Paper-based microfluidics has recently received considerable interest due to their ease and low cost, making them extremely attractive as point-of-care diagnostic devices. The incorporation of basic fluid actuation and manipulation schemes on paper substrates, however, afford the possibility to extend the functionality of this simple technology to a much wider range of typical lab-on-a-chip operations, given its considerable advantages in terms of cost, size and integrability over conventional microfluidic substrates. We present a convective actuation mechanism in a simple paper-based microfluidic device using surface acoustic waves to drive mixing. Employing a Y-channel structure patterned onto paper, the mixing induced by the 30 MHz acoustic waves is shown to be consistent and rapid, overcoming several limitations associated with its capillary-driven passive mixing counterpart wherein irreproducibilities and nonuniformities are often encountered in the mixing along the channel--capillary-driven passive mixing offers only poor control, is strongly dependent on the paper's texture and fibre alignment, and permits backflow, all due to the scale of the fibres being significant in comparison to the length scales of the features in a microfluidic system. Using a novel hue-based colourimetric technique, the mixing speed and efficiency is compared between the two methods, and used to assess the effects of changing the input power, channel tortuousity and fibre/flow alignment for the acoustically-driven mixing. The hue-based technique offers several advantages over grayscale pixel intensity analysis techniques in facilitating quantification without limitations on the colour contrast of the samples, and can be used, for example, for quantification in on-chip immunochromatographic assays.