In this paper, theoretical and experimental approaches to flow, hydrodynamic dispersion, and miscible and immiscible displacement processes in reservoir rocks are reviewed and discussed. Both macroscopically homogeneous and heterogeneous rocks are considered. The latter are characterized by large-scale spatial variations and correlations in their effective properties and include rocks that may be characterized by several distinct degrees of porosity, a well-known example of which is a fractured rock with two degrees of porosity---those of the pores and of the fractures. First, the diagenetic processes that give rise to the present reservoir rocks are discussed and a few geometrical models of such processes are described. Then, measurement and characterization of important properties, such as pore-size distribution, pore-space topology, and pore surface roughness, and morphological properties of fracture networks are discussed. It is shown that fractal and percolation concepts play important roles in the characterization of rocks, from the smallest length scale at the pore level to the largest length scales at the fracture and fault scales. Next, various structural models of homogeneous and heterogeneous rock are discussed, and theoretical and computer simulation approaches to flow, dispersion, and displacement in such systems are reviewed. Two different modeling approaches to these phenomena are compared. The first approach is based on the classical equations of transport supplemented with constitutive equations describing the transport and other important coefficients and parameters. These are called the continuum models. The second approach is based on network models of pore space and fractured rocks; it models the phenomena at the smallest scale, a pore or fracture, and then employs large-scale simulation and modern concepts of the statistical physics of disordered systems, such as scaling and universality, to obtain the macroscopic properties of the system. The fundamental roles of the interconnectivity of the rock and its wetting properties in dispersion and two-phase flows, and those of microscopic and macroscopic heterogeneities in miscible displacements are emphasized. Two important conceptual advances for modeling fractured rocks and studying flow phenomena in porous media are also discussed. The first, based on cellular automata, can in principle be used for computing macroscopic properties of flow phenomena in any porous medium, regardless of the complexity of its structure. The second, simulated annealing, borrowed from optimization processes and the statistical mechanics of spin glasses, is used for finding the optimum structure of a fractured reservoir that honors a limited amount of experimental data.

Flow phenomena in rocks : from continuum models to fractals, percolation, cellular automata, and simulated annealing

Deep eutectic solvents (DESs) are an emerging class of mixtures characterized by significant depressions in melting points compared to those of the neat constituent components. These materials are promising for applications as inexpensive "designer" solvents exhibiting a host of tunable physicochemical properties. A detailed review of the current literature reveals the lack of predictive understanding of the microscopic mechanisms that govern the structure-property relationships in this class of solvents. Complex hydrogen bonding is postulated as the root cause of their melting point depressions and physicochemical properties; to understand these hydrogen bonded networks, it is imperative to study these systems as dynamic entities using both simulations and experiments. This review emphasizes recent research efforts in order to elucidate the next steps needed to develop a fundamental framework needed for a deeper understanding of DESs. It covers recent developments in DES research, frames outstanding scientific questions, and identifies promising research thrusts aligned with the advancement of the field toward predictive models and fundamental understanding of these solvents.

Deep Eutectic Solvents: A Review of Fundamentals and Applications.

Magnetic flux can penetrate a type-II superconductor in the form of Abrikosov vortices (also called flux lines, flux tubes, or fluxons) each carrying a quantum of magnetic flux phi 0=h/2e. These tiny vortices of supercurrent tend to arrange themselves in a triangular flux-line lattice (FLL), which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-Tc superconductors (HTSCs) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSCs the FLL is very soft mainly because of the large magnetic penetration depth lambda . The shear modulus of the FLL is c66~1/ lambda 2, and the tilt modulus c44(k)~(1+k2 lambda 2)-1 is dispersive and becomes very small for short distortion wavelengths 2 pi /k<< lambda . This softness is enhanced further by the pronounced anisotropy and layered structure of HTSCs, which strongly increases the penetration depth for currents along the c axis of these (nearly uniaxial) crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may `melt` the FLL and cause thermally activated depinning of the flux lines or ofthe two-dimensional `pancake vortices` in the layers. Various phase transitions are predicted for the FLL in layered HTSCs. Although large pinning forces and high critical currents have been achieved, the small depinning energy so far prevents the application of HTSCs as conductors at high temperatures except in cases when the applied current and the surrounding magnetic field are small.

https://iopscience.iop.org/article/10.1088/0034-4885/58/11/003/pdf

The flux-line lattice in superconductors

Magnetic flux can penetrate a type-II superconductor in form of Abrikosov vortices. These tend to arrange in a triangular flux-line lattice (FLL) which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-$T_c$ supercon- ductors (HTSC's) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft mainly because of the large magnetic penetration depth: The shear modulus of the FLL is thus small and the tilt modulus is dispersive and becomes very small for short distortion wavelength. This softness of the FLL is enhanced further by the pronounced anisotropy and layered structure of HTSC's, which strongly increases the penetration depth for currents along the c-axis of these uniaxial crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may melt the FLL and cause thermally activated depinning of the flux lines or of the 2D pancake vortices in the layers. Various phase transitions are predicted for the FLL in layered HTSC's. The linear and nonlinear magnetic response of HTSC's gives rise to interesting effects which strongly depend on the geometry of the experiment.

The Flux-Line Lattice in Superconductors

Stretched exponential relaxation, , fits many relaxation processes in disordered and quenched electronic and molecular systems, but it is widely believed that this function has no microscopic basis, especially in the case of molecular relaxation. For electronic relaxation the appearance of the stretched exponential is often described in the context of dispersive transport, where is treated as an adjustable parameter, but in almost all cases it is generally assumed that no microscopic meaning can be assigned to even at , a glass transition temperature. We show that for molecular relaxation can be understood, providing that one separates extrinsic and intrinsic effects, and that the intrinsic effects are dominated by two magic numbers, for short-range forces, and for long-range Coulomb forces, as originally observed by Kohlrausch for the decay of residual charge on a Leyden jar. Our mathematical model treats relaxation kinetics using the Lifshitz - Kac - Luttinger diffusion to traps depletion model in a configuration space of effective dimensionality, the latter being determined using axiomatic set theory and Phillips - Thorpe constraint theory. The experiments discussed include ns neutron scattering experiments, particularly those based on neutron spin echoes which measure S( Q,t) directly, and the traditional linear response measurements which span the range from to s, as collected and analysed phenomenologically by Angell, Ngai, Bohmer and others. The electronic materials discussed include a-Si:H, granular , semiconductor nanocrystallites, charge density waves in , spin glasses, and vortex glasses in high-temperature semiconductors. The molecular materials discussed include polymers, network glasses, electrolytes and alcohols, Van der Waals supercooled liquids and glasses, orientational glasses, water, fused salts, and heme proteins. In the intrinsic cases the theory of is often accurate to 2%, which is often better than the quoted experimental accuracies . The extrinsic cases are identified by explicit structural signatures which are discussed at length. The discussion also includes recent molecular dynamical simulations for metallic glasses, spin glasses, quasicrystals and polymers which have achieved the intermediate relaxed Kohlrausch state and which have obtained values of in excellent agreement with the prediction of the microscopic theory.

https://iopscience.iop.org/article/10.1088/0034-4885/59/9/003/pdf

Stretched exponential relaxation in molecular and electronic glasses

A multilayer high Tc superconducting field‐effect transistor‐like structure was made from ultrathin YBa2Cu3O7−x films. An epitaxially grown dielectric SrTiO3 insulation layer, which had a forward bias breakdown voltage of about 20 V, allowed an electric field induced change in the channel layer of 1.25×1013 carrier/cm2 per volt of the gate voltage. A significant modulation of the normal state and superconducting properties was observed in samples with YBa2Cu3O7−x channel layers of a few unit cells thick. By applying gate voltage of different polarities, Tc was both suppressed and enhanced by ∼1 K. The resistance was modulated by as much as 20% in the normal state and by over 1500% near the zero resistance temperature.

Electric field effect in high Tc superconducting ultrathin YBa2Cu3O7−x films

We have measured, as a function of temperature and frequency, the velocity and attenuation of ultrasound near the glass transition of glycerol. The data are compared with that from frequency-dependent specific-heat measurements recently performed on the same sample. When the difference between adiabatic and isothermal processes is taken into account, we find that the relaxation time associated with the ultrasonic measurements is the same as that responsible for the dispersion seen in the specific-heat experiment. We also compare our results with recent hydrodynamic theories of the glass transition. The relaxation time that we measure can be fitted equally well either by a scaling form \ensuremath{\tau}=${\ensuremath{\tau}}_{0}$[(T-${T}_{h}$)/${T}_{h}$${]}^{\mathrm{\ensuremath{-}}\ensuremath{\alpha}}$, as these theories predict, or by the Vogel-Tamman-Fulcher law \ensuremath{\tau}=${\ensuremath{\tau}}_{0}$exp[E/${k}_{B}$(T-${T}_{0}$)], which has often been used to fit relaxation behavior in glasses. In the scaling-law fit, \ensuremath{\alpha}=12.5, which is unexpectedly large. The recent theory of Marchetti, which includes the wave-vector dependence of the mode-coupling vertex, provides a good fit to the frequency dependence of the data at constant temperature.

Ultrasonic investigation of the glass transition in glycerol

A steady-state inhomogeneous flow of a slowly moving flux-line lattice shows the fingerprint of the specific realization of dynamically generated disorder obtained through the interaction between the lattice and the quenched pinning centers. This is characteristic of ``tearing`` of a soft lattice and is pronounced in a narrow regime of the ({ital H},{ital T}) phase diagram where the system is neither a stiff lattice nor a fluid. A first-order depinning transition accompanying this nonequilibrium dynamical phenomenon is fundamentally different from an equilibrium ``melting`` of a flux-line lattice. A length scale is proposed to describe the dynamics.

Flux-flow fingerprint of disorder: Melting versus tearing of a flux-line lattice.

Dynamics of a ``quasi-two-dimensional'' flux-line lattice in the layered superconductor 2H-${\mathrm{NbSe}}_{2}$ for field normal to the layers is investigated at high fields. Comparisons with numerical simulations imply the presence of plastic flow for soft lattices. Dimensionality effects are more pronounced in the disorder-dominated regime, where a power-law scaling form for the I-V curve yields the conductivity exponent above the percolation threshold.

Peak effect and anomalous flow behavior of a flux-line lattice.

We use the pressure generated by a small-amplitude oscillatory flow to probe the dynamics of moving contact lines By measuring the Fourier amplitude at harmonics of the applied frequency as a function of the steady-state velocity, we are able to determine the velocity dependence of the excess dissipation caused by the moving contact line We find that the pressure drop associated with this dissipation scales as a power of the contact-line velocity V as ${\mathit{P}}_{\mathrm{cap}}$\ensuremath{\propto}${\mathit{V}}^{\mathit{x}}$, with x=040\ifmmode\pm\else\textpm\fi{}005 We discuss these results in terms of recent theoretical models

S. Bhattacharya

Papers

Electric field effect in high Tc superconducting ultrathin YBa2Cu3O7−x films

Ultrasonic investigation of the glass transition in glycerol

Flux-flow fingerprint of disorder: Melting versus tearing of a flux-line lattice.

Peak effect and anomalous flow behavior of a flux-line lattice.

Harmonic generation as a probe of dissipation at a moving contact line.