Influence of lift forces on particle capture on a functionalized surface

Numerous situations involve the capture of particles onto a functionalized surface in a laminar flow, such as classical biomedical assays, lab on a chip devices or even biological research protocols. Being able to control this capture is thus an important issue that we address in this paper. We focus on a simple and widely used geometry, the straight microfluidic channel, in which particles undergo two weak effects: diffusion towards the functionalized surface and lift forces expelling them away from it. We show that the competition between these two weak mechanisms yields strongly different capture behavior whose occurrence depends on the value of a new lifto-diffusive dimensionless number N-LD. We show that tuning the flow rate and the channel dimension to get proper values of this number allow to trigger, via a pure hydrodynamic effect, the capture or non-capture of particles on surfaces. For example, we show that, under certain conditions, doubling the flow rate reduces the capture rate by four orders of magnitude. Additionally, we provide the particle distribution in the liquid along the channel, resulting from this competition, for different N-LD values. We believe that this work opens new perspectives for analysis and biotechnology applications. More precisely, the proposed model should extend to any transverse force that can be written in the form of a potential energy.