Hydrodynamic Drainage Forces Research Articles

Large Effective Slip on Lubricated Surfaces Measured with Colloidal Probe AFM.

In this work, we study the interfacial boundary conditions at the interface between two immiscible liquids under a laminar flow. We measure the hydrodynamic drainage forces acting on a colloid probe as it approaches a flat and smooth Teflon film coated with silicone oil films, submerged in a sucrose solution using atomic force microscopy. On Teflon substrates, silicone oil films of thickness several hundred nanometers could be stabilized, and we found the effective slip length over these to be of the order of several hundred nanometers which increases with increasing silicone oil film thickness, as expected. The fitted slip length values weakly increased with increasing shear rates. The high values of effective slip length indicate that lubricant-infused surfaces are likely to reduce drag on length scales that approach the macroscopic scales.

Forces between oil drops in polymer-surfactant systems: Linking direct force measurements to microfluidic observations

HypothesisLinking atomic force microscopy and microfluidics opens up the possibility of probing adhesive interactions between drops in a high-throughput context. A microfluidic device designed to form, and subsequently break-up, chains of drops, where the drop break-up is sensitive to the underlying surface forces between drops, not hydrodynamic drainage forces, would play a key role in developing this link. ExperimentsBoth techniques have been used to quantify the forces between oil drops in the presence of complexes formed with anionic surfactant, sodium dodecylsulphate, and neutral, water soluble polymer, poly(vinylpyrrolidone). Measurement and modelling of the interaction forces between both rigid and deformable surfaces demonstrated that the attraction between the drops is due to depletion forces, whereas the repulsive force is a combination of electrical double layer and steric forces, indicating complexes exist both in the bulk and at the drop interface. FindingsThe interaction behaviour between the force measurements and the microfluidic observations showed a strong correlation, where the observed adhesion between drops in the microfluidics is sensitive to the drop deformation and Laplace pressure. Correlation between the two techniques provides insight into the surface forces between drops in flowing systems and has potential utility in the formulation of emulsions.

How Slippery are SLIPS? Measuring Effective Slip on Lubricated Surfaces with Colloidal Probe Atmoc Force Microscopy.

Lubricant-infused surfaces have attracted great attention recently and are described as slippery liquid-infused porous surfaces (SLIPS). Here, we measured the hydrodynamic drainage forces on SLIPS by colloid probe atomic force microscopy (AFM) and quantified the effective slip length over a nanothin silicone oil layer on hydrophobized [octadecyltrichlorosilane (OTS)-coated] silicon wafers. The thickness of a stable silicone oil film on OTS-Si under sucrose solution was determined to be 1.8 ± 1.3 nm and was found to induce an average effective slip length of 29 ± 3 nm, very close to that of an uninfused OTS substrate. These relatively low values of effective slip are confirmed by the relatively large macroscopic roll-off angle values of water droplets on the same substrates. Both nano- and macroscale results reflect the immobilized nature of a silicone oil layer of thickness around 2 nm within an underlying monolayer. These results have important implications in the design of drag-reducing coatings using lubricant infusion.

Scaling Hydrodynamic Boundary Conditions of Microstructured Surfaces in the Thin Channel Limit

Despite its importance in many applications and processes, a complete and unified view on how nano- and microscale asperities influence hydrodynamic interactions has yet to be reached. In particular, the effects of surface structure can be expected to become more dominant when the length scale of the asperities or textures becomes comparable to that of the fluid flow. Here we analyze the hydrodynamic drainage of a viscous silicone oil squeezed between a smooth plane and a surface decorated with hexagonal arrays of lyophilic microsized cylindrical posts. For all micropost arrays studied, the periodicity of the structures was much larger than the separation range of our measurements. In this thin channel geometry, we find the hydrodynamic drainage and separation forces for the micropost arrays cannot be fully described by existing boundary condition models for interfacial slip or a no-slip shifted plane. Instead, our results show that the influence of the microposts on the hydrodynamic drag exhibits three distinct regimes as a function of separation. For large separations, a no slip boundary condition (Reynolds theory) is observed for all surfaces until a critical (intermediate) separation, below which the position of the no-slip plane scales with surface separation until reaching a maximum, just before contact. Below this separation, a sharp decrease in the no-slip plane position then suggests that a boundary condition of a smooth surface is recovered at contact.

Boundary flow on end-grafted PEG brushes.

We investigated the boundary conditions for flow of a Newtonian liquid over soft interfaces by measuring hydrodynamic drainage forces with colloid probe atomic force microscopy in a viscous liquid. The investigated soft surfaces are end-grafted brushes of thiolated poly(ethylene glycol) (PEG), of molecular weight 1k and 30k, grafted-to gold. The conditions for brush preparation were optimized as to meet the stringent conditions required for surface force measurements, namely reproducible and uniform surface composition and roughness. The fit of a slip model to the experimental data returned a slip length of 16 nm on the PEG 1k brush and 25 nm on the PEG30k brush. The slip length can be interpreted as a penetration length, which accounts for flow within the top half of the brush for the PEG30k case, and within the brush and surface roughness for the PEG1k case. These findings confirm earlier simulation studies by our group on the flow of liquids within polymer brushes.

Hydrodynamic force between a sphere and a soft, elastic surface.

The hydrodynamic drainage force between a spherical silica particle and a soft, elastic polydimethylsiloxane surface was measured using the colloidal probe technique. The experimental force curves were compared to finite element simulations and an analytical model. The hydrodynamic repulsion decreased when the particle approached the soft surface as compared to a hard substrate. In contrast, when the particle was pulled away from the surface again, the attractive hydrodynamic force was increased. The hydrodynamic attraction increased because the effective area of the narrow gap between sphere and the plane on soft surfaces is larger than on rigid ones.

Measurement and Scaling of Hydrodynamic Interactions in the Presence of Draining Channels

Central to the adhesion and locomotion of tree frogs are their structured toe pads, which consist of an array of 10 μm hexagonal epithelial cells separated by interconnected channels that are 1 μm wide and 10 μm deep. It has been proposed that the channels facilitate the drainage of excess fluid trapped between the toe pads and the contacting surface, and thus reduce the hydrodynamic repulsion during approach. We performed direct force measurement of the normal hydrodynamic interactions during the drainage of fluid from the gap between a structured and a smooth surface using surface force apparatus. The structured surface consisted of a hexagonal array of cylindrical posts to represent the network of interconnected channels. The measured hydrodynamic drainage forces agree with the predictions from Reynolds' theory for smooth surfaces at large separations. Deviations from theory, characterized by a reduction in the hydrodynamic repulsion, are observed below some critical separation (h(c)), which is independent of drive velocity. We employ a scaling analysis to establish the relationship between structural features (channel depth, width, and post diameter) and the critical separation for the onset of deviations. We find agreement between our experiments and the scaling analysis, which allows us to estimate a characteristic length scale that corresponds to the transition from the fluid being radially squeezed out of the nominal contact area to being squeezed out through the network of interconnected channels.

Reliable Measurements of Interfacial Slip by Colloid Probe Atomic Force Microscopy. II. Hydrodynamic Force Measurements

Here we report a new study on the boundary conditions for the flow of a simple liquid in a confined geometry obtained by measuring hydrodynamic drainage forces with colloid probe atomic force microscopy (AFM). In this work, we provide experimental data obtained using a best practice experimental protocol and fitted with a new theoretical calculation (Zhu, L.; Attard, P.; Neto, C. Langmuir 2010, submitted for publication, preceding paper). We investigated the hydrodynamic forces acting on a silica colloid probe approaching a hydrophobized silicon surface in a single-component viscous Newtonian liquid (di-n-octylphthalate), a partially wetting system. The measured average slip lengths were in the range of 24-31 nm at approach velocities of between 10 and 80 μm/s. Using our experimental approach, the presence of nanoparticle contaminants in the system can be indentified, which is important because it has been shown that nanoparticles lead to a large apparent slip length. Under our stringent control of experimental conditions, the measurement of the slip length is reproducible and independent of the spring constant of the cantilever.

Viscosity Effects on Hydrodynamic Drainage Force Measurements Involving Deformable Bodies

Dynamic force measurements have been made between an oil drop and a silica particle in surfactant and sucrose solutions with viscosities that range up to 50 times that of water. These conditions provide variations in the shear rate and the relative time scales of droplet deformation and hydrodynamic drainage in a soft matter system. The results obtained indicate that soft deformable boundaries have a natural response that limits the maximum shear rate that can be sustained in thin films compared to shear rates that can be attained in films bounded by rigid boundaries. In addition, to extend boundary slip studies on rigid surfaces, we use a smooth deformable droplet surface to probe the dependence of the boundary slip on fluid viscosity without the added complications of surface roughness or heterogeneity. Imposing a Navier slip model to characterize possible slip at the deformable oil-sucrose solution interface gives results that are consistent with a slip length of no larger than 10 nm over the range of solution viscosity studied, although an immobile (zero slip length) condition at the oil-sucrose solution interface is perfectly adequate. In high viscosity solutions, cantilever motion at high scan rates induces a significant cantilever deflection. A method has been developed to account for this effect in order to extract the correct dynamic force between the deformable drop and the particle.

Hydrodynamic drainage force in a highly confined geometry: role of surface roughness on different length scales

We measured the hydrodynamic drainage force of an aqueous, Newtonian liquid squeezed between two hydrophobic or two hydrophilic surfaces by means of the colloidal probe technique. We controlled the wettability, the roughness, the topology, and also the approaching velocity of the surfaces. We found that asperities on the surfaces caused an artificial decrease of the measured drainage force that must be considered by the interpretation of the force curves. Even considering the effect of asperities, our experimental results could be interpreted only with the aid of a partial slip model. Or else, interpreted assuming that the viscosity close to the surfaces is different from bulk. On patterned hydrophilic surfaces, we demonstrated that the drainage force depends not only on the overall surface roughness or micro structuring but also on the specific length scale of the surface nanostructures.

Silica nano-particle super-hydrophobic surfaces: the effects of surface morphology and trapped air pockets on hydrodynamic drainage forces

We used atomic force microscopy to study dynamic forces between a rigid silica sphere (radius approximately 45 microm) and a silica nano-particle super-hydrophobic surface (SNP-SHS) in aqueous electrolyte, in the presence and absence of surfactant. Characterization of the SNP-SHS surface in air showed a surface roughness of up to two microns. When in contact with an aqueous phase, the SNP-SHS traps large, soft and stable air pockets in the surface interstices. The inherent roughness of the SNP-SHS together with the trapped air pockets are responsible for the superior hydrophobic properties of SNP-SHS such as high equilibrium contact angle (> 140 degrees) of water sessile drops on these surfaces and low hydrodynamic friction as observed in force measurements. We also observed that added surfactants adsorbed at the surface of air pockets magnified hydrodynamic interactions involving the SNP-SHS. The dynamic forces between the same silica sphere and a laterally smooth mica surface showed that the fitted Navier slip lengths using the Reynolds lubrication model were an order of magnitude larger than the length scale of the sphere surface roughness. The surface roughness and the lateral heterogeneity of the SNP-SHS hindered attempts to characterize the dynamic response using the Reynolds lubrication model even when augmented with a Navier slip boundary.

Measurement of no-slip and slip boundary conditions in confined Newtonian fluids using atomic force microscopy

We report measurements of slip length at smooth and rough hydrophilic silica surfaces, using the hydrodynamic force measurement atomic force microscope (AFM). There has been some debate in the literature as to whether the boundary condition between a solid and a wetting fluid is one of no-slip or partial-slip; in particular the results of Neto et al. (C. Neto, V. S. J. Craig and D. R. M. Williams, Eur. Phys. J. E, 2003, 12, S71-S74) and of Honig and Ducker (C. D. F. Honig and W. A. Ducker, Phys. Rev. Lett., 2007, 98, 028305) are inconsistent. Unexpectedly, the AFM cantilever geometry leads to a different measurement of hydrodynamic drainage force. Rectangular cantilevers give results consistent with a no-slip boundary condition on smooth and rough surfaces, while v-shaped cantilever measurements show variability and can produce a finding of apparent partial-slip, consistent with earlier results in the literature. Possible reasons for the discrepancy are discussed. Equilibrium force measurements show no cantilever shape dependence. We conclude that the appropriate boundary condition for aqueous solutions on smooth and nanoscale-rough hydrophilic surfaces is one of no-slip.

Influence of wettability and surface charge on the interaction between an aqueous electrolyte solution and a solid surface

The hydrodynamic drainage force of a Newtonian aqueous electrolyte solution squeezed between two surfaces of different wettability was measured using the AFM colloidal probe technique. The surface hydrophobicity, roughness, polarity and approach velocity, and thus the shearing rate of the liquid, were controlled. A direct relationship between the mobility of the aqueous electrolyte solution close to the surfaces and the hydrophobicity of the surfaces was not established. We predict that the mobility of the liquid depends in a more complex fashion on the polarity and charge of the surfaces and on the properties of the electrolyte.

Nonconstant piezo velocity in highly dynamic atomic force spectroscopy

In this Note we examine six atomic force microscopes or similar instruments for the measurement of surface forces, and we find that they suffer in various degrees from a nonideal performance of the piezo scanner during the acquisition of force curves. This is negligible at low scanning speeds but becomes relevant at higher speeds. In the three most favorable cases the set velocity is attained only after a settling time, which varies among the instruments. In the three least favorable cases, the set velocity is neither attained nor constant. We indicate how to work out the true piezo velocity from experimental force data. We also show that utilizing the wrong velocity leads to misinterpreting the collected data, and we do this on the example of a hydrodynamic drainage force measurement between a colloid and a flat surface in aqueous solution.

Atomic Force Microscopy Study of the Interaction between Adsorbed Poly(ethylene oxide) Layers: Effects of Surface Modification and Approach Velocity

The interaction forces between layers of the triblock copolymer Pluronic F108 adsorbed onto hydrophobic radio frequency glow discharge (RFGD) thin film surfaces and hydrophilic silica, in polymer-free 0.15 M NaCl solution, have been measured using the atomic force microscope (AFM) colloid probe technique. Compression of Pluronic F108 layers adsorbed on the hydrophobic RFGD surfaces results in a purely repulsive force due to the steric overlap of the layers, the form of which suggests that the PEO chains adopt a brush conformation. Subsequent fitting of these data to the polymer brush models of Alexander-de Gennes and Milner, Witten, and Cates confirms that the adsorbed Pluronic F108 adsorbs onto hydrophobic surfaces as a polymer brush with a parabolic segment density profile. In comparison, the interaction between Pluronic F108 layers adsorbed on silica exhibits a long ranged shallow attractive force and a weaker steric repulsion. The attractive component is reasonably well described by van der Waals forces, but polymer bridging cannot be ruled out. The weaker steric component of the force suggests that the polymer is less densely packed on the surface and is less extended into solution, existing as polymeric isolated mushrooms. When the surfaces are driven together at high piezo ramp velocities, an additional repulsive force is measured, attributable to hydrodynamic drainage forces between the surfaces. In comparing theoretical predictions of the hydrodynamic force to the experimentally obtained data, agreement could only be obtained if the flow profile of the aqueous solution penetrated significantly into the polymer brush. This finding is in line with the theoretical predictions of Milner and provides further evidence that the segment density profile of the adsorbed polymer brush is parabolic. A velocity dependent additional stepped repulsive force, reminiscent of a solvation oscillatory force, is also observed when the adsorbed layers are compressed under high loads. This additional force is presumably a result of hindered drainage of water due to the presence of a high volume fraction of polymer chains between the surfaces.

Evidence of shear-dependent boundary slip in Newtonian liquids.

The flow of Newtonian fluids was studied by directly measuring the hydrodynamic drainage force acting on a sphere approaching a flat surface. Our force measurements provide clear evidence of boundary slip and show that the degree of boundary slip is a function of the liquid viscosity and the shear rate. A shear-dependent boundary slippage was also observed in experiments with a polymer (PDMS). The liquids wetted the bounding surfaces either partially or completely. Our results have important consequences for the design of microfluidic devices, and in technological processes, such as lubrication and permeability of microporous media.

Surface roughness and hydrodynamic boundary slip of a newtonian fluid in a completely wetting system.

The influence of surface roughness on the boundary condition for the flow of a Newtonian fluid near a hard wall has been investigated by measurement of the hydrodynamic drainage force. The degree of slip is found to increase with surface roughness. This leads to the conclusion that in most practical situations boundary slip takes place, leading to a reduction of the drainage force.

Hydrodynamic force measurements: boundary slip of water on hydrophilic surfaces and electrokinetic effects.

The hydrodynamic drainage force of aqueous medium between smooth hydrophilic surfaces was measured with the colloidal probe technique up to shear rates of typically 10(4) s(-1). Measured force curves were compared to simulations. To reach agreement between experimental and simulated force curves, the hydrodynamic force had to be fitted with a model allowing for boundary slippage. Boundary slip was characterized by a slip length of 8-9 nm. Force measurements with charged surfaces could be simulated taking only hydrodynamic and electrostatic double-layer forces into account.

Shear-dependent boundary slip in an aqueous Newtonian liquid.

We report direct measurements of hydrodynamic drainage forces, which show clear evidence of boundary slip in a Newtonian liquid. The degree of boundary slip is found to be a function of the liquid viscosity and the shear rate, as characterized by the slip length, and is up to approximately 20 nm. This has implications for confined biological systems, the permeability of microporous media, and for the lubrication of nanomachines, and will be important in the microcontrol of liquid flow. We also show that current theories of slip do not adequately describe the experimental data.