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We demonstrate that aqueous suspensions of microbubbles, formed into arrays using standing surface acoustic waves (SSAWs), can be transported by controlled modulation of the SSAW frequency. The array is repeatedly captured at a sequence of spatial positions along the acoustic beam path and long-range transportation is achieved by periodic cycling of the applied frequency across the transducer bandwidth. We also demonstrate that controllable alignment and transport can be achieved in a detachable microfluidic device, where the microfluidic channel, in which particle transport occurs, is separated from the piezoelectric substrate by an acoustic coupling gel. Proof-of-concept transport is first discussed using a test system of latex particles before the non-invasive manipulation technique is applied to arrays of microbubbles. We explore the role of acoustic radiation forces in the spatial control of particles by analysing the dynamics of particle manipulation by SSAWs. Our results highlight the exquisite control which we have over the position and transport of particles and we anticipate that this technique could find wide applications for the accurate and programmable, non-invasive ordering and transport of biological samples in microfluidic systems.