  The control of solute fluxes through either microscopic phoresis or
hydrodynamic advection is a fundamental way to transport molecules, which are
ubiquitously present in nature and technology. We study the transport of large
solute such as DNA driven by a time-dependent thermal field in a polymer
solution. Heat propagation of a single heat spot moving back and forth gives
rise to the molecular focusing of DNA with frequency-tunable control. We
developed a theoretical model, where heat conduction, viscoelastic expansion of
walls, and the viscosity gradient of a smaller solute are coupled, and that can
explain the underlying hydrodynamic focusing and its interplay with phoretic
transports. This cross effect may allow one to design a unique miniaturized
pump in microfluidics.
