Roughness induced boundary slip in microchannel flows

Surface roughness becomes relevant if typical length scales of the system are comparable to the scale of the variations as it is the case in microfluidic setups. Here, an apparent boundary slip is often detected which can have its origin in the assumption of perfectly smooth boundaries. We investigate the problem by means of lattice Boltzmann (LB) simulations and introduce an ``effective no-slip plane'' at an intermediate position between peaks and valleys of the surface. Our simulations show good agreement with analytical results for sinusoidal boundaries, but can be extended to arbitrary geometries and experimentally obtained surface data. We find that the detected apparent slip is independent of the detailed boundary shape, but only given by the distribution of surface heights. Further, we show that the slip diverges as the amplitude of the roughness increases.Comment: 4 pages, 6 figure

Tensorial hydrodynamic slip

We describe a tensorial generalization of the Navier slip boundary condition and illustrate its use in solving for flows around anisotropic textured surfaces. Tensorial slip can be derived from molecular or microstructural theories or simply postulated as an constitutive relation, subject to certain general constraints on the interfacial mobility. The power of the tensor formalism is to capture complicated effects of surface anisotropy, while preserving a simple fluid domain. This is demonstrated by exact solutions for laminar shear flow and pressure-driven flow between parallel plates of arbitrary and different textures. From such solutions, the effects of rotating a texture follow from simple matrix algebra. Our results may be useful to extracting local slip tensors from global measurements, such as the permeability of a textured channel or the force required to move a patterned surface, in experiments or simulations.Comment: 10 page

Simulation of fluid flow in hydrophobic rough microchannels

Surface effects become important in microfluidic setups because the surface to volume ratio becomes large. In such setups the surface roughness is not any longer small compared to the length scale of the system and the wetting properties of the wall have an important influence on the flow. However, the knowledge about the interplay of surface roughness and hydrophobic fluid-surface interaction is still very limited because these properties cannot be decoupled easily in experiments. We investigate the problem by means of lattice Boltzmann (LB) simulations of rough microchannels with a tunable fluid-wall interaction. We introduce an ``effective no-slip plane'' at an intermediate position between peaks and valleys of the surface and observe how the position of the wall may change due to surface roughness and hydrophobic interactions. We find that the position of the effective wall, in the case of a Gaussian distributed roughness depends linearly on the width of the distribution. Further we are able to show that roughness creates a non-linear effect on the slip length for hydrophobic boundaries.Comment: 10 pages, 5 figure

Longitudinal and transversal flow over a cavity containing a second immiscible fluid

An analytical solution for the flow field of a shear flow over a rectangular cavity containing a second immiscible fluid is derived. While flow of a single-phase fluid over a cavity is a standard case investigated in fluid dynamics, flow over a cavity which is filled with a second immiscible fluid, has received little attention. The flow filed inside the cavity is considered to define a boundary condition for the outer flow which takes the form of a Navier slip condition with locally varying slip length. The slip-length function is determined from the related problem of lid-driven cavity flow. Based on the Stokes equations and complex analysis it is then possible to derive a closed analytical expression for the flow field over the cavity for both the transversal and the longitudinal case. The result is a comparatively simple function, which displays the dependence of the flow field on the cavity geometry and the medium filling the cavity. The analytically computed flow field agrees well with results obtained from a numerical solution of the Navier-Stokes equations. The studies presented in this article are of considerable practical relevance, for example for the flow over superhydrophobic surfaces.Comment: http://journals.cambridge.or

Slip or not slip? A methodical examination of the interface formation model using two-dimensional droplet spreading on a horizontal planar substrate as a prototype system

We consider the spreading of a thin two-dimensional droplet on a planar substrate as a prototype system to compare the contemporary model for contact line motion based on interface formation of Shikhmurzaev [Int. J. Multiphas. Flow 19, 589 (1993)], to the more commonly used continuum fluid dynamical equations augmented with the Navier-slip condition. Considering quasistatic droplet evolution and using the method of matched asymptotics, we find that the evolution of the droplet radius using the interface formation model reduces to an equivalent expression for a slip model, where the prescribed microscopic dynamic contact angle has a velocity dependent correction to its static value. This result is found for both the original interface formation model formulation and for a more recent version, where mass transfer from bulk to surface layers is accounted for through the boundary conditions. Various features of the model, such as the pressure behaviour and rolling motion at the contact line, and their relevance, are also considered in the prototype system we adopt.Comment: 45 pages, 18 figure

Cyclic motion and inversion of surface flow direction in a dense polymer brush under shear

Using molecular simulations, we study the properties of a polymer brush in contact with an explicit solvent under Couette and Poiseuille flow. The solvent is comprised of chemically identical chains. We present evidence that individual, unentangled chains in the dense brush exhibit cyclic, tumbling motion and non-Gaussian fluctuations of the molecular orientations similar to the behaviour of isolated tethered chains in shear flow. The collective molecular motion gives rise to an inversion of hydrodynamic flow direction in the vicinity of the brush-coated surface. Utilising Couette and Poiseuille flow, we investigate to what extend the effect of a brush-coated surface can be described by a Navier slip condition.Comment: 6 pages, 6 figures, submitted for publicatio

Measurement of Newtonian fluid slip using a torsional ultrasonic oscillator

The composite torsional ultrasonic oscillator, a versatile experimental system, can be used to investigate slip of Newtonian fluid at a smooth surface. A rigorous analysis of slip-dependent damping for the oscillator is presented. Initially, the phenomenon of finite surface slip and the slip length are considered for a half-space of Newtonian fluid in contact with a smooth, oscillating solid surface. Definitions are revisited and clarified in light of inconsistencies in the literature. We point out that, in general oscillating flows, Navier's slip length b is a complex number. An intuitive velocity discontinuity parameter of unrestricted phase is used to describe the effect of slip on measurement of viscous shear damping. The analysis is applied to the composite oscillator and preliminary experimental work for a 40 kHz oscillator is presented. The Non-Slip Boundary Condition (NSBC) has been verified for a hydrophobic surface in water to within ~60 nm of |b|=0 nm. Experiments were carried out at shear rate amplitudes between 230 and 6800 /s, corresponding to linear displacement amplitudes between 3.2 and 96 nm.Comment: Revised with minor edits for revie

Hydraulic engineering legends Listed on the Eiffel Tower

While the Eiffel Tower has become a landmark of Paris and France, few know about the names of 72 scientists engraved around the first floor. Herein, the names of 14 hydraulic engineers and scholars are reviewed and their selection is discussed. It is shown that most were leading engineers and lecturers during the French Revolution and early 19th century, and Gustave Eiffel's selection highlighted the influence of leading engineers on the French Society

Statics and dynamics of a cylindrical droplet under an external body force

We study the rolling and sliding motion of droplets on a corrugated substrate by Molecular Dynamics simulations. Droplets are driven by an external body force (gravity) and we investigate the velocity profile and dissipation mechanisms in the steady state. The cylindrical geometry allows us to consider a large range of droplet sizes. The velocity of small droplets with a large contact angle is dominated by the friction at the substrate and the velocity of the center of mass scales like the square root of the droplet size. For large droplets or small contact angles, however, viscous dissipation of the flow inside the volume of the droplet dictates the center of mass velocity that scales linearly with the size. We derive a simple analytical description predicting the dependence of the center of mass velocity on droplet size and the slip length at the substrate. In the limit of vanishing droplet velocity we quantitatively compare our simulation results to the predictions and good agreement without adjustable parameters is found.Comment: Submitted to the Journal of Chemical Physic