Influence of the spring constant of cantilevers on hydrodynamic force measurements by the colloidal probe technique

Attachment of bioinspired microfibrils in fluids: transition from a hydrodynamic to hydrostatic mechanism

Reversible and switchable adhesion of elastomeric microstructures has attracted significant interest in the development of grippers for object manipulation. Their applications, however, have often been limited to dry conditions and adhesion of such deformable microfibrils in the fluid environment is less understood. In the present study, we performed adhesion tests in silicone oil using single cylindrical microfibrils of a flat-punch shape with a radius of 80 µm. Stiff fibrils were created using three-dimensional printing of an elastomeric resin with an elastic modulus of 500 MPa, and soft fibrils, with a modulus of 3.3 MPa, were moulded in polyurethane. Our results suggest that adhesion is dominated by hydrodynamic forces, which can be maximized by stiff materials and high retraction velocities, in line with theoretical predictions. The maximum pull-off stress of stiff cylindrical fibrils is 0.6 MPa, limited by cavitation and viscous fingering, occurring at retraction velocities greater than 2 µm s-1. Next, we add a mushroom cap to the microfibrils, which, in the case of the softer material, deforms upon retraction and leads to a transition to a hydrostatic suction regime with higher pull-off stresses ranging from 0.7 to 0.9 MPa. The effects of elastic modulus, fibril size and viscosity for underwater applications are illustrated in a mechanism map to provide guidance for design optimization.

Application of New Energy Thermochromic Composite Thermosensitive Materials of Smart Windows in Recent Years

Thermochromic smart windows technology can intelligently regulate indoor solar radiation by changing indoor light transmittance in response to thermal stimulation, thus reducing energy consumption of the building. In recent years, with the development of new energy-saving materials and the combination with practical technology, energy-saving smart windows technology has received more and more attention from scientific research. Based on the summary of thermochromic smart windows by Yi Long research groups, this review described the applications of thermal responsive organic materials in smart windows, including poly(N-isopropylacrylamide) (PNIPAm) hydrogels, hydroxypropyl cellulose (HPC) hydrogels, ionic liquids and liquid crystals. Besides, the mechanism of various organic materials and the properties of functional materials were also introduced. Finally, opportunities and challenges relating to thermochromic smart windows and prospects for future development are discussed.

Microsphere Adhesion on Rubber Films Accompanied by Sphere Sedimentation

Understanding the adhesion process between a rigid material (filler) and a viscoelastic material is important for designing an enhanced industrial material. However, the adhesion process is not simple because the properties of the adhesive, adherend, and interface are intricately influenced by this process. Here we investigate the adhesion of microspheres onto rubber films to clarify the dominant factor in the adhesion process. A rubber meniscus first forms on the sphere surface, followed by sedimentation of the sphere into the rubber film. This sedimentation is even observed when the surface free energy of the sphere is lower than that of the rubber film, which indicates that the driving force of meniscus formation obeys Young's equation on a tangential line of the sphere. The dominant factor of the sedimentation behavior is investigated by using atomic force microscopy force-sample deformation curve measurements and creep tests on the rubber films. These experimental results demonstrate that the adhesion process is strongly dominated by the viscoelastic property of the bulk rubber as opposed to the sphere and interface properties.

Effect of the Surfactant Charge and Concentration on the Change in the Forces between Two Charged Surfaces in Surfactant Solutions by a Liquid Flow

A combined atomic force microscope (AFM)-peristaltic pump system was used to determine the effect of a flow on the forces between two negatively charged surfaces (silica particle and silicon wafer) in aqueous solutions containing surfactants. The effect of the surfactant charge on the forces was determined by using an anionic surfactant (sodium dodecyl sulfate, SDS) and a cationic surfactant (dodecyltrimethylammonium bromide, DTAB) of the same chain length. The surfactant concentration effect was determined by using concentrations up to the critical micelle concentration. In the case of SDS, a flow reduced the range and magnitude of the repulsive forces. The force range reduction was explained by a shrinking of the diffuse layers, due to the deformation of the diffuse layer by the flow. The force magnitude reduction was explained by (1) the increased electrostatic screening due to the thinner diffuse layers and (2) an increased adsorption of specific ions, such as Na⁺, to the silica surfaces. In the case of DTAB, a concentration (8.0 mM) that gave an attractive force in the absence of a flow gave a repulsive force in the presence of a flow. Comparison of AFM images of a silicon wafer in DTAB measured in the absence and presence of a liquid flow showed that the number of DTAB patches adsorbed to the silicon wafer increased with a liquid flow. The change in the forces with a flow was therefore explained by this change in the DTAB adsorption to the negatively charged surfaces. As a liquid flow can change the charge of a surface, it may be possible to control the aggregation/dispersion of charged particles via the flow rate, if the appropriate surfactant type and concentration are used.

Establishment of a Standard Method for Boundary Slip Measurement on Smooth Surfaces Based on AFM

Typically, it is difficult to analyze and design a micro/nanofluid system, and the design process cannot follow the traditional law of hydrodynamics. The boundary condition is very important in the applications of a micro/nanofluid system. The existence of boundary slip can reduce the hydrodynamic resistance and enhance fluid flow. How to accurately determine the dynamic boundary conditions is increasingly concerned by researchers. Atomic force microscope (AFM) is proven to be the most advanced experimental instrument for studying the characteristics of the surface and the interaction interface. Most studies on the application of atomic force microscopy to the measurement of the boundary slip do not describe a systematic standard process, leading to many differences in the measurement results. In this paper, a standard process of measuring slip on smooth and flat surfaces is developed, including the data processing methods that minimize the interference factors in the original data as well as simplify the data expression. Thus, the boundary slip can be obtained more easily and accurately.

Effect of a liquid flow on the forces between charged solid surfaces and the non-equilibrium electric double layer

The physical properties of fluids can change as they flow through confined charged solid areas, such as a charged pore or channel, allowing the transport of fluid through the channels to be controlled. The liquid flow is influenced by the electrical double layer (EDL) that is next to the charged surface. The overlap of the EDL of two nearby charged solid surfaces results in the formation of an electrostatic force. A flow will change the EDL from an equilibrium state to a non-equilibrium state, causing the forces to also change from an equilibrium (static) state to a non-equilibrium (dynamic) state. There are numerous studies that have been performed by molecular dynamics (MD) simulations and surface force experiments which concern the equilibrium EDL and the equilibrium surface forces. However, there are significantly less studies concerning the non-equilibrium EDL and non-equilibrium surface forces, including the effect of a liquid flow on the EDL and the surface forces. This review will focus on how a liquid flow changes the EDL and the surface forces of charged hydrophilic solid surfaces in aqueous electrolyte solutions. Results obtained by MD simulations and surface force experiments are discussed in this review. A flow was seen to be able to distort the EDL, causing the surface forces to change. The EDL and surface forces were affected by the surface charge, the structuring ability of the liquid molecules and ions near the surfaces, the ion type and their specificity towards the surface, the ionic concentration, and the rate of flow of the liquid. The physical properties of the system were shown to change with a flow, e.g. the increase in the fluid viscosity next to a charged solid surface that accompanies a flow. The number of counterions adsorbed to a charged solid surface was also seen to affect the direction of flow in an EDL. The surface forces were shown to change with a flow due to changes in hydrodynamic and electrostatic forces. Information on the effect of the liquid flow on the EDL and surface forces will help improve applications that require fluid to be transported in a defined way through a charged solid vessel.

Review and perspectives of AFM application on the study of deformable drop/bubble interactions

The applications of Atomic Force Microscopy (AFM) on the study of dynamic interactions and film drainage between deformable bodies dispersed in aqueous solutions are reviewed in this article. Novel experimental designs and recent advances in experimental methodologies are presented, which show the advantage of using AFM as a tool for probing colloidal interactions. The effects of both DLVO and non-DLVO forces on the colloid stabilization mechanism are discussed. Good agreement is found between the force - drop/bubble deformation behaviour revealed by AFM measurements and the theoretical modeling of film drainage process, giving a convincing explanation of the occurrence of certain phenomenon. However, the behaviour and shape of deformable drops as they approach or retract is still not well resolved. In addition, when surfactants are present further research is needed on the absorption of surfactant molecules into the interfaces, their mobility and the effects on interfacial film properties.

Near surface properties of mixtures of propylammonium nitrate with n-alkanols 2. Nanotribology and fluid dynamics

Colloid probe friction force microscopy (FFM) has been used to study the lubricity of propylammonium nitrate (PAN) mixed with n-alkanols confined between sliding silica and mica surfaces.

Interfacial slip on rough, patterned and soft surfaces: a review of experiments and simulations

Advancements in the fabrication of microfluidic and nanofluidic devices and the study of liquids in confined geometries rely on understanding the boundary conditions for the flow of liquids at solid surfaces. Over the past ten years, a large number of research groups have turned to investigating flow boundary conditions, and the occurrence of interfacial slip has become increasingly well-accepted and understood. While the dependence of slip on surface wettability is fairly well understood, the effect of other surface modifications that affect surface roughness, structure and compliance, on interfacial slip is still under intense investigation. In this paper we review investigations published in the past ten years on boundary conditions for flow on complex surfaces, by which we mean rough and structured surfaces, surfaces decorated with chemical patterns, grafted with polymer layers, with adsorbed nanobubbles, and superhydrophobic surfaces. The review is divided in two interconnected parts, the first dedicated to physical experiments and the second to computational experiments on interfacial slip of simple (Newtonian) liquids on these complex surfaces. Our work is intended as an entry-level review for researchers moving into the field of interfacial slip, and as an indication of outstanding problems that need to be addressed for the field to reach full maturity.

Hydrodynamic boundary condition of water on hydrophobic surfaces

By combining total internal reflection fluorescence cross-correlation spectroscopy with Brownian dynamics simulations, we were able to measure the hydrodynamic boundary condition of water flowing over a smooth solid surface with exceptional accuracy. We analyzed the flow of aqueous electrolytes over glass coated with a layer of poly(dimethylsiloxane) (advancing contact angle Θ = 108°) or perfluorosilane (Θ = 113°). Within an error of better than 10 nm the slip length was indistinguishable from zero on all surfaces.

Stokesian dynamics of pill-shaped Janus particles with stick and slip boundary conditions

We study the forces and torques experienced by pill-shaped Janus particles of different aspect ratios where half of the surface obeys the no-slip boundary condition and the other half obeys the Navier slip condition of varying slip lengths. Using a recently developed boundary integral formulation whereby the traditional singular behavior of this approach is removed analytically, we quantify the strength of the forces and torques experienced by such particles in a uniform flow field in the Stokes regime. Depending on the aspect ratio and the slip length, the force transverse to the flow direction can change sign. This is a novel property unique to the Janus nature of the particles.

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.

Interpreting atomic force microscopy measurements of hydrodynamic and surface forces with nonlinear parametric estimation

A nonlinear parameter estimation method has been developed to extract the separation-dependent surface force and cantilever spring constant from atomic force microscope data taken at different speeds for the interaction between a silica colloidal probe and plate in aqueous solution. The distinguishing feature of this approach is that it exploits information from the velocity dependence of the force-displacement data due to hydrodynamic interaction to provide an unbiased estimate of the functional form of the separation-dependent surface force. An assumed function for the surface force with unknown parameters is not required. In addition, the analysis also yields a consistent estimate of the in situ cantilever spring constant. In combination with data from static force measurements, this approach can further be used to quantify the extent of hydrodynamic slip.

Reconciling slip measurements in symmetric and asymmetric systems

In the past decade, the slip of simple liquids on solid surfaces has been demonstrated by many groups. However, the slip of liquids on wettable surfaces is heavily debated. Using colloid probe atomic force microscopy (AFM), we found the slip length of di-n-octylphthalate in a symmetric wettable system (silica) to be around 11 nm, which raises the question of what the measured slip length in an asymmetric hydrophilic-hydrophobic system would be. To answer this question, we investigated liquid slip in one symmetric nonwettable system (hydrophobic DCDMS or OTS) and in one asymmetric hydrophilic (silica)-hydrophobic (DCDMS) system by the same method at driving velocities of between 10 and 80 μm/s. The slip results obtained from the three systems are in agreement with each other, and this comparison provides a means to self-assess the accuracy and reproducibility of the measured force curves and the fitted slip length in our systems. Furthermore, this method provides access to reliable values of the actual slip length on any investigated flat surface in an asymmetric system, avoiding the difficulty of preparing a symmetric probe/flat surface system in a colloid probe AFM force measurement.

Studying flow close to an interface by total internal reflection fluorescence cross-correlation spectroscopy: quantitative data analysis

Total internal reflection fluorescence cross-correlation spectroscopy (TIR-FCCS) has recently [S. Yordanov et al., Optics Express 17, 21149 (2009)] been established as an experimental method to probe hydrodynamic flows near surfaces, on length scales of tens of nanometers. Its main advantage is that fluorescence occurs only for tracer particles close to the surface, thus resulting in high sensitivity. However, the measured correlation functions provide only rather indirect information about the flow parameters of interest, such as the shear rate and the slip length. In the present paper, we show how to combine detailed and fairly realistic theoretical modeling of the phenomena by Brownian dynamics simulations with accurate measurements of the correlation functions, in order to establish a quantitative method to retrieve the flow properties from the experiments. First, Brownian dynamics is used to sample highly accurate correlation functions for a fixed set of model parameters. Second, these parameters are varied systematically by means of an importance-sampling Monte Carlo procedure in order to fit the experiments. This provides the optimum parameter values together with their statistical error bars. The approach is well suited for massively parallel computers, which allows us to do the data analysis within moderate computing times. The method is applied to flow near a hydrophilic surface, where the slip length is observed to be smaller than 10nm, and, within the limitations of the experiments and the model, indistinguishable from zero.

Theory of non-equilibrium force measurements involving deformable drops and bubbles

Over the past decade, direct force measurements using the Atomic Force Microscope (AFM) have been extended to study non-equilibrium interactions. Perhaps the more scientifically interesting and technically challenging of such studies involved deformable drops and bubbles in relative motion. The scientific interest stems from the rich complexity that arises from the combination of separation dependent surface forces such as Van der Waals, electrical double layer and steric interactions with velocity dependent forces from hydrodynamic interactions. Moreover the effects of these forces also depend on the deformations of the surfaces of the drops and bubbles that alter local conditions on the nanometer scale, with deformations that can extend over micrometers. Because of incompressibility, effects of such deformations are strongly influenced by small changes of the sizes of the drops and bubbles that may be in the millimeter range. Our focus is on interactions between emulsion drops and bubbles at around 100 μm size range. At the typical velocities in dynamic force measurements with the AFM which span the range of Brownian velocities of such emulsions, the ratio of hydrodynamic force to surface tension force, as characterized by the capillary number, is ~10(-6) or smaller, which poses challenges to modeling using direct numerical simulations. However, the qualitative and quantitative features of the dynamic forces between interacting drops and bubbles are sensitive to the detailed space and time-dependent deformations. It is this dynamic coupling between forces and deformations that requires a detailed quantitative theoretical framework to help interpret experimental measurements. Theories that do not treat forces and deformations in a consistent way simply will not have much predictive power. The technical challenges of undertaking force measurements are substantial. These range from generating drop and bubble of the appropriate size range to controlling the physicochemical environment to finding the optimal and quantifiable way to place and secure the drops and bubbles in the AFM to make reproducible measurements. It is perhaps no surprise that it is only recently that direct measurements of non-equilibrium forces between two drops or two bubbles colliding in a controlled manner have been possible. This review covers the development of a consistent theory to describe non-equilibrium force measurements involving deformable drops and bubbles. Predictions of this model are also tested on dynamic film drainage experiments involving deformable drops and bubbles that use very different techniques to the AFM to demonstrate that it is capable of providing accurate quantitative predictions of both dynamic forces and dynamic deformations. In the low capillary number regime of interest, we observe that the dynamic behavior of all experimental results reviewed here are consistent with the tangentially immobile hydrodynamic boundary condition at liquid-liquid or liquid-gas interfaces. The most likely explanation for this observation is the presence of trace amounts of surface-active species that are responsible for arresting interfacial flow.

Reliable measurements of interfacial slip by colloid probe atomic force microscopy. I. Mathematical modeling

We developed a stable spread-sheet algorithm for the calculation of the hydrodynamic forces measured by colloid probe atomic force microscopy to be used in investigations of interfacial slip. The algorithm quantifies the effect on the slip hydrodynamic force for factors commonly encountered in experimental measurements such as nanoparticle contamination, nonconstant drag force due to cantilever bending that varies with different cantilevers, flattening of the microsphere, and calibration at large separations. We found that all of these experimental factors significantly affect the fitted slip length, approximately in the order listed. Our modeling is applied to fit new experimental data reproducibly. Using this new algorithm, it is shown that the fitting of hydrodynamic theories to experimental data is reliable and the fitted slip length is accurate. A "blind test" protocol was developed that produces a reliable estimate of the fitting error in the determination of both the slip length and spring constant. By this blind test, we estimate that our modeling determines the fitted slip length with an average systematic error of 2 nm and the fitted spring constant with a 3% error. Our exact calculation of the drag force may explain previous reports that the fitted slip length depends upon the shape and spring constant of the cantilever used to perform the measurements.

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.

Improved in situ spring constant calibration for colloidal probe atomic force microscopy

In colloidal probe atomic force microscopy (AFM) surface forces cannot be measured without an accurate determination of the cantilever spring constant. The effective spring constant k depends upon the cantilever geometry and therefore should be measured in situ; additionally, k may be coupled to other measurement parameters. For example, colloidal probe AFM is frequently used to measure the slip length b at solid/liquid boundaries by comparing the measured hydrodynamic force with Vinogradova slip theory (V-theory). However, in this measurement k and b are coupled, hence, b cannot be accurately determined without knowing k to high precision. In this paper, a new in situ spring constant calibration method based upon the residuals, namely, the difference between experimental force-distance data and V-theory is presented and contrasted with two other popular spring constant determination methods. In this residuals calibration method, V-theory is fitted to the experimental force-distance data for a range of systematically varied spring constants where the only adjustable parameter in V-theory is the slip length b. The optimal spring constant k is that value where the residuals are symmetrically displaced about zero for all colloidal probe separations. This residual spring constant calibration method is demonstrated by studying three different liquids (n-decanol, n-hexadecane, and n-octane) and two different silane coated colloidal probe-silicon wafer systems (n-hexadecyltrichlorosilane and n-dodecyltrichlorosilane).