Deformation and nano-rheology of red blood cells: an AFM investigation

Interaction forces, deformation and nano-rheology of individual red blood cells in physiologically relevant solution conditions have been determined by colloid probe atomic force microscopy (AFM). On approach of the physically immobilised cell and silica glass spherical probe surfaces, deformation of the red blood cell was observed in the force curves. At low levels of deformation, spring constants were determined in the range 3-6 m Nm(-1), whereas for higher levels of deformation, the forces increase non-linearly and on retraction, significant force curve hysteresis is observed (i.e. lower forces upon retraction). The extent of force curve hysteresis was dependent on both the drive velocity and loading force, typical of a viscoelastic system. The response of the red blood cell has been described by viscoelastic theory, where the short and long time scale elastic moduli and relaxation times are determined, i.e. the cell's nano-rheological properties elucidated. In addition to a time independent elastic modulus of 4.0 x 10(3)Nm(-2) at low levels of deformation, time-dependent elastic moduli ranges are observed (3.5 x 10(4) to 5.5 x 10(4)Nm(-2) at intermediate levels of deformation and 1.5 x 10(5) to 3.0 x 10(5)Nm(-2) at higher levels of deformation). That is, one elastic and more than one viscoelastic response to the red blood cell deformation is evident, which is considered to reflect the cellular structure.     

Microrheology of aggregated emulsion droplet networks, studied with AFM-CSLM

We studied the mechanical behavior of densely packed (up to approximately 30% v/v), sedimented layers of (1 microm) water-in-oil W/O emulsion droplets, upon indentation with a (10 microm) large spherical probe. In the presence of attractive forces, the droplets form solid like networks which can resist deformation. Adding a polymer to the oil phase was used to control droplet attraction. The droplet layers were assembled via normal gravity settling. Considering that both the network structure and the droplet interactions play a key role, we used a combination of atomic force microscopy (AFM) and confocal scanning laser microscopy (CSLM) to characterize the mechanical behavior. Here the AFM was used both as indentation tool and as force sensor. Indentation experiments were performed via a protocol consisting of approach, waiting, and retract stages. CSLM was used to observe the network structure at micron resolution in real time. Use of refractive index matched fluorescent droplets allowed the visualization of the entire layer. Upon compression with the probe, a markedly nonhomogeneous deformation occurred, evidenced by the formation of a dense corona (containing practically all of the displaced droplets) in the direct vicinity of the probe, as well as more subtle deformations of force-chains at larger distances. Upon decompression, both the imprint of the indenter and the corona remained, even long after the load was released. The force-distance curves recorded with the AFM correspond well to these observations. For each deformation cycle performed on fresh material, the retract curve was much steeper than the approach curve, thus corroborating the occurrence of irreversible compaction. Contrary to classic linear viscoelastic materials, this hysteresis did not show any dependence on the deformation speed. Our force-indentation approach curves were seen to scale roughly as F approximately delta(3/2). The pre-factor was found to increase with the polymer concentration and with the density of the network. These findings suggest that this new AFM-CSLM method could be used for rheological characterization of small volumes of "granular networks" in liquid. Our hypothesis that the mechanical resistance of the networks originates from interdroplet friction forces, which in turn are set by the interdroplet potential forces, is supported by the predictions from a new mechanical model in which the interdroplet bonds are represented by stick-slip elements.     

Impact of diblock copolymers on droplet coalescence, emulsification, and aggregation in immiscible homopolymer blends

Using rheo-optical techniques, we investigated the impact of interfacial wetting of symmetric diblock copolymers (BCPs) on the coalescence and aggregation of polydimethylsiloxane (PDMS) droplets in immiscible polyethylene-propylene (PEP) homopolymers. Anionic polymerization was used to synthesize well-defined matrix homopolymers and symmetric 16 kg/mol-to-16 kg/mol PDMS-b-PEP diblock copolymers with low polydispersity (PDI ≈ 1.02) as characterized with size exclusion chromatography and nuclear magnetic resonance spectroscopy. Blends were formulated to match the viscosities between the droplets and the matrix. Moreover, molecular weights of these components were varied to ensure that the inner block of the copolymer inside the droplet was collapsed and dry, whereas the outer block of the copolymer outside of the droplet was stretched and wet. Droplet breakup and coalescence as well as interfacial tensions were measured using rheo-optical experiments with Linkam shearing stage and an optical microscope. Subsequent to droplet breakup at high shear rates, we found that the BCPs mitigated shear-induced coalescence at lower shear rates. Based on surface tension measurements, the stretching of the BCP increased in lower molecular weight matrices, causing the droplet surface to saturate at lower coverage in line with theoretical predictions. Droplet aggregation was detected with further reductions in shear rate, which was attributed to the dewetting or the expulsion of the matrix from a saturated brush. Ultimately, the regions of droplet coalescence and aggregation were scaled by balancing the forces of shear with those due to the attraction between BCP-coated droplets.     

Experimental determination of interfacial tension by different dynamical methods under simple shear flow conditions with a novel computer-controlled parallel band apparatus

We present experimental investigations on droplet deformation under simple shear flow conditions, using a computer-controlled parallel band apparatus and an optical device which allows us to record the time dependence of the droplet shape. Several methods are applied to determine the interfacial tension from the observed shape and relaxation mechanism. Specific software developed in our laboratory allows the droplet to be fixed in a certain position for extended times, in fact, indefinite. This is an advantage over most other work done in this area, where only limited time is available. In our experiments, the transient deformation of sheared droplets can be observed to reach the steady state. The measured systems were Newtonian, both droplet and fluid phase. Droplet deformation, orientation angle and retraction were studied and compared to several models. The interfacial tension of the different systems was calculated using the theories of Taylor, Rallison, and Hinch and Acrivos. The results obtained from the analysis of the droplet deformation were in very good agreement with drop detachment experiments of Feigl and co-workers. The study of orientation angle shows qualitative agreement to the theory of Hinch and Acrivos but reveals larger quantitative discrepancies for several empirical fitting parameters of the used model. Analysis of the relaxation of sheared drops provided estimates of the interfacial tension that were in very good agreement with the steady-state measurements.     

Influence of interfacial characteristics on Ostwald ripening in hydrocarbon oil-in-water emulsions

The influence of the nature of the interfacial membrane on the kinetics of droplet growth in hydrocarbon oil-in-water emulsions was investigated. Droplet growth rates were determined by measuring changes in the droplet size distribution of 1 wt % n-tetradecane or n-octadecane oil-in-water emulsions using laser diffraction. The interfacial properties of the droplets were manipulated by coating them with either an SDS layer or with an SDS-chitosan layer using an electrostatic deposition method. The emulsion containing SDS-coated octadecane droplets did not exhibit droplet growth during storage for 400 h, which showed that it was stable to Ostwald ripening because of this oils extremely low water-solubility. The emulsion containing SDS-coated n-tetradecane droplets showed a considerable increase in mean droplet size with time, which was attributed to Ostwald ripening associated with this oils appreciable water-solubility. On the other hand, an emulsion containing SDS-chitosan coated n-tetradecane droplets was stable to droplet growth, which was attributed to the ability of the interfacial membrane to resist deformation because of its elastic modulus and thickness. This study shows that the stability of emulsion droplets to Ostwald ripening can be improved by using an electrostatic deposition method to form thick elastic membranes around the droplets.     

The influence of electric field-induced orientation on the retraction of a liquid crystal droplet immersed in a flexible polymer matrix

We measured the apparent interfacial tension between a liquid crystal and a flexible polymer by deformed droplet retraction method. An external electric field is applied to change the director orientation in liquid crystal droplet. The deformation and recovery of a single liquid crystal droplet dispersed in a polydimethylsiloxane (PDMS) matrix were realized by a transient shear flow and observed by polarized optical microscope. In order to control the director orientation in LC droplet, the electric field is applied perpendicular and parallel to the flow field, respectively. The different orientation induced by electric field in liquid crystal droplet has different behavior during droplet retraction and affect the apparent interfacial tension between liquid crystal and flexible polymer.     

An empirically validated analytical model of droplet dynamics in electrowetting on dielectric devices

Explicit analytical models that describe the capillary force on confined droplets actuated in electrowetting on dielectric devices and the reduction in that force by contact angle hysteresis as a function of the three-dimensional shape of the droplet interface are presented. These models are used to develop an analytical model for the transient position and velocity of the droplet. An order of magnitude analysis showed that droplet motion could be modeled using the driving capillary force opposed by contact angle hysteresis, wall shear, and contact line friction. Droplet dynamics were found to be a function of gap height, droplet radius, surface tension, fluid density, the initial and deformed contact angles, contact angle hysteresis, and friction coefficients pertaining to viscous wall friction and contact line friction. The first four parameters describe the device geometry and fluid properties; the remaining parameters were determined experimentally. Images of the droplet during motion were used to determine the evolution of the shape, position, and velocity of the droplet with time. Comparisons between the measured and predicted results show that the proposed model provides good accuracy over a range of practical voltages and droplet aspect ratios.     

Forces between two oil drops in aqueous solution measured by AFM

The surface and hydrodynamic forces between individual oil droplets in solution can provide insight into both emulsion stability and processes such as drop coalescence in liquid-liquid extraction. We present the first measurements of the interaction forces between alkane droplets in aqueous solution using atomic force microscopy. The radii of the droplets were well below the capillary lengths for the system, thus gravity effects are negligible, and interfacial tension and interaction forces governed the system behavior. The effects of modulating electrostatic double-layer interactions and interfacial tension through the presence of an anionic surfactant are demonstrated. Challenges in interpretation of the force data due to drop deformation are also discussed. A range of drop approach and retract speeds was used to determine the regime where hydrodynamic drainage effects had significant impact on the measurement.     

DLVO AND NON-DLVO SURFACE FORCES AND INTERACTIONS IN COLLOIDAL DISPERSIONS

Some aspects of DLVO and non-DLVO forces in colloidal systems are over-viewed. The influence of long range interactions on some kinetic properties of dispersions, as Brownian diffusion, is discussed. It is shown, both theoretically and experimentally, that the electrostatic repulsion increases the collective diffusivity. The film stratification and oscillatory structure forces in colloidal suspensions are considered within the framework of an uniform approach The presence of small colloidal species (e. g. micelles or polymer molecules) may lead to several maxima and minima in the disjoining pressure isotherm. The particular case of interacting emulsion droplets is examined accounting for the interfacial deformability. The droplet deformation acts as a soft repulsion but affects also the remaining contributions to the interaction energy due to changes of the droplet shape. A general procedure for calculating the inter-droplet interaction energy, as well as the equilibrium film radius and thickness in a doublet of droplets, is suggested. The energy of interaction between charged colloidal particles, due to correlations of the density fluctuations in the electric double layer is also studied. It is found that this effect may lead to attraction greater than the van der Waals contribution, especially when multivale counter ions are present.     

Investigation of macroscopic interfacial dynamics between clathrate hydrates and surfactant solutions

Macroscopic interfacial interactions between cyclopentane (CP) hydrates and various surfactants droplets are examined in a CP/n-decane oil mixture. Initial contact force and subsequent z-axis dependent retraction force are measured utilizing a high-resolution microbalance integrated with a micrometer-precision stage. The resulting retraction force is utilized to determine the overall adhesion energy of the system. In addition, interfacial tensions and contact angles of the system are examined to further understand the effect of surface-active agents and substrates on the initial contact and retraction forces.     

Numerical simulation of deformation behavior of droplet in gas under the electric field and flow field coupling

The water droplets in the process of electrostatic coalescence are important when studying electrohydrodynamics. In the present study, the electric field and flow field are coupled through the phase field method based on the Cahn–Hilliard formulation. A numerical simulation model of single droplet deformation under the coupling field was established. It simulated the deformation behavior of the movement of a droplet in the continuous phase and took the impact of droplet deformation into consideration which is affected by two-phase flow velocity, electric field strength, the droplet diameter, and the interfacial tension. The results indicated that under the single action of the flow field, when the flow velocity was lower, the droplet diameter was greater as was the droplet deformation degree. When the flow velocity was increased, the droplet deformation degree of a small-diameter droplet was at its maximum size, the large-diameter droplet had a smaller deformation degree, and the middle-diameter droplet was at a minimum deformation degree. When the flow velocity was further increased, the droplet diameter was smaller, and the droplet deformation degree was greater. Under the coupled effect of the electric field and flow field, the two-phase flow velocity and the electric field strength were greater, and the degree of droplet deformation was greater. While the droplet diameter and interfacial tension were smaller, the degree of droplet deformation was greater. Droplet deformation degree increased along with the two-phase flow velocity. The research results provided a theoretical basis for gas–liquid separation with electrostatic coalescence technology.     

Influence of bulk elasticity and interfacial tension on the deformation of gelled water-in-oil emulsion droplets: an AFM study

We used atomic force microscopy (AFM) to study the deformation and wetting behavior of large (50-250 microm) emulsion droplets upon mechanical loading with a colloidal glass probe. Our droplets were obtained from water-in-oil emulsions. By adding gelatin to the water prior to emulsification, also droplets with a bulk elasticity were prepared. Systematic variations of surfactant and gelatin concentrations were made, to investigate their effect on the deformation and wetting behavior of the droplets and to identify the contributions of interfacial tension, bulk elasticity, and expelled water. The AFM experiments were performed in force--distance mode and showed on approach a repulsive regime which in many cases was terminated by a jump-in of the probe. In the case of pure water (i.e. gelatin-free) droplets, the repulsive part of the curve showed a good linearity, thus allowing the extraction of an effective droplet spring constant. This quantity was found to decrease on raising the surfactant concentration from below the critical micelle concentration (cmc) to well above the cmc, and its numerical values were found to correspond remarkably well to literature values for the interfacial tension. Our findings indicate that, on gelatin increase inside the droplets, the bulk elasticity gradually becomes dominant and the droplets' stiffness does not depend anymore on surfactant concentration. Also the stability of the droplet interface against wetting, as measured by the force at which the jump-in instability occurs, was enhanced by gelatin. For gelatin concentrations of > or =15 wt %, the droplets were found to behave like purely elastic bodies. Both gelatin and surfactant contribute positively to the stability against interface breakup.     

Measurement of dynamical forces between deformable drops using the atomic force microscope. I. Theory

Recent experimental developments have enabled the measurement of dynamical forces between two moving liquid drops in solution using an atomic force microscope (AFM). The drop sizes, interfacial tension, and approach velocities used in the experiments are in a regime where surface forces, hydrodynamics, and drop deformation are all significant. A detailed theoretical model of the experimental setup which accounts for surface forces, hydrodynamic interactions, droplet deformation, and AFM cantilever deflection has been developed. In agreement with experimental observations, the calculated force curves show pseudo-constant compliance regions due to drop flattening, as well as attractive pull-off forces due mainly to hydrodynamic lubrication forces.     

A study on interfacial tension between flexible polymer and liquid crystal

The interfacial property in polymer-liquid crystal systems is quite different from flexible polymer-polymer mixtures due to the anisotropic properties of liquid crystals. The apparent interfacial tension between a liquid crystal and a flexible polymer was measured by deformed droplet retraction method. The deformation and recovery of a single liquid crystal droplet dispersed in a poly(dimethylsiloxane) matrix were realized by a transient shear flow and observed by polarized optical microscope. The apparent interfacial tension of polymer-liquid crystal system was found to be greatly dependent on the temperature, initial droplet deformation and liquid crystal droplet size.     

Shape-gradient composite surfaces: water droplets move uphill

The approach of water droplets self-running horizontally and uphill without any other forces was proposed by patterning the shape-gradient hydrophilic material (i.e., mica) to the hydrophobic matrix (i.e., wax or low-density polyethylene (LDPE)). The shape-gradient composite surface is the best one to drive water droplet self-running both at the high velocity and the maximal distance among four different geometrical mica/wax composite surfaces. The driving force for the water droplets self-running includes: (1) the great difference in wettability of surface materials, (2) the low contact angle hysteresis of surface materials, and (3) the space limitation of the shape-gradient transportation area. Furthermore, the average velocity and the maximal distance of the self-running were mainly determined by the gradient angle (alpha), the droplet volume, and the difference of the contact angle hysteresis. Theoretical analysis is in agreement with the experimental results.     

Origin and control of adhesion between emulsion drops stabilized by thermally sensitive soft colloidal particles

We used soft microgels made of poly(N-isopropylacrylamide) (pNIPAM) of variable cross-linking degrees and the same colloidal size to stabilize oil-in-water Pickering emulsions. The extent of droplet flocculation increased and the resistance of the emulsions to mechanical stresses decreased as the cross-linking density was augmented. Large flat films were separating the droplets, and we could measure the adhesion angle at the junction with the free interfaces through several microscopy methods. The size of the flat films and the values of the angles were reflecting strong adhesive interactions between the interfaces as a result of microgel bridging. In parallel, cryo-SEM imaging of the thin films allowed a precise determination of their structure. The evolution of the adhesion angle and of the film structure as a function of microgels cross-linking density provided interesting insights into the impact of particle softness on film adhesiveness and emulsion stability. We exploited our main findings to propose a novel route for controlling the emulsions end-use properties (flocculation and stability). Owing to particle softness and thermal sensitivity, the interfacial coverage was a path function (it depended on the sample "history"). As a consequence, by adapting the emulsification conditions, the interfacial monolayer could be trapped in a very dense and rigid configuration, providing improved resistance to bridging flocculation and to flow-induced coalescence.     

Systematic investigation of droplet generation at T-junctions

Droplet microfluidics has attracted much attention in recent years. For many droplet-based applications, researchers want to predict the size of the droplets in a certain experimental condition. To meet this need, van Steijn and colleagues proposed an elegant theoretical model that predicts the volume of droplets generated in a common channel configuration for forming a steady-state, continuous stream of droplets, the T-junction geometry. To determine the accuracy of this model in predicting droplet volume, we performed a systematic experimental study over two orders of magnitude in capillary number. We found that this model, albeit elegant, has a limited range of interfacial tension over which it can predict accurately the droplet volume. Our experimental results, together with fluid dynamic simulations, allowed us to highlight the importance of physical fluid properties when employing theoretical models.     

Ultrasonic attenuation spectroscopy study of flocculation in protein stabilized emulsions

The extent and kinetics of droplet flocculation in emulsions was studied using ultrasonic attenuation spectroscopy. Flocculation in 10 wt.% soybean oil-in-water emulsions, stabilized by whey protein isolate (0.75 wt.%), was controlled by adjusting the pH (between 3 and 7) to alter the electrostatic interactions between the droplets. Droplet flocculation was then monitored by measuring the ultrasonic attenuation spectra (1–150 MHz) and by using laser light scattering. Extensive droplet flocculation was observed in the emulsions around the isoelectric point of the proteins (pH 3.5–5.5). Flocculation caused an appreciable change in the ultrasonic attenuation spectra, which was in good qualitative agreement with a theory recently developed to describe the ultrasonic properties of flocculated emulsions. Our results indicate that ultrasonic spectroscopy is a powerful tool for monitoring both the extent and kinetics of flocculation in concentrated emulsions in situ.     

A self-consistent field study of a hydrocarbon droplet at the air-water interface

A molecularly detailed self-consistent field (SCF) approach is applied to describe a sessile hydrocarbon droplet placed at the air-water interface. Predictions of the contact angle for macroscopic droplets follow from using Neumann's equation, wherein the macroscopic interfacial tensions are computed from one-gradient calculations for flat interfaces. A two-gradient cylindrical coordinate system with mirror-like boundary conditions is used to analyse the three dimensional shape of the nano-scale oil droplet at the air-water interface. These small droplets have a finite value of the Laplace pressure and concomitant line tension. It has been calculated that the oil-water and oil-vapour interfacial tensions are curvature dependent and increase slightly with increasing interfacial curvature. In contrast, the line tension tends to decrease with curvature. In all cases there is only a weak influence of the line tension on the droplet shape. We therefore argue that the nano-scale droplets, which are described in the SCF approach, are representative for macroscopic droplets and that the method can be used to efficiently generate accurate information on the spreading of oil droplets at the air-water interface in molecularly more complex situations. As an example, non-ionic surfactants have been included in the system to illustrate how a molecularly more complex situation will change the wetting properties of the sessile drop. This short forecast is aimed to outline and to stress the potential of the method.     

Design of microfluidic channel geometries for the control of droplet volume, chemical concentration, and sorting

Passive microfluidic channel geometries for control of droplet fission, fusion and sorting are designed, fabricated, and tested. In droplet fission, the inlet width of the bifurcating junction is used to control the range of breakable droplet sizes and the relative resistances of the daughter channels were used to control the volume of the daughter droplets. Droplet fission is shown to produce concentration differences in the daughter droplets generated from a primary drop with an incompletely mixed chemical gradient, and for droplets in each of the bifurcated channels, droplets were found to be monodispersed with a less than 2% variation in size. Droplet fusion is demonstrated using a flow rectifying design that can fuse multiple droplets of same or different sizes generated at various frequencies. Droplet sorting is achieved using a bifurcating flow design that allows droplets to be separated base on their sizes by controlling the widths of the daughter channels. Using this sorting design, submicron satellite droplets are separated from the larger droplets.