal-phase silica columns to remove adsorbed polar contaminants. In RP applications, acetonitrile yields better peaks but is too expensive.
For essential oils, the separation can be achieved using a mixture of 30 mM ammonium acetate buffer (pH 4.7), methanol and acetonitrile in different ratio as mobile phase in a ternary linear gradient mode. For such study, please see a recent publication entitled " Simultaneous HPLC Determination of 22 Components of Essential Oils; Method Robustness with Experimental Design" contained in the following link:
The aim of the present study was the development and validation of a simple, precise and specific reversed phase HPLC method for the simultaneous determination of 22 components present in different essential oils namely cinnamon bark oil, caraway oil and cardamom fruit oil. The chromatographic separation of all the components was achieved on Wakosil–II C18 column with mixture of 30 mM ammonium acetate buffer (pH 4.7), methanol and acetonitrile in different ratio as mobile phase in a ternary linear gradient mode. The calibration graphs plotted with five different concentrations of each component were linear with a regression coefficient R2 >0.999. The limit of detection and limit of quantitation were estimated for all the components. Effect on analytical responses by small and deliberate variation of critical factors was examined by robustness testing with Design of Experiment employing Central Composite Design and established that this method was robust. The method was then validated for linearity, precision, accuracy, specificity and demonstrated to be applicable to the determination of the ingredients in commercial sample of essential oil.
In addition, attached please find a Handbook of Essential Oils- Science, Technology & Application which contains a comprehensive chapter on the analysis of essential oils (pages 151-184).