Abstract. We discuss how the wettability and roughness of a solid impacts its hydrodynamic properties. We see in particular that hydrophobic slippage can be dramatically affected by the presence of roughness. Owing to the development of refined methods for setting very well-controlled micro-or nanotextures on a solid, these effects are being exploited to induce novel hydrodynamic properties, such as giant interfacial slip, superfluidity, mixing, and low hydrodynamic drag, that could not be achieved without roughness.

Super-hydrophobic array of grooves containing trapped gas (stripes), have the potential to greatly reduce drag and enhance mixing phenomena in microfluidic devices. Recent work has focused on idealized cases of stick-perfect slip stripes. Here, we analyze the experimentally more relevant situation of a pressure-driven flow past striped slip-stick surfaces with arbitrary local slip at the gas sectors. We derive approximate formulas for maximal (longitudinal) and minimal (transverse) directional effective slip lengths, that are in a good agreement with the exact numerical solution for any surface slip fraction. By representing eigenvalues of the slip length-tensor, they allow us to obtain the effective slip for any orientation of stripes with respect to the mean flow. Our results imply that flow past stripes is controlled by the ratio of the local slip length to texture size. In case of a large (compared to the texture period) slip at the gas areas, surface anisotropy leads to a tensorial effective slip, by attaining the values predicted earlier for a perfect local slip. Both effective slip lengths and anisotropy of the flow decrease when local slip becomes of the order of texture period. In the case of small slip, we predict simple surface-averaged, isotropic flows (independent of orientation).

Surface conduction in presence of slip is characterized by full Dukhin number, which is given by [1]:where m = 2ε(k B T /ze) 2 /(ηD), and D is the ion diffusivity, which is assumed equal for both types of ions. The first term in (1) is the Dukhin number for the no-slip surface, Du b=0 , while the second one, Du b , is due to hydrodynamic slip. In the Debye-Hückel modelThis restriction (2) allows the simplification:The parameter m ≈ 100/z 2 , and κL ≫ 1 since EDL is thin. Whence Du b=0 ≈ 1/(z 2 κL) ≪ 1 provided the potential is low. For a "slippery part" of Du we evaluate01. Therefore for increasing surface charge (potential) and b/L, the conductivity of the diffuse layer can become comparable to the bulk, and surface condition must be considered. The Péclet number, P e = U L/D , in presence of slip can be evaluated asTypically, electroosmotic velocity is of order is of order micrometers per second for no-slip surfaces [2]. For nanoscale patterns L < 1 µm and typical ion diffusivities D ≈ 10 −6 cm 2 /s this gives P e b=0 < 0.01 ≪ 1. The slip implies a correction factor (1 + bκ) , which suggests that the convective ion transport can safely be neglected only for bκ < 10. Larger values of bκ should relax this standard approximation of small P e. ELECTRO-OSMOTIC VELOCITY IN EIGENDIRECTIONSLongitudinal stripes.-In this configuration only x−velocity component remains, and the Stokes equation takes the formWe expand surface charge density in a Fourier series, and the potential is thenwhere ξ n = κ 2 + λ 2 n , λ n = 2nπ/L , q = q 1 φ 1 + q 2 φ 2 is the mean surface charge, andThe general solution to (6) for u(y, z) has the formwhere U n and U are determined by the slip boundary conditions. Imposing them on (9) in a thin EDL limit yields a dual serieswhich can be solved exactly by using a technique [3] to obtain the thin-EDL electro-osmotic velocity:Transverse stripes.-Although an external pressure gradient is equal to zero, local pressure variations contribute into a non-zero term ∇p in the Stokes equation, so that the flow is essentially two-dimensional. We first introduce a stream function f (x, y)2 which obeys inhomogeneous biharmonic equation:Here u and v are x and y velocity components, correspondingly. The general periodic solution to (14) has the formE t q n κ 2 η + g n y e −λny cos λ n x + + E t ε κ 2 η ∂ψ ∂y (15)Here the potential ψ(x, y) has exactly the form (7) with z replaced by x. The dual series problem in a thin EDL limit can be written aswhere a n = g n + E t q n ηκ 2 (ξ n − λ n ).These dual series can be solved exactly to obtainWe emphasize that a comparison of Eqs. (12) and (18) indicates that the EO flow is generally anisotropic, so that our results do not support an earlier conclusion [4] that the electro-osmotic mobility tensor is isotropic in the thin EDL limit. This inconsistensy [4] (due to an erroneous expression for a transverse electro-osmotic velocity, where factor of 2 was lost) has been corrected for a case b 2 = ∞ in [5]. Sciences, 31 Leninsky Prospect, 119991 Moscow, Russia 3 ITMC and...

We show that an electro-osmotic flow near the slippery hydrophobic surface depends strongly on the mobility of surface charges, which are balanced by counterions of the electrostatic diffuse layer. For a hydrophobic surface with immobile charges, the fluid transport is considerably amplified by the existence of a hydrodynamic slippage. In contrast, near the hydrophobic surface with mobile adsorbed charges, it is also controlled by an additional electric force, which increases the shear stress at the slipping interface. To account for this, we formulate electrohydrodynamic boundary conditions at the slipping interface, which should be applied to quantify electro-osmotic flows instead of hydrodynamic boundary conditions. Our theoretical predictions are fully supported by dissipative particle dynamics simulations with explicit charges. These results lead to a new interpretation of zeta potential of hydrophobic surfaces.

We describe a generalization of the tensorial slip boundary condition, originally justified for a thick (compared to texture period) channel, to any channel thickness. The eigenvalues of the effective slip-length tensor, however, in general case become dependent on the gap and cannot be viewed as a local property of the surface, being a global characteristic of the channel. To illustrate the use of the tensor formalism we develop a semianalytical theory of an effective slip in a parallel-plate channel with one superhydrophobic striped and one hydrophilic surface. Our approach is valid for any local slip at the gas sectors and an arbitrary distance between the plates, ranging from a thick to a thin channel. We then present results of lattice Boltzmann simulations to validate the analysis. Our results may be useful for extracting effective slip tensors from global measurements, such as the permeability of a channel, in experiments or simulations.

Hemostasis is a complex physiological mechanism that functions to maintain vascular integrity under any conditions. Its primary components are blood platelets and a coagulation network that interact to form the hemostatic plug, a combination of cell aggregate and gelatinous fibrin clot that stops bleeding upon vascular injury. Disorders of hemostasis result in bleeding or thrombosis, and are the major immediate cause of mortality and morbidity in the world. Regulation of hemostasis and thrombosis is immensely complex, as it depends on blood cell adhesion and mechanics, hydrodynamics and mass transport of various species, huge signal transduction networks in platelets, as well as spatiotemporal regulation of the blood coagulation network. Mathematical and computational modeling has been increasingly used to gain insight into this complexity over the last 30 years, but the limitations of the existing models remain profound. Here we review state-of-the-art-methods for computational modeling of thrombosis with the specific focus on the analysis of unresolved challenges. They include: a) fundamental issues related to physics of platelet aggregates and fibrin gels; b) computational challenges and limitations for solution of the models that combine cell adhesion, hydrodynamics and chemistry; c) biological mysteries and unknown parameters of processes; d) biophysical complexities of the spatiotemporal networks' regulation. Both relatively classical approaches and innovative computational techniques for their solution are considered; the subjects discussed with relation to thrombosis modeling include coarse-graining, continuum versus particle-based modeling, multiscale models, hybrid models, parameter estimation and others. Fundamental understanding gained from theoretical models are highlighted and a description of future prospects in the field and the nearest possible aims are given.

We report results of dissipative particle dynamics simulations and develop a semi-analytical theory of an anisotropic flow in a parallel-plate channel with two superhydrophobic striped walls. Our approach is valid for any local slip at the gas sectors and an arbitrary distance between the plates, ranging from a thick to a thin channel. It allows us to optimize area fractions, slip lengths, channel thickness and texture orientation to maximize a transverse flow. Our results may be useful for extracting effective slip tensors from global measurements, such as the permeability of a channel, in experiments or simulations, and may also find applications in passive microfluidic mixing.

We analyze theoretically a high-speed drainage of liquid films squeezed between a hydrophilic sphere and a textured superhydrophobic plane that contains trapped gas bubbles. A superhydrophobic wall is characterized by parameters L (texture characteristic length), b1 and b2 (local slip lengths at solid and gas areas), and φ1 and φ2 (fractions of solid and gas areas). Hydrodynamic properties of the plane are fully expressed in terms of the effective slip-length tensor with eigenvalues that depend on texture parameters and H (local separation). The effect of effective slip is predicted to decrease the force as compared with what is expected for two hydrophilic surfaces and described by the Taylor equation. The presence of additional length scales, L, b1, and b2, implies that a film drainage can be much richer than in the case of a sphere moving toward a hydrophilic plane. For a large (compared to L) gap the reduction of the force is small, and for all textures the force is similar to expected when a sphere is moving toward a smooth hydrophilic plane that is shifted down from the superhydrophobic wall. The value of this shift is equal to the average of the eigenvalues of the slip-length tensor. By analyzing striped superhydrophobic surfaces, we then compute the correction to the Taylor equation for an arbitrary gap. We show that at a thinner gap the force reduction becomes more pronounced, and that it depends strongly on the fraction of the gas area and local slip lengths. For small separations we derive an exact equation, which relates a correction for effective slip to texture parameters. Our analysis provides a framework for interpreting recent force measurements in the presence of a superhydrophobic surface.