Surface tension and elasticity of gel studied with laser-induced surface-deformation spectroscopy

Crossover of surface waves and capillary-viscous-elastic transition in soft biomaterials detected by resonant acoustic rheometry

Viscoelastic properties of hydrogels are important for their application in science and industry. However, rheological assessment of soft hydrogel biomaterials is challenging due to their complex, rapid, and often time-dependent behaviors. Resonant acoustic rheometry (RAR) is a newly developed technique capable of inducing and measuring resonant surface waves in samples in a non-contact fashion. By applying RAR at high temporal resolution during thrombin-induced fibrin gelation and ultraviolet-initiated polyethylene glycol (PEG) polymerization, we observed distinct changes in both frequency and amplitude of the resonant surface waves as the materials changed over time. RAR detected a series of capillary-elastic, capillary-viscous, and visco-elastic transitions that are uniquely manifested as crossover of different types of surface waves in the temporally evolving materials. These results reveal the dynamic interplay of surface tension, viscosity, and elasticity that is controlled by the kinetics of polymerization and crosslinking during hydrogel formation. RAR overcomes many limitations of conventional rheological approaches by offering a new way to comprehensively and longitudinally characterize soft materials during dynamic processes.

Simple method to measure rheological properties of soft surfaces by a micro-needle contact

We developed a simple method to investigate rheological properties of soft surfaces, such as polymeric liquids and colloidal suspensions, by capturing the images of a metal micro-needle inserted into the surface. At contact, a meniscus-like deformation is formed on the surface. By relating the shape of the deformation to the balance of applied forces, local elasticity and viscosity just inside the surface are obtained. With a facile setup and rapid measurement process, the present method can be implemented to variety of systems, for instance, drying sessile drops and small volume of liquid confined in a capillary.

Pulsed laser activated impulse response encoder (PLAIRE): sensitive evaluation of surface cellular stiffness on zebrafish embryos

Mechanical properties of cells and tissues closely link to their architectures and physiological functions. To obtain the mechanical information of submillimeter scale small biological objects, we recently focused on the object vibration responses when excited by a femtosecond laser-induced impulsive force. These responses are monitored by the motion of an AFM cantilever placed on top of a sample. In this paper, we examined the surface cellular stiffness of zebrafish embryos based on excited vibration forms in different cytoskeletal states. The vibration responses were more sensitive to their surface cellular stiffness in comparison to the Young's modulus obtained by a conventional AFM force curve measurement.

Contactless thin-film rheology unveiled by laser-induced nanoscale interface dynamics

One of the classical limitations for the investigation of the local rheology of small scale soft objects and/or confined fluids is related to the difficulty to control mechanical contact and its consequences. In order to overcome these issues, we implement a new local, active, fast and contactless optical strategy, called optorheology, which is based on both the optical radiation pressure of a laser wave to dynamically deform a fluid interface and interferometry to probe this deformation with nanometric resolution. This optical approach is first validated by measuring the surface tension and the viscosity of transparent Newtonian liquids. We also show how non-equilibrium situations, such as continuous evaporation, can be used to deduce the thickness dependence of the rheology of thin films and the concentration dependence of the viscosity of binary liquid mixtures and suspensions. We further extend the investigation to elasticity and viscoelasticity measurements of polymer solutions. Finally, since liquids may absorb light, we discuss the influence of a weak laser heating and the triggering of interface deformations by thermocapillary tangential stresses that could represent a complementary approach to probe the rheology at small scale.

Surface Response of a Polymer Network: Semi-infinite Network

We study theoretically the surface response of a semi-infinite viscoelastic polymer network using the two-fluid model. We focus on the overdamped limit and on the effect of the network's intrinsic length scales. We calculate the decay rate of slow surface fluctuations, and the surface displacement in response to a localized force. Deviations from the large-scale continuum response are found at length scales much larger than the network's mesh size. We discuss implications for surface scattering and microrheology. We provide closed-form expressions that can be used for surface microrheology: the extraction of viscoelastic moduli and intrinsic length scales from the motions of tracer particles lying on the surface without doping the bulk material.

Mechanisms for bacterial gliding motility on soft substrates

The motility mechanism of certain prokaryotes has long been a mystery, since their motion, known as gliding, involves no external appendages. The physical principles behind gliding still remain poorly understood. Using myxobacteria as an example of such organisms, we identify here the physical principles behind gliding motility and develop a theoretical model that predicts a 2-regime behavior of the gliding speed as a function of the substrate stiffness. Our theory describes the elasto-capillary-hydrodynamic interactions between the membrane of the bacteria, the slime it secretes, and the soft substrate underneath. Defining gliding as the horizontal translation under zero net force, we find the 2-regime behavior is due to 2 distinct mechanisms of motility thrust. On mildly soft substrates, the thrust arises from bacterial shape deformations creating a flow of slime that exerts a pressure along the bacterial length. This pressure in conjunction with the bacterial shape provides the necessary thrust for propulsion. On very soft substrates, however, we show that capillary effects must be considered that lead to the formation of a ridge at the slime-substrate-air interface, thereby creating a thrust in the form of a localized pressure gradient at the bacterial leading edge. To test our theory, we perform experiments with isolated cells on agar substrates of varying stiffness and find the measured gliding speeds in good agreement with the predictions from our elasto-capillary-hydrodynamic model. The mechanisms reported here serve as an important step toward an accurate theory of friction and substrate-mediated interactions between bacteria proliferating in soft media.

Laser-induced surface deformation microscope for the study of the dynamic viscoelasticity of plasma membrane in a living cell

A laser-induced surface deformation (LISD) microscope is developed and applied to measurement of the dynamic relaxation responses of the plasma membrane in a living cell. A laser beam is tightly focused on an optional area of cell surface and the focused light induces microscopic deformation on the surface via radiation pressure. The LISD microscope not only allows non-contact and destruction-free measurement but provides power spectra of the surface responses depending on the frequency of the intensity of the laser beam. An optical system for the LISD is equipped via a microscope, allowing us to measure the relaxation responses in sub-cellular-sized regions of the plasma membrane. In addition, the forced oscillation caused by the radiation pressure for surface deformation extends the upper limit of the frequency range in the obtained power spectra to 106 Hz, which enables us to measure relaxation responses in local regions within the plasma membrane. From differences in power-law exponents at higher frequencies, it is realized that a cancerous cell obeys a weaker single power-law than a normal fibroblast cell. Furthermore, the power spectrum of a keratinocyte cell obeys a power-law with two exponents, indicating that alternative mechanical models to a conventional soft glassy rheology model (where single power-laws explain cells' responses below about 103 Hz) are needed for the understanding over a wider frequency range. The LISD microscope would contribute to investigation of microscopic cell rheology, which is important for clarifying the mechanisms of cell migration and tissue construction.

Surface hydrodynamics of viscoelastic fluids and soft solids: Surfing bulk rheology on capillary and Rayleigh waves

From the recent advent of the new soft-micro technologies, the hydrodynamic theory of surface modes propagating on viscoelastic bodies has reinvigorated this field of technology with interesting predictions and new possible applications, so recovering its scientific interest very limited at birth to the academic scope. Today, a myriad of soft small objects, deformable meso- and micro-structures, and macroscopically viscoelastic bodies fabricated from colloids and polymers are already available in the materials catalogue. Thus, one can envisage a constellation of new soft objects fabricated by-design with a functional dynamics based on the mechanical interplay of the viscoelastic material with the medium through their interfaces. In this review, we recapitulate the field from its birth and theoretical foundation in the latest 1980s up today, through its flourishing in the 90s from the prediction of extraordinary Rayleigh modes in coexistence with ordinary capillary waves on the surface of viscoelastic fluids, a fact first confirmed in experiments by Dominique Langevin and me with soft gels [Monroy and Langevin, Phys. Rev. Lett. 81, 3167 (1998)]. With this observational discovery at sight, we not only settled the theory previously formulated a few years before, but mainly opened a new field of applications with soft materials where the mechanical interplay between surface and bulk motions matters. Also, new unpublished results from surface wave experiments performed with soft colloids are reported in this contribution, in which the analytic methods of wave surfing synthetized together with the concept of coexisting capillary-shear modes are claimed as an integrated tool to insightfully scrutinize the bulk rheology of soft solids and viscoelastic fluids. This dedicatory to the figure of Dominique Langevin includes an appraisal of the relevant theoretical aspects of the surface hydrodynamics of viscoelastic fluids, and the coverage of the most important experimental results obtained during the three decades of research on this field.

Measurement of membrane tension of free standing lipid bilayers via laser-induced surface deformation spectroscopy

Non-invasive measurement of the membrane tension of free-standing black lipid membranes (BLMs), with sensitivity on the order of μN m(-1), was achieved using laser-induced surface deformation (LISD) spectroscopy. A BLM was vertically formed via the folding method and aqueous phases with different refractive indices were added on each side in order to induce radiation pressure by a laser beam. The dynamic response of the deformed BLMs was measured under periodic intensity modulation and their tensions could be estimated. The dependence of membrane tension on the cholesterol concentration of BLMs composed of phosphatidylcholine and phosphatidylethanolamine was investigated, with the membrane tension increasing from 1.3 μN m(-1) to 68.1 μN m(-1) when the cholesterol concentration increased from zero to 33%. These tension values are much smaller than some of those previously reported, because this method does not suppress membrane fluctuation unlike other conventional methods. Our LISD system can be a promising tool for the measurement of membrane tension in BLMs.

A liquid contact line receding on a soft gel surface: dip-coating geometry investigation

We studied the dynamics of a liquid contact line receding on a hydrophobic soft gel (SBS-paraffin). In order to realize a well-defined geometry with an accurate control of velocity, a dip-coating setup was implemented. Provided that the elastic modulus is small enough, a significant deformation takes place near the contact line, which in turn drastically influences the wetting behaviour. Depending on the translation velocity of the substrate, the contact line exhibits different regimes of motions. Continuous motions are observed at high and low velocities, meanwhile two types of stick-slip motion - periodic and erratic - appear at intermediate velocities. We suggest that the observed transitions could be explained in terms of the competition between different frequencies, i.e., the frequency of the strain field variation induced by the contact line motion and the crossover frequency of the gel related to the material relaxation. Our results provide systematic views on how the wetting of liquid is modified by the rheological properties of a complex soft substrate.

Exploring a direct injection method for microfluidic generation of polymer microgels

Microfluidics (MFs) offers a promising method for the preparation of polymer microgels with exquisite control over their dimensions, shapes and morphologies. A challenging task in this process is the generation of droplets (precursors for microgels) from highly viscous polymer solutions. Spatial separation of MF emulsification and gelation of the precursor droplets on chip can address this challenge. In the present work, we explored the application of the "direct injection" method for the preparation of microgels by adding a highly concentrated polymer solution or a gelling agent directly into the precursor droplets. In the first system, primary droplets were generated from a dilute aqueous solution of agarose, followed by the injection of the concentrated agarose solution directly in the primary droplets. The secondary droplets served as precursors for microgels. In the second system, primary droplets were generated from the low-viscous solution of methyl-β-cyclodextrin and poly(ethylene glycol) end-terminated with octadecyl hydrophobic groups. Addition of surfactant directly into the primary droplets led to the binding of methyl-β-cyclodextrin to the surfactant, thereby releasing hydrophobized poly(ethylene glycol) to form polymer microgels. Our results show that, when optimized, the direct injection method can be used for microgel preparation from highly viscous liquids and thus this method expands the range of polymers used for MF generation of microgels.

Straight contact lines on a soft, incompressible solid

The deformation of a soft substrate by a straight contact line is calculated, and the result applied to a static rivulet between two parallel contact lines. The substrate is supposed to be incompressible (Stokes-like description of elasticity), and having a non-zero surface tension, that eventually differs depending on whether its surface is dry or wet. For a single straight line separating two domains with the same substrate surface tension, the ridge profile is shown to be very close to that of Shanahan and de Gennes, but shifts from the contact line of a distance equal to the elastocapillary length built upon substrate surface tension and shear modulus. As a result, the divergence near contact line disappears and is replaced by a balance of surface tensions at the contact line (Neumann equilibrium), though the profile remains nearly logarithmic. In the rivulet case, using the previous solution as a Green function allows one to calculate analytically the geometry of the distorted substrate, and in particular its slope on each side (wet and dry) of the contact lines. These two slopes are shown to be nearly proportional to the inverse of substrate surface tensions, though the respective weight of each side (wet and dry) in the final expressions is difficult to establish because of the linear nature of standard elasticity. A simple argument combining Neumann and Young equations is however provided to overcome this limitation. The result may have surprising implications for the modelling of hysteresis on systems having both plastic and elastic properties, as initiated long ago by Extrand and Kumagai.

Low-power laser deformation of an air-liquid interface

We report on the deformation of an air-water surface with a totally reflected low-power laser beam, inducing a convex mirror effect on the beam propagation. This bending is stronger close to the critical angle and depends on the polarization of the laser light. A model, leading to a simple dependence between the Goos-Hänchen shift and the radius of curvature of the interface, supports these observations. Bendings with radius of curvature as low as 0.10 m are demonstrated.