The control of solute flux by 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 solutes such as DNA driven by a time-dependent thermal field in a polymer solution. Heat propagation of a heat spot moving back and forth gives rise to the molecular focusing of DNA with frequency-tunable control. We develop a model where the viscoelastic expansion of a solution and the viscosity gradient of a smaller solute are coupled, which explains the underlying hydrodynamic focusing. This effect offers novel non-invasive manipulation of soft and biological materials in a frequency-tunable manner.
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