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Non-monotonic hydrodynamic lift force on highly-extended polymers near surfaces

The hydrodynamic lift force that polymers experience near boundaries is known to be a crucial element when considering rheological flows of dilute polymer solutions. Here we develop theory to describe the hydrodynamic lift force on extended polymers flowing near flat surfaces. The lift force is shown to display a non-monotonic character increasing linearly with the distance to the wall $Z$ in the near-surface regime defined as $Z<L$, with $L$ being the contour length of the polymer. At heights $Z \sim L$ the lift force displays a maximum, and for $Z>L$ we recover the well known far-field result in which the force decays as $Z^{-2}$. Our analytical theory has important implications in understanding adsorption, desorption, and depletion layers of highly extended objects in flow.