Effect of Surfactant on Retention Behaviors of Polystyrene Latex Particles in Sedimentation Field-Flow Fractionation: Effective Boundary Slip Model Approach

Abstract

A retention theory in sedimentation field-flow fractionation (SdFFF) was developed by exploiting the effective slip boundary condition (BC) that allows a finite velocity for particles to have at the wall, thereby alleviating the limitations set by the no-slip BC constraint bound to the standard retention theory (SRT). This led to an expression for the retention ratio R as R = (R(o) + v*(b))/(R(o) + v*(b)), where R(o) is the sterically corrected SRT retention ratio and v*(b) is the reduced boundary velocity. Then, v*(b) was modeled as v*(b) = v*(b,o)/[1 + (7K*S(o))(1/2)], where S(o) is the surfactant (FL-70) concentration and K* is the distribution coefficient associated with the langmuirian isotherm of the apparent effective mass against S(o). We applied this to study the surfactant effect on the retention behaviors of polystyrene (PS) latex beads of 170-500 nm in diameter. As a result, an empirical relation was found to hold between v*(b,o) and d(o) (estimated from R(o) at S(o) = 0) as v*(b,o) - v*(o,o)[1 - (d(c)/d(o))], where v*(o,o) is the asymptotic value of v*(b,o) in the vanishing d(c)/d(o) limit and d(c) is the cutoff value at which v*(b,o) would vanish. According to the present approach, the no-slip BC (v*(b,o) = 0) was predicted to recover when d(o) ∼ d(c), and the boundary slip effect could be significant for S(o) ≤ 0.05%, particularly for large latex beads.