Methods and apparatus for moving and concentrating particles by applying an alternating driving field and an alternating field that alters mobility of the particles. The driving field and mobility-varying field are correlated with one another. The methods and apparatus may be used to concentrate DNA or RNA in a medium, for example. Methods and apparatus for extracting particles from one medium into another involve applying an alternating driving field that causes net drift of the particles from the first medium into the second medium but no net drift of the particles in the second medium.