Continuous electroosmotic sorting of particles in grooved microchannels.

We propose a novel microfluidic fractionation concept suitable for neutrally buoyant micron-sized particles. This approach takes advantage of the ability of grooved channel walls oriented at an angle to the direction of an external electric field to generate a transverse electroosmotic flow. Using computer simulations, we first demonstrate that the velocity of this secondary transverse flow depends on the distance from the wall, so neutrally buoyant particles, depending on their size and initial location, will experience different lateral displacements. We then optimize the geometry and orientation of the surface texture of the channel walls to maximize the efficiency of particle fractionation. Our method is illustrated in a full scale computer experiment where we mimic the typical microchannel with a bottom grooved wall and a source of polydisperse particles that are carried along the channel by the forward electroosmotic flow. Our simulations show that the particle dispersion can be efficiently separated by size even in a channel that is only a few texture periods long. These results can guide the design of novel microfluidic devices for efficient sorting of microparticles.

Probing effective slippage on superhydrophobic stripes by atomic force microscopy.

While the effective slippage of water past superhydrophobic surfaces has been studied over a decade, theoretical predictions have never been properly confirmed by experiments. Here we measure a drag force on a sphere approaching a plane decorated by superhydrophobic grooves and compare the results with the predictions of semi-analytical theory developed here, which employs the gas cushion model to calculate the local slip length at the gas sectors. We demonstrate that at intermediate and large (compared to a texture period) separations the half-sum of longitudinal and transverse effective slip lengths can be deduced from the force-distance curve by using the known analytical theory of hydrodynamic interaction of a sphere with a homogeneous slipping plane. This half-sum is shown to depend on the fraction of gas sectors and its value is in excellent agreement with theoretical predictions. At small distances the half-sum of effective longitudinal and transverse slip lengths becomes separation-dependent, and is in quantitative agreement with the predictions of our semi-analytical theory.

Contact angle hysteresis on superhydrophobic stripes.

We study experimentally and discuss quantitatively the contact angle hysteresis on striped superhydrophobic surfaces as a function of a solid fraction, ϕS. It is shown that the receding regime is determined by a longitudinal sliding motion of the deformed contact line. Despite an anisotropy of the texture the receding contact angle remains isotropic, i.e., is practically the same in the longitudinal and transverse directions. The cosine of the receding angle grows nonlinearly with ϕS. To interpret this we develop a theoretical model, which shows that the value of the receding angle depends both on weak defects at smooth solid areas and on the strong defects due to the elastic energy of the deformed contact line, which scales as ϕS(2)lnϕS. The advancing contact angle was found to be anisotropic, except in a dilute regime, and its value is shown to be determined by the rolling motion of the drop. The cosine of the longitudinal advancing angle depends linearly on ϕS, but a satisfactory fit to the data can only be provided if we generalize the Cassie equation to account for weak defects. The cosine of the transverse advancing angle is much smaller and is maximized at ϕS ≃ 0.5. An explanation of its value can be obtained if we invoke an additional energy due to strong defects in this direction, which is shown to be caused by the adhesion of the drop on solid sectors and is proportional to ϕS(2). Finally, the contact angle hysteresis is found to be quite large and generally anisotropic, but it becomes isotropic when ϕS ≤ 0.2.

Lattice-Boltzmann simulations of the drag force on a sphere approaching a superhydrophobic striped plane.

By means of lattice-Boltzmann simulations the drag force on a sphere of radius R approaching a superhydrophobic striped wall has been investigated as a function of arbitrary separation h. Superhydrophobic (perfect-slip vs. no-slip) stripes are characterized by a texture period L and a fraction of the gas area ϕ. For very large values of h/R, we recover the macroscopic formulae for a sphere moving towards a hydrophilic no-slip plane. For h/R = O(1), the drag force is smaller than predicted by classical theories for hydrophilic no-slip surfaces, but larger than expected for a sphere interacting with a uniform perfectly slipping wall. At a thinner gap, h ≪ R the force reduction compared to a classical result becomes more pronounced, and is maximized by increasing ϕ. In the limit of very small separations, our simulation data are in quantitative agreement with an asymptotic equation, which relates a correction to a force for superhydrophobic slip to texture parameters. In addition, we examine the flow and pressure field and observe their oscillatory character in the transverse direction in the vicinity of the wall, which reflects the influence of the heterogeneity and anisotropy of the striped texture. Finally, we investigate the lateral force on the sphere, which is detectable in case of very small separations and is maximized by stripes with ϕ = 0.5.

Principles of transverse flow fractionation of microparticles in superhydrophobic channels.

We propose a concept of fractionation of micron-sized particles in a microfluidic device with a bottom wall decorated by superhydrophobic stripes. The stripes are oriented at an angle α to the direction of a driving force, G, which generally includes an applied pressure gradient and gravity. Separation relies on the initial sedimentation of particles under gravity in the main forward flow, and their subsequent lateral deflection near a superhydrophobic wall due to generation of a secondary flow transverse to G. We provide some theoretical arguments allowing us to quantify the transverse displacement of particles in the microfluidic channel, and confirm the validity of theoretical predictions in test experiments with monodisperse fractions of microparticles. Our results can guide the design of superhydrophobic microfluidic devices for efficient sorting of microparticles with a relatively small difference in size and density.