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.
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