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Stretching dynamics of polymers in microfluidics is of particular interest for polymer scientists. As a charged polymer, a polyelectrolyte (PE) can be deformed from its coiled equilibrium configuration to an extended chain by applying uniform or nonuniform electric fields. By means of hybrid lattice Boltzmann (LB)-molecular dynamics (MD) simulations, we investigate how the condensed counterions (CIs) around the PE contribute to the polymer stretching in inhomogeneous fields. As an application, we discuss the translocation phenomena and entropic traps, when the driving force is an applied external electric field.