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

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

Effective slip boundary conditions for flows over nanoscale chemical heterogeneities

We study slip boundary conditions for simple fluids at surfaces with nanoscale chemical heterogeneities. Using a perturbative approach, we examine the flow of a Newtonian fluid far from a surface described by a heterogeneous Navier slip boundary condition. In the far-field, we obtain expressions for an effective slip boundary condition in certain limiting cases. These expressions are compared to numerical solutions which show they work well when applied in the appropriate limits. The implications for experimental measurements and for the design of surfaces that exhibit large slip lengths are discussed.Comment: 14 pages, 3 figure

Lattice Boltzmann simulations of apparent slip in hydrophobic microchannels

Various experiments have found a boundary slip in hydrophobic microchannel flows, but a consistent understanding of the results is still lacking. While Molecular Dynamics (MD) simulations cannot reach the low shear rates and large system sizes of the experiments, it is often impossible to resolve the needed details with macroscopic approaches. We model the interaction between hydrophobic channel walls and a fluid by means of a multi-phase lattice Boltzmann model. Our mesoscopic approach overcomes the limitations of MD simulations and can reach the small flow velocities of known experiments. We reproduce results from experiments at small Knudsen numbers and other simulations, namely an increase of slip with increasing liquid-solid interactions, the slip being independent of the flow velocity, and a decreasing slip with increasing bulk pressure. Within our model we develop a semi-analytic approximation of the dependence of the slip on the pressure.Comment: 7 pages, 4 figure

The Dynamics of Liquid Drops and their Interaction with Solids of Varying Wettabilites

Microdrop impact and spreading phenomena are explored as an interface formation process using a recently developed computational framework. The accuracy of the results obtained from this framework for the simulation of high deformation free-surface flows is confirmed by a comparison with previous numerical studies for the large amplitude oscillations of free liquid drops. Our code's ability to produce high resolution benchmark calculations for dynamic wetting flows is then demonstrated by simulating microdrop impact and spreading on surfaces of greatly differing wettability. The simulations allow one to see features of the process which go beyond the resolution available to experimental analysis. Strong interfacial effects which are observed at the microfluidic scale are then harnessed by designing surfaces of varying wettability that allow new methods of flow control to be developed

Effect of Patterned Slip on Micro and Nanofluidic Flows

We consider the flow of a Newtonian fluid in a nano or microchannel with walls that have patterned variations in slip length. We formulate a set of equations to describe the effects on an incompressible Newtonian flow of small variations in slip, and solve these equations for slow flows. We test these equations using molecular dynamics simulations of flow between two walls which have patterned variations in wettability. Good qualitative agreement and a reasonable degree of quantitative agreement is found between the theory and the molecular dynamics simulations. The results of both analyses show that patterned wettability can be used to induce complex variations in flow. Finally we discuss the implications of our results for the design of microfluidic mixers using slip.Comment: 13 pages, 12 figures, final version for publicatio

Equilibrium Simulation of the Slip Coefficient in Nanoscale Pores

Accurate prediction of interfacial slip in nanoscale channels is required by many microfluidic applications. Existing hydrodynamic solutions based on Maxwellian boundary conditions include an empirical parameter that depends on material properties and pore dimensions. This paper presents a derivation of a new expression for the slip coefficient that is not based on the assumptions concerning the details of solid-fluid collisions and whose parameters are obtainable from \textit{equilibrium} simulation. The results for the slip coefficient and flow rates are in good agreement with non-equilibrium molecular dynamics simulation.Comment: 11 pages, 4 figures, submitted to Phys Rev Let

Giant slip lengths of a simple fluid at vibrating solid interfaces

It has been shown recently [PRL 102, 254503 (2009)] that in the plane-plane configuration a mechanical resonator vibrating close to a rigid wall in a simple fluid can be overdamped to a frozen regime. Here, by solving analytically the Navier Stokes equations with partial slip boundary conditions at the solid fluid interface, we develop a theoretical approach justifying and extending these earlier findings. We show in particular that in the perfect slip regime the above mentioned results are, in the plane-plane configuration, very general and robust with respect to lever geometry considerations. We compare the results with those obtained previously for the sphere moving perpendicularly and close to a plane in a simple fluid and discuss in more details the differences concerning the dependence of the friction forces with the gap distance separating the moving object (i.e., plane or sphere) from the fixed plane. Finally, we show that the submicron fluidic effect reported in the reference above, and discussed further in the present work, can have dramatic implications in the design of nano-electromechanical systems (NEMS).Comment: submitted to PRE (see also PRL 102, 254503 (2009)

Statics of polymer droplets on deformable surfaces

The equilibrium properties of polymer droplets on a soft deformable surface are investigated by molecular dynamics simulations of a bead-spring model. The surface consists of a polymer brush with irreversibly end-tethered linear homopolymer chains onto a flat solid substrate. We tune the softness of the surface by varying the grafting density. Droplets are comprised of bead-spring polymers of various chain lengths. First, both systems, brush and polymer liquid, are studied independently in order to determine their static and dynamic properties. In particular, using a numerical implementation of an AFM experiment, we measure the shear modulus of the brush surface and compare the results to theoretical predictions. Then, we study the wetting behavior of polymer droplets with different contact angles and on substrates that differ in softness. Density profiles reveal, under certain conditions, the formation of a wetting ridge beneath the three-phase contact line. Cap-shaped droplets and cylindrical droplets are also compared to estimate the effect of the line tension with respect to the droplet size. Finally, the results of the simulations are compared to a phenomenological free-energy calculation that accounts for the surface tensions and the compliance of the soft substrate. Depending on the surface/drop compatibility, surface softness and drop size, a transition between two regimes is observed: from one where the drop surface energy balances the adhesion with the surface, which is the classical Young-Dupr\'e wetting regime, to another one where a coupling occurs between adhesion, droplet and surface elastic energies.Comment: 13 pages, 11 figure