We construct a phase field model including hydrodynamics and elasticity in one-component systems. It can be used to investigate solid-liquid and liquid-liquid phase transitions. Upon first-order phase transition, a velocity field is induced around interfaces in the presence of a density difference between the two phases even without applied shear flow. As applications, we present simulation results on two cases of melting, where a solid domain is placed on a heated wall in one case and is suspended in a warmer liquid under shear flow in the other. We find that the solid domain moves or rotates as a whole due to elasticity, releasing latent heat. We also examine the liquid-liquid phase transition of a highly viscous domain into a less viscous liquid on a heated wall, where an inhomogeneous velocity field is induced within a projected part of the domain. In these phase transitions, the interface temperature is nearly equal to the coexisting temperature $T_{\rm cx}(p)$ away from the heated wall in the presence of heat flow in the surrounding liquid.
Liquid-crystal networks consist of weakly crosslinked polymers that are coupled to liquid-crystal molecules. The resultant hybrid system has rich elastic properties. We develop a phase field model to describe mechanical properties of a hexagonal liquid-crystal network. The hexagonal liquid-crystal network is found to have soft shear deformations. The elastic properties are predicted analytically and confirmed with numerical simulations. In addition the model incorporates non-linear elasticity and dislocations or disclinations.
Spatial correlations for sheared isothermal elastic liquids and granular liquids are theoretically investigated. Using the generalized fluctuating hydrodynamics, correlation functions for both the microscopic scale and the macroscopic scale are obtained. The existence of the long-range correlation functions obeying power laws has been confirmed. The validity of our theoretical predictions have been verified from the molecular dynamics simulation.
Recent progress in approaches to determine the elastic constants of solids starting from the microscopic particle interactions is reviewed. On the theoretical side, density functional theory approaches are discussed and compared to more classical ones using the actual pair potentials. On the experimental side, video microscopy has been introduced to measure the elastic constants in colloidal solids. For glasses and disordered systems, the theoretical basis is given for this novel technique, and some challenges and recent advances are reviewed.
In this paper, we propose a new derivation for the Green-Kubo relationship for the liquid-solid friction coefficient, characterizing hydrodynamic slippage at a wall. It is based on a general Langevin approach for the fluctuating wall velocity, involving a non-markovian memory kernel with vanishing time integral. The calculation highlights some subtleties of the wall-liquid dynamics, leading to superdiffusive motion of the fluctuating wall position.
We have developed a Green-Kubo relation that enables accurate calculations of friction at solid-liquid interfaces directly from equilibrium molecular dynamics (MD) simulations and that provides a pathway to bypass the time-scale limitations of typical nonequilibrium MD simulations. The theory has been validated for a number of different interfaces and it is demonstrated that the liquid-solid slip is an intrinsic property of an interface. Because of the high numerical efficiency of our method, it can be used in the design of interfaces for applications in aqueous environments, such as nano- and…
We study the elastic theory of amorphous solids made of particles with finite range interactions in the thermodynamic limit. For the elastic theory to exist one requires all the elastic coefficients, linear and nonlinear, to attain a finite thermodynamic limit. We show that for such systems the existence of non-affine mechanical responses results in anomalous fluctuations of all the nonlinear coefficients of the elastic theory. While the shear modulus exists, the first nonlinear coefficient B_2 has anomalous fluctuations and the second nonlinear coefficient B_3 and all the higher order coeffic…
We investigate the deformation of elastic microcapsules adsorbed at liquid-liquid interfaces. An initially spherical elastic capsule at a liquid-liquid interface undergoes circumferential stretching due to the liquid-liquid surface tension and becomes lens- or discus-shaped, depending on its bending rigidity. The resulting elastic capsule deformation is qualitatively similar, but distinct from the deformation of a liquid droplet into a liquid lens at a liquid-liquid interface. We discuss the deformed shapes of droplets and capsules adsorbed at liquid-liquid interfaces for a whole range of diff…
By reinforcing the interaction energy of the liquid with respect to the surface using total wetting boundary conditions, the response of liquids to mechanical shear stress is stronger and exhibits at sub-millimeter scale elastic properties. This study extends here to liquids with strong electrostatic interactions such as ionic liquids and paramagnetic liquids. We show that it is also possible to identify and measure a non-zero low-frequency shear elasticity at sub-millimeter scale. The observation of mesoscopic elastic properties in liquids generally considered as viscous away from any phase t…
When two elastic solids with randomly rough surfaces are brought in contact, a very inhomogeneous stress distribution sigma(x) will occur at the interface. Here I study the elastic energy and the correlation function <sigma(q)sigma(-q)>, where sigma(q) is the Fourier transform of sigma(x) and where <...> stands for ensemble average. I relate <sigma(q})sigma(-q)> to the elastic energy stored at the interface, and I show that for self affine fractal surfaces, quite generally <sigma(q)sigma(-q)> \sim q^{-(1+H)}, where H is the Hurst exponent of the self-affine fractal surface.
Although fully elastic when static, granular media become transiently elastic when being slowly sheared -- during which both the elastic energy and stress relax. Starting from this observation, we cogently derive the framework for granular hydrodynamics, a set of differential equations consistent with general principles of physics, especially reversible and irreversible thermodynamics. In addition, an expression for the granular elastic energy is reviewed and further discussed.
Fundamental thermodynamical concepts and a solid-state point defect elastic model are used to formulate a diffusivity-density scaling function for viscous liquids. It is proved in a straightforward manner that the scaling exponent describing the density scaling of the diffusivity, is related with the pressure derivative of the isothermal bulk modulus.
We have established the surface tension relaxation time in the liquid-solid interfaces of Lennard-Jones (LJ) liquids by means of direct measurements in molecular dynamics (MD) simulations. The main result is that the relaxation time is found to be weakly dependent on the molecular structures used in our study and lies in such a range that in slow hydrodynamic motion the interfaces are expected to be at equilibrium. The implications of our results for the modelling of dynamic wetting processes and interpretation of dynamic contact angle data are discussed.
Solid interfaces have intrinsic elasticity. However, in most experiments, this is obscured by bulk stresses. Through microscopic observations of the contact-line geometry of a partially wetting droplet on an anisotropically stretched substrate, we measure two surface-elastic constants that quantify the linear dependence of the surface stress of a soft polymer gel on its strain. With these two parameters, one can predict surface stresses for general deformations of the material in the linear-elastic limit.
There has been long-standing debate about the physical state and possible phase transformations of confined liquids. In this report we show that a model confined liquid can behave both as a Newtonian liquid with very little change in its dynamics or as a pseudo-solid depending solely on the {\it rate} of approach of the confining surfaces. Thus, the confined liquid does {\it not} exhibit any confinement induced solidification in thermodynamic equilibrium. Instead, solidification is induced kinetically, when the two confining surfaces are approached with a minimum critical rate. This critical r…
For a deeply supercooled liquid just above its glass transition temperature, we present a simple thermodynamic model, where the deeply supercooled liquid is assumed to be a mixture of solid-like and liquid-like micro regions. The mole fraction of the liquid-like regions controls the thermodynamic properties of the supercooled liquid while that of the solid-like regions controls its relaxation time or viscosity. From the universal temperature dependence of the molar excess entropy for the deeply supercooled liquids, we derive the temperature dependence of the mole fraction of the liquid-like re…
We show that the electric field driven surface instability of visco-elastic films has two distinct regimes: (1) The visco-elastic films behaving like a liquid display long wavelengths governed by applied voltage and surface tension, independent of its elastic storage and viscous loss moduli, and (2) the films behaving like a solid require a threshold voltage for the instability whose wavelength always scales as ~ 4 x film thickness, independent of its surface tension, applied voltage, loss and storage moduli. Wavelength in a narrow transition zone between these regimes depends on the storage m…
Plasticity in amorphous solids is mediated by localized quadrupolar instabilities, but the mechanism by which an amorphous solid eventually fails or melts is debated. In this work we argue that these phenomena can be investigated in the model problem of an elastic continuum with quadrupolar defects, at finite temperature. This problem is posed and the collective behavior of the defects is analytically investigated. Using both renormalization group and field-theoretic techniques, it is found that the model has a yielding/melting transition of spinodal type.
We show that the elastic charge of colloids in a nematic liquid crystal can be generated by the vector of external torque. The torque components play the role of two component charge (dyad) and give rise to the Coulomb-like potential, while their conservation law plays the role similar to that of Gauss' theorem in the electrostatics. The theory is applied to the colloid-surface interaction. A wall with homeotropic or planar director is shown to induce a repulsive 1/r^4 force on the elastic dipole. The external torque, however, induces the elastic charge in this colloid and triggers switching t…
An approach to calculate high-frequency bulk and shear modului of two-dimensional (2D) weakly screened Yukawa fluids and solids is presented. Elastic moduli are directly related to sound velocities and other important characteristics of the system. In this article we discuss these relations and present exemplary calculation of the longitudinal, transverse, and instantaneous sound velocities and derive a differential equation for the Einstein frequency. Simple analytical results presented demonstrate good accuracy when compared with numerical calculations. The obtained results can be particular…
The effective solid liquid interfacial tension (SL IFT) between pure liquids and rough solid surfaces is studied through coarse grained simulations. Using the dissipative particle dynamics method, we design solid liquid interfaces, confining a pure liquid between two explicit solid surfaces with different roughness degrees. The roughness of the solid phase was characterized by Wenzel roughness factor and the effective SL IFT (γ_sl^') is reported as a function of it also. Two solid liquid systems differentiated from each other by their solid liquid repulsion strength are studied to measure the …
The thermodynamics and dynamics of supercooled liquids correlate with their elasticity. In particular for covalent networks, the jump of specific heat is small and the liquid is {\it strong} near the threshold valence where the network acquires rigidity. By contrast, the jump of specific heat and the fragility are large away from this threshold valence. In a previous work [Proc. Natl. Acad. Sci. U.S.A., 110, 6307 (2013)], we could explain these behaviors by introducing a model of supercooled liquids in which local rearrangements interact via elasticity. However, in that model the disorder char…
I study how the contact area and the work of adhesion, between two elastic solids with randomly rough surfaces, depend on the relative humidity. The surfaces are assumed to be hydrophilic, and capillary bridges form at the interface between the solids. For elastically hard solids with relative smooth surfaces, the area of real contact and therefore also the sliding friction, are maximal when there is just enough liquid to fill out the interfacial space between the solids, which typically occurs for $d_{\rm K} \approx 3 h_{\rm rms}$, where $d_{\rm K}$ is the height of the capillary bridge and $…
What characterises a solid is its way to respond to external stresses. Ordered solids, such crystals, display an elastic regime followed by a plastic one, both well understood microscopically in terms of lattice distortion and dislocations. For amorphous solids the situation is instead less clear, and the microscopic understanding of the response to deformation and stress is a very active research topic. Several studies have revealed that even in the elastic regime the response is very jerky at low temperature, resembling very much the one of disordered magnetic materials. Here we show that in…
The Ginzburg-Landau free energy functional for hard-spheres is constructed using the Fundamental Measure Theory approach to Density Functional Theory as a starting point. The functional is used to study the liquid-fcc solid planer interface and the properties of small solid clusters nucleating within a liquid. The surface tension for planer interfaces agrees well with simulation and it is found that the properties of the solid clusters are consistent with classical nucleation theory.
The nonlinear elastic properties of nematic liquid crystals have acquired new interest with the recent experimental observation of bulk modulated nematic phases which are composed by achiral molecules. We extend the Oseen-Zocher-Frank's elastic theory for nematic liquid crystals by including gradients of the nematic strain tensor in the elastic deformation energy. The invariants of the elastic tensor fields, up to the fourth order in the nematic director spatial derivatives, are calculated. An alternative approach that consists in the extension of the linear elastic energy to higher powers of …
We show numerically that the response of simple amorphous solids (elastic networks and particle packings) to a local force dipole is characterized by a lengthscale $\ell_c$ that diverges as unjamming is approached as $\ell_c \sim (z - 2d)^{-1/2}$, where $z \ge 2d$ is the mean coordination, and $d$ is the spatial dimension, at odds with previous numerical claims. We also show how the magnitude of the lengthscale $\ell_c$ is amplified by the presence of internal stresses in the disordered solid. Our data suggests a divergence of $\ell_c\sim (p_c-p)^{-1/4}$ with proximity to a critical internal s…
Deformation due to embedded fluidic networks is currently studied in the context of soft-actuators and soft-robotics. Expanding on this concept, beams can be designed so that the pressure in the channel-network is created directly from external forces acting on the beam, and thus can be viewed as passive solid-liquid composite structure. We obtain a continuous function relating the network geometry to the deformation. This enables design of networks creating arbitrary steady and time varying deformation-fields as well as to eliminate deformation created by external forces.
Using laser tweezers and fluorescence confocal polarizing microscopy, we study colloidal interactions of solid microspheres in the nematic bulk caused by elastic distortions around the particles with strong tangential surface anchoring. The particles aggregate into chains directed at about 30 degrees to the far field director and, at higher concentrations, form complex kinetically trapped structures. We characterize the distance and angular dependencies of the colloidal interaction forces.
We study the average separation between an elastic solid and a hard solid with a nominal flat but randomly rough surface, as a function of the squeezing pressure. We present experimental results for a silicon rubber (PDMS) block with a flat surface squeezed against an asphalt road surface. The theory shows that an effective repulse pressure act between the surfaces of the form p proportional to exp(-u/u0), where u is the average separation between the surfaces and u0 a constant of order the root-mean-square roughness, in good agreement with the experimental results.
When deformed, liquid foams tend to raise their liquid contents like immersed granular materials, a phenomenon called dilatancy. We have aready described a geometrical interpretation of elastic dilatancy in 3D foams and in very dry foams squeezed between two solid plates (2D GG foams). Here, we complement this work in the regime of less dry 2D GG foams. In particular, we highlight the relatively strong dilatancy effects expected in the regime where we have predicted rapid Plateau border variations.
We investigate numerically the behaviour of a phase-separating mixture of a blue phase I liquid crystal with an isotropic fluid. The resulting morphology is primarily controlled by an inverse capillary number, $χ$, setting the balance between interfacial and elastic forces. When $χ$ and the concentration of the isotropic component are both low, the blue phase disclination lattice templates a cubic array of fluid cylinders. For larger $χ$, the isotropic phase arranges primarily into liquid emulsion droplets which coarsen very slowly, rewiring the blue phase disclination lines into an amorphous …
We first review the phenomenology of viscous liquids and the standard models used for explaining the non-Arrhenius average relaxation time. Then the focus is turned to the so-called elastic models, arguing that these models are all equivalent in the Einstein approximation (where the short-time elastic properties are all determined by just one effective, temperature-dependent force constant). We finally discuss the connection between the elastic models and two well-established research fields of condensed-matter physics: point defects in crystals and solid-state diffusion.
We study the distribution of interfacial separations P(u) at the contact region between two elastic solids with randomly rough surfaces. An analytical expression is derived for P(u) using Persson's theory of contact mechanics, and is compared to numerical solutions obtained using (a) a half-space method based on the Boussinesq equation, (b) a Green's function molecular dynamics technique and (c) smart-block classical molecular dynamics. Overall, we find good agreement between all the different approaches.
Acousto-elasticity is concerned with the propagation of small-amplitude waves in deformed solids. Results previously established for the incremental elastodynamics of exact non-linear elasticity are useful for the determination of third- and fourth-order elastic constants, especially in the case of incompressible isotropic soft solids, where the expressions are particularly simple. Specifically, it is simply a matter of expanding the expression for $ρv^2$, where $ρ$ is the mass density and v the wave speed, in terms of the elongation $e$ of a block subject to a uniaxial tension. The analysis s…
A theory for the non-local stress in liquids captures the crossover from viscous to elastic correlations upon supercooling. It explains the emergence of long-ranged stress fields in glass which originate from the coupling of shear stress to transverse deformations. The Goldstone mode in colloidal glass is shown to be diffusive.
We demonstrate the instability of the free surface of a soft elastic solid facing downwards. Experiments are carried out using a gel of constant density $ρ$, shear modulus $μ$, put in a rigid cylindrical dish of depth $h$. When turned upside down, the free surface of the gel undergoes a normal outgoing acceleration $g$. It remains perfectly flat for $ρg h/μ<α^* $ with $α^*\simeq 6$, whereas a steady pattern spontaneously appears in the opposite case. This phenomenon results from the interplay between the gravitational energy and the elastic energy of deformation, which reduces the Rayleigh wav…
Living and engineered systems rely on the stable coexistence of two interspersed liquid phases. Yet surface tension drives their complete separation. Here we show that stable droplets of uniform and tuneable size can be produced through arrested phase separation in an elastic matrix. Starting with an elastic polymer network swollen by a solvent mixture, we change the temperature or composition to drive demixing. Droplets nucleate and grow to a stable size that is tuneable by the network cross-linking density, the cooling rate, and the composition of the solvent mixture. We discuss thermodynami…
We study the heat transfer between elastic solids with randomly rough surfaces. We include both the heat transfer from the area of real contact, and the heat transfer between the surfaces in the noncontact regions. We apply a recently developed contact mechanics theory, which accounts for the hierarchical nature of the contact between solids with roughness on many different length scales. For elastic contact, at the highest (atomic) resolution the area of real contact typically consists of atomic (nanometer) sized regions, and we discuss the implications of this for the heat transfer. For soli…
Johnson-Kendall-Robert (JKR) theory is the basis of modern contact mechanics. It describes how two deformable objects adhere together, driven by adhesion energy and opposed by elasticity. However, it does not include solid surface tension, which also opposes adhesion by acting to flatten the surface of soft solids. We tested JKR theory to see if solid surface tension affects indentation behaviour. Using confocal microscopy, we characterised the indentation of glass particles into soft, silicone substrates. While JKR theory held for particles larger than a critical, elastocapillary lengthscale,…
The physical mechanism of elasticity of liquid surfaces coated with colloidal particles is proposed. It is suggested that particles are separated by water clearings and the capillary interaction between them is negligible. The case is treated when the colloidal layer is deformed normally to its surface. The elasticity arises as an interfacial effect. The effective Young modulus of a surface depends on the interfacial tension, equilibrium contact angle, radius of colloidal particles and their surface density. For the nanometrically scaled particles the line tension becomes essential and has an …
The holographic duality has proven successful in linking seemingly unrelated problems in physics.Recently, intriguing correspondences between the physics of soft matter and gravity are emerging,including strong similarities between the rheology of amorphous solids, effective field theories for elasticity and the physics of black holes. However, direct comparisons between theoretical predictions and experimental/simulation observations remain limited. Here, we study the effects of non-linear elasticity on the mechanical and thermodynamic properties of amorphous materials responding to shear, us…
Liquid marbles are non-stick droplets covered with micro-scaled particles. Liquid marbles demonstrate quasi-elastic properties when pressed. The interpretation of the phenomenon of elasticity of liquid marbles is proposed. The model considering the growth in the marble surface in the course of deformation under the conservation of marbles volume explains semi-quantitatively the elastic properties of marbles in satisfactory agreement with the reported experimental data. The estimation of the effective Young modulus of marbles and its dependence on the marble volume are reported.
In this supplementary paper we present some details on the solid-liquid interface detection, the deduction of the non-equilibrium free energy, the analysis of the granular temperature and energy per mode, a validation of the small slope approximation, a description of the Langevin dynamics, and the error analysis.
A liquid drop sitting on an elastic rod may act as a winch, or windlass, and pull the rod inside itself and coil it. This windlass effect has been shown to be generated by surface tension forces and to work best for small systems. Here we study the case where the drop is large enough so that its weight interferes with surface tension and modifies the windlass mechanics.
The capillary-induced structural instability of an elastic circular tube partially filled by a liquid is studied by combining theoretical analysis and molecular dynamics simulations. The analysis shows that, associated with the instability, there is a well-defined length scale (elasto-capillary length), which exhibits a scaling relationship with the characteristic length of the tube, regardless of the interaction details. We validate this scaling relationship for a carbon nanotube partially filled by liquid iron. The capillary-induced structural transformation could have potential applications…
From bone and wood to concrete and carbon fibre, composites are ubiquitous natural and engineering materials. Eshelby's inclusion theory describes how macroscopic stress fields couple to isolated microscopic inclusions, allowing prediction of a composite's bulk mechanical properties from a knowledge of its microstructure. It has been extended to describe a wide variety of phenomena from solid fracture to cell adhesion. Here, we show experimentally and theoretically that Eshelby's theory breaks down for small liquid inclusions in a soft solid. In this limit, an isolated droplet's deformation is…
We study the interaction of a liquid drop with an elastic beam in the case where bending effects dominate. We use a variational approach to derive equilibrium equations for the system in the presence of gravity and in the presence or absence of contact line pinning. We show that the derived equilibrium equations for the beam subsystem reveal the external forces applied on the beam by the liquid and vapor phases. Among these, the force applied at the triple line (the curve where the three phases meet) is found to lie along the liquid-vapor interface.
The anisotropic, stress-dependent velocity of elastic waves in glass beads -- as observed by Y. Khidas and X. Jia, see [Phys. Rev. E, 81:021303, Feb. 2010] -- is shown to be well accounted for by ``granular solid hydrodynamics,'' a broad-range macroscopic theory of granular behavior. As the theory makes no reference to fabric anisotropy, the influence of which on sound is in doubt.
We study the immersion of a ferromagnetic nanowire within a nematic liquid crystal using a lattice Boltzmann algorithm to solve the full three-dimensional equations of hydrodynamics. We present an algorithm for including a moving boundary, to simulate a nanowire, in a lattice Boltzmann simulation. The nematic imposes a torque on a wire that increases linearly with the angle between the wire and the equilibrium direction of the director field. By rotation of these nanowires, one can determine the elastic constants of the nematic.
We have given theoretical expressions for the forces exerted on a quasi-2D flat and smooth solid plate immersed into a liquid pool of a simple liquid. All forces given by the theory, the local forces on the top, the contact line and the bottom of the plate as well as the total force, showed an excellent agreement with the MD simulation results. We also revealed that the local forces around the bottom and top of the solid plate can be related to the SL and SV interfacial tensions γ_{SL} and γ_{SV}, and this was verified through the comparison with the SL and SV works of adhesion obtained by the…
Spatial heterogeneity in the elastic properties of soft random solids is examined via vulcanization theory. The spatial heterogeneity in the \emph{structure} of soft random solids is a result of the fluctuations locked-in at their synthesis, which also brings heterogeneity in their \emph{elastic properties}. Vulcanization theory studies semi-microscopic models of random-solid-forming systems, and applies replica field theory to deal with their quenched disorder and thermal fluctuations. The elastic deformations of soft random solids are argued to be described by the Goldstone sector of fluctua…
This paper first reviews the shoving model for the non-Arrhenius viscosity of viscous liquids. According to this model the main contribution to the activation energy of a flow event is the energy needed for molecules to shove aside the surrounding, an energy which is proportional to the instantaneous shear modulus of the liquid. Data are presented supporting the model. It is shown that the fractional Debye-Stokes-Einstein relation, that quantitatively expresses the frequently observed decoupling of, e.g., conductivity from viscous flow, may be understood within the model. The paper goes on to …
Ginzburg-Landau-de Gennes -type covariant theories are extensively used in connection with twist grain boundary (TGB) phases of chiral smectogens. We analyze the stability conditions for the linear, covariant elasticity theory of smectic-C liquid crystals in the context of achiral materials, and predict an equilibrium modulated structure with an oblique wavevector. We suggest that a previous experimental observation of stripes in smectic-C is consistent with the predicted structure.
Mixed mode (I+III) loading induces segmented crack front échelon structures connected by steps. We study this instability in a highly deformable, strain-hardening material. We find that échelons develop beyond a finite, size-independent mode mixity threshold, markedly growing with energy release rate. They appear via nucleation of localized helical front distortions, and their emergence is the continuation of the mode I cross-hatching instability of gels and rubbers, shifted by the biasing effect of shear. This result, at odds with the direct bifurcation predicted by linear elastic fracture me…
A solid withdrawn from a liquid bath entrains a film. In this review, after recalling the predictions and results for pure Newtonian liquids coated on simple solids, we analyze the deviations to this ideal case exploring successively three potential sources of complexity: the liquid-air interface, the bulk rheological properties of the liquid and the mechanical or chemical properties of the solid. For these different complexities, we show that significant effects on the film thickness are observed experimentally and we summarize the theoretical analysis presented in the literature, which attem…
