We present a theory of viscoelasticity of amorphous media, which takes into account the effects of confinement along one of three spatial dimensions. The framework is based on the nonaffine extension of lattice dynamics to amorphous systems, or nonaffine response theory. The size effects due to the confinement are taken into account via the nonaffine part of the shear storage modulus $G'$. The nonaffine contribution is written as a sum over modes in $k$-space. With a rigorous argument based on the analysis of the $k$-space integral over modes, it is shown that the confinement size $L$ in one spatial dimension, e.g. the $z$ axis, leads to a infrared cut-off for the modes contributing to the nonaffine (softening) correction to the modulus that scales as $L^{-3}$. Corrections for finite sample size $D$ in the two perpendicular dimensions scale as $\sim (L/D)^4$, and are negligible for $L \ll D$. For liquids it is predicted that $G'\sim L^{-3}$ in agreement with a previous more approximate analysis, whereas for amorphous materials $G' \sim G'_{bulk} + βL^{-3}$. For the case of liquids, four different experimental systems are shown to be very well described by the $L^{-3}$ law.
We generalise the non-affine theory of viscoelasticity for use with large, well-sampled systems of arbitrary chemical complexity. Having in mind predictions of mechanical and vibrational properties of amorphous systems with atomistic resolution, we propose an extension of the Kernel Polynomial Method (KPM) for the computation of the vibrational density of states (VDOS) and the eigenmodes, including the $Γ$-correlator of the affine force-field, which is a key ingredient of lattice-dynamic calculations of viscoelasticity. We show that the results converge well to the solution obtained by direct …
We present a theoretical derivation of acoustic phonon damping in amorphous solids based on the nonaffine response formalism for the viscoelasticity of amorphous solids. The analytical theory takes into account the nonaffine displacements in transverse waves and is able to predict both the ubiquitous low-energy diffusive damping $\sim k^{2}$, as well as a novel contribution to the Rayleigh damping $\sim k^{4}$ at higher wavevectors and the crossover between the two regimes observed experimentally. The coefficient of the diffusive term is proportional to the microscopic viscous (Langevin-type) …
The effects of viscoelasticity on the dynamics and break-up of fluid threads in microfluidic T-junctions are investigated using numerical simulations of dilute polymer solutions at changing the Capillary number ($\mbox {Ca}$), i.e. at changing the balance between the viscous forces and the surface tension at the interface, up to $\mbox{Ca} \approx 3 \times 10^{-2}$. A Navier-Stokes (NS) description of the solvent based on the lattice Boltzmann models (LBM) is here coupled to constitutive equations for finite extensible non-linear elastic dumbbells with the closure proposed by Peterlin (FENE-P …
We present a mathematical description of amorphous solid deformation and plasticity by extending the concept of instantaneous normal modes (INMs) to deformed systems, which allows us to retain the effect of strain on the vibrational density of states (VDOS). Starting from the nonaffine lattice dynamics (NALD) description of elasticity and viscoelasticity of glasses, we formulate the linear response theory up to large deformations by considering the strain-dependent tangent modulus at finite values of shear strain. The (nonaffine) tangent shear modulus is computed from the vibrational density o…
We investigate the break-up of Newtonian/viscoelastic droplets in a viscoelastic/Newtonian matrix under the hydrodynamic conditions of a confined shear flow. Our numerical approach is based on a combination of Lattice-Boltzmann models (LBM) and Finite Difference (FD) schemes. LBM are used to model two immiscible fluids with variable viscosity ratio (i.e. the ratio of the droplet to matrix viscosity); FD schemes are used to model viscoelasticity, and the kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbe…
Amorphous solids, confined on the nano-scale, exhibit a wealth of novel phenomena yet to be explored. In particular, the response of such solids to a mechanical load is not well understood and, as has been demonstrated experimentally, it differs strongly from bulk samples made of the same materials. Failure patterns and mechanisms are strongly affected by the geometry of the confinement and the interplay between interfacial effects in the sample and the time scale, imposed by an external mechanical field. Here, we present the mechanism of cavity formation in a confined model glass, subjected t…
Being able to reduce the size of a rheometer down to the micron scale is a unique opportunity to explore the mechanical response of expensive and/or confined liquids and gels. To this aim, we synthesize micron size wires with magnetic properties and examine the possibility of using them as microrheology probes. In this work, we exploit the technique of rotational magnetic spectroscopy by placing a wire in a rotating magnetic field and monitor its temporal evolution by time-lapse microscopy. The wire-based microrheology technique is tested on wormlike micellar surfactant solutions showing very …
Analytic theory of shear localization in amorphous solids confined by Couette geometry
Hangzhou International Innovation Institute, Beihang University（北京航空航天大学杭州创新研究院）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Center for Theoretical Interdisciplinary Sciences, Wenzhou Institute, University of Chinese Academy of Sciences（中国科学院大学温州研究院交叉科学研究中心）；Sino-Europe Complex Science Center, School of Mathematics, North University of China（中北大学数学学院中欧复杂科学中心）；Department of Chemical Physics, The Weizmann Institute of Science（魏茨曼科学研究所化学物理系）
Recent theories predict that when a supercooled liquid approaches the glass transition, particle clusters with a special "amorphous order" nucleate within the liquid, which lead to static correlations dictating the dramatic slowdown of liquid relaxation. The prediction, however, has yet to be verified in 3D experiments. Here, we design a colloidal system, where particles are confined inside spherical cavities with an amorphous layer of particles pinned at the boundary. Using this novel system, we capture the amorphous-order particle clusters and demonstrate the development of a static correlat…
The effects of elasticity on the break-up of liquid threads in microfluidic cross-junctions is investigated using numerical simulations based on the "lattice Boltzmann models" (LBM). Working at small Capillary numbers, we investigate the effects of non-Newtonian phases in the transition from droplet formation at the cross-junction (DCJ) and droplet formation downstream of the cross-junction (DC) (Liu & Zhang, ${\it Phys. Fluids.}$ ${\bf 23}$, 082101 (2011)). Viscoelasticity is found to influence the break-up point of the threads, which moves closer to the cross-junction and stabilizes. This is…
Cooperative effects of membrane confinement and gelation on PEG crystallization pathway
The University of Tokyo（东京大学）；Komaba Institute for Science, Graduate School of Arts and Sciences, The University of Tokyo（东京大学综合文化研究科驹场科学研究所）；Institute of Industrial Science, The University of Tokyo（东京大学工业科学研究所）
Fluid-induced alteration of rocks and mineral-based materials often starts at confined mineral interfaces where nm-thick water films can persist even at high overburden pressures and at low vapor pressures. These films enable transport of reactants and affect forces acting between mineral surfaces. However, the feedback between the surface forces and reactivity of confined solids is not fully understood. We used the surface forces apparatus (SFA) to follow surface reactivity in confinement and measure nm-range forces between two rough calcite surfaces in NaCl, CaCl$_2$, or MgCl$_2$ solutions w…
A possible role of quantum effects, such as tunneling and zero-point energy, in the structural dynamics of supercooled liquids is studied by dielectric spectroscopy. Presented results demonstrate that the liquids, bulk 3-methylpentane 3MP and confined normal and deuterated water have low glass transition temperature and unusually low for their class of materials steepness of the temperature dependence of structural relaxation, or fragility. Although we do not find any signs of tunneling in structural relaxation of these liquids, their unusually low fragility can be well described by the influe…
The deformation of disordered solids relies on swift and localised rearrangements of particles. The inspection of soft vibrational modes can help predict the locations of these rearrangements, while the strain that they actually redistribute mediates collective effects. Here, we study soft modes and strain redistribution in a two-dimensional continuous mesoscopic model based on a Ginzburg-Landau free energy for perfect solids, supplemented with a plastic disorder potential that accounts for shear softening and rearrangements. Regardless of the disorder strength, our numerical simulations show …
The phase behavior of hydrocarbon fluids confined in porous media has been reported to deviate significantly from that in the bulk environment due to the existence of sub-10nm pores. Though experiments and simulations have measured the bubble/dew points and sorption isotherms of hydrocarbons confined in both natural and synthetic nanopores, the confinement effects in terms of the strength of fluid-pore interactions tuned by surface wettability and chemistry have received comparably less discussion. More importantly, the underlying physics of confinement-induced phenomena remain obfuscated. In …
