Improved methods and apparatus for cleaning substrates and enhancing diffusion limited reaction at substrate surfaces use piezoelectric transducers operating in the gigasonic domain. The resonator assemblies include plural transducer stacks each including a thin film piezoelectric element coupled to a resonator plate that faces the substrate. At the disclosed frequencies and powers used, Eckart or Rayleigh streaming can be induced in a liquid treatment medium without substantial generation of cavitation.