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Solvents like turpentine or mineral spirits are used to thin down paint because they will evaporate out, leaving paint without an excessive amount of oil and thus a strong structure. There are other ingredients (look up "organoclay" for example) which are widely used in modern artists' paints that in addition to rheological benefits can provide this structure or even better structure if properly incorporated into the pigment and oil, and that's why it isn't necessary for us to add solvent to Geneva paint. While clove oil evaporates out completely (albeit far more slowly than volatile solvents), it is not used for this property but rather for its drying retardant properties.