Lubricated viscous gravity currents

AbstractWe present a theoretical and experimental study of viscous gravity currents lubricated by another viscous fluid from below. We use lubrication theory to model both layers as Newtonian fluids spreading under their own weight in two-dimensional and axisymmetric settings over a smooth rigid horizontal surface and consider the limit in which vertical shear provides the dominant resistance to the flow in both layers. There are contributions from Poiseuille-like flow driven by buoyancy and Couette-like flow driven by viscous coupling between the layers. The flow is self-similar if both fluids are released simultaneously, and exhibits initial transient behaviour when there is a delay between the initiation of flow in the two layers. We solve for both situations and show that the latter converges towards self-similarity at late times. The flow depends on three key dimensionless parameters relating the relative dynamic viscosities, input fluxes and density differences between the two layers. Provided the density difference between the two layers is bounded away from zero, we find an asymptotic solution in which the front of the lubricant is driven by its own gravitational spreading. There is a singular limit of equal densities in which the lubricant no longer spreads under its own weight in the vicinity of its nose and ends abruptly with a non-zero thickness there. We explore various regimes, from thin lubricating layers underneath a more viscous current to thin surface films coating an underlying more viscous current and find that although a thin film does not greatly influence the more viscous current if it forms a surface coating, it begins to cause interesting dynamics if it lubricates the more viscous current from below. We find experimentally that a lubricated gravity current is prone to a fingering instability.We are grateful to Dr Mark Hallworth for his valuable help wit h our experiments and the technicians of the G.K. Batchelor Laboratory for assist ance with the setup of our experiments. KNK is supported by a NERC PhD studentship.This is the author accepted manuscript. The final version is available via CUP at http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9553100&fileId=S0022112015000300

The formation of grounding zone wedges: Theory and experiments

NER

Strong shear-flow modulation of instabilities in rapid directional solidification

We examine the effect of a strong shear flow on morphological instabilities that occur in the directional solidification of a dilute, binary alloy when the interface departs from local thermal equilibrium in a frozen-temperature, one-sided model. In particular, the flow velocity U∞ is much larger than the rate of solidification V and the Schmidt number is arbitrary. In contrast to solidification processes under small or no flow, for which both a cellular and an oscillatory mode of instability appear, the liquid-solid interface under flows of large magnitude is susceptible to a single mode of instability. All experiments on banding occur in the overlap region between these modes under no flow and since these two primary modes coalesce into one time-dependent, spatially-dependent mode, there is no mechanism for the production of bands anymore in the large-flow regime. No experiments have been conducted to date on this rapid solidification under flow and this suggests that such experiments would show no bands. The flow significantly stabilizes and selects higher wavenumbers for the preferred form of instability in comparison to systems involving small or no flow. The introduction of a strong flow provides an effective mechanism to eliminate instabilities at high solidification rates. However, stability thresholds at low solidification rates remain mainly indifferent to the presence of flow.This work is supported by the National Institute of Stan- dards and Technology (Grant No. 70NANB14H012) as part of the Center for Hierarchical Material Design (CHiMaD)

Stability of lubricated viscous gravity currents. Part 1. Internal and frontal analyses and stabilisation by horizontal shear

A novel viscous fingering instability, involving a less viscous fluid intruding underneath a current of more viscous fluid, was recently observed in the experiments of Kowal & Worster (J. Fluid Mech., vol. 766, 2015, pp. 626-655). We examine the origin of the instability by asking whether the instability is an internal instability, arising from internal dynamics, or a frontal instability, arising from viscous intrusion. We find it is the latter and characterise the instability criterion in terms of viscosity difference or, equivalently, the jump in hydrostatic pressure gradient at the intrusion front. The mechanism of this instability is similar to, but contrasts with, the Saffman-Taylor instability, which occurs as a result of a jump in dynamic pressure gradient across the intrusion front. We focus on the limit in which the two viscous fluids are of equal density, in which a frontal singularity, arising at the intrusion, or lubrication, front, becomes a jump discontinuity, and perform a local analysis in an inner region near the lubrication front, which we match asymptotically to the far field. We also investigate the large-wavenumber stabilisation by transverse shear stresses in two dynamical regimes: A regime in which the wavelength of the perturbations is much smaller than the thickness of both layers of fluid, in which case the flow of the perturbations is resisted dominantly by horizontal shear stresses; and an intermediate regime, in which both vertical and horizontal shear stresses are important.K.N.K. acknowledges the support of a NERC PhD studentship

Dynamics of laterally confined marine ice sheets

We present an experimental and theoretical study of the dynamics of laterally confined marine ice sheets in the natural limit in which the long, narrow channel into which they flow is wider than the depth of the ice. A marine ice sheet comprises a grounded ice sheet in contact with bedrock that floats away from the bedrock at a ‘grounding line’ to form a floating ice shelf. We model the grounded ice sheet as a viscous gravity current resisted dominantly by vertical shear stresses owing to the no-slip boundary condition applied at the bedrock. We model the ice shelf as a floating viscous current resisted dominantly by horizontal shear stresses owing to no-slip boundary conditions applied at the sidewalls of the channel. The two shear-dominated regions are coupled by jump conditions relating force and fluid flux across a short transition region downstream of the grounding line. We find that the influence of the stresses within the transition region becomes negligible at long times and we model the transition region as a singular interface across which the ice thickness and mass flux can be discontinuous. The confined shelf buttresses the sheet, causing the grounding line to advance more than it would otherwise. In the case that the sheet flows on a base of uniform slope, we find asymptotically that the grounding line advances indefinitely as $t^{1/3}$, where $t$ is time. This contrasts with the two-dimensional counterpart, for which the shelf provides no buttressing and the grounding line reaches a steady state (Robison, J. Fluid Mech., vol. 648, 2010, pp. 363–380).We would like to thank Dr M. Hallworth for valuable help with running the experiments and the technicians of the DAMTP G. K. Batchelor Laboratory for help with the set-up of the experimental apparatus. K.N.K. is supported by a NERC PhD studentship. The experimental data are available as supplementary material.This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/jfm.2016.3

Stability of lubricated viscous gravity currents. Part 2. Global analysis and stabilisation by buoyancy forces

The novel viscous fingering instability recently found in the experiments of Kowal & Worster (J. Fluid Mech., vol. 766, 2015, pp. 626–655), involving two superposed currents of viscous fluid, has been shown to originate at the lubrication front when the fluids are of equal density. However, when the densities are unequal, additional buoyancy forces associated with the underlying layer act to suppress this instability and are largest at the lubrication front, which is where the instability originates. In this paper, we investigate the interaction between the mechanism of the instability and the stabilising influence of these buoyancy forces by performing a global and fully time-dependent analysis, which does not use the frozen-time approximation. We determine a critical condition for instability in terms of the viscosity ratio and the density difference between the two layers. Consistently with the local analysis of the companion paper, instabilities occur when the jump in hydrostatic pressure gradient across the lubrication front is negative, or, equivalently, when the intruding fluid is less viscous than the overlying fluid, provided the two fluids are of equal densities. Once there is a non-zero density difference, these driving buoyancy forces suppress the instability for large wavelengths, giving rise to wavelength selection. As the density difference increases, the instability criterion requires higher viscosity ratios for any instability to occur, and the band of unstable wavenumbers becomes bounded. Large enough density differences suppress the instability completely.K.N.K. acknowledges the support of a NERC PhD studentship

Thermocapillary instabilities in a horizontal liquid layer under partial basal slip

We investigate the onset of three-dimensional hydrothermal waves in a low-capillary-number liquid layer of arbitrary depth, bounded by a free liquid–gas interface from above and a partial slip, rigid surface from below. A selection of two- and three-dimensional hydrothermal waves, longitudinal rolls and longitudinal travelling waves, form the preferred mode of instability, which depends intricately on the magnitude of the basal slip. Partial slip is destabilizing for all modes of instability. Specifically, the minimal Marangoni number required for the onset of instability follows M_{m}\sim a(\unicode[STIX]{x1D6FD}^{-1}+b)^{-c} for each mode, where a,b,c>0 and \unicode[STIX]{x1D6FD}^{-1} is the slip parameter. In the limit of free slip, longitudinal travelling waves disappear in favour of longitudinal rolls. With increasing slip, it is common for two-dimensional hydrothermal waves to exchange stability in favour of longitudinal rolls and oblique hydrothermal waves. Two types of oblique hydrothermal waves appear under partial slip, which exchange stability with increasing slip. The oblique mode that is preferred under no slip persists and remains near longitudinal for small slip parameters.This work is supported by the National Institute of Stan- dards and Technology (Grant No. 70NANB14H012) as part of the Center for Hierarchical Material Design (CHiMaD)

Phenotypic Characterization of Autoreactive B Cells—Checkpoints of B Cell Tolerance in Patients with Systemic Lupus Erythematosus

DNA-reactive B cells play a central role in systemic lupus erythematosus (SLE); DNA antibodies precede clinical disease and in established disease correlate with renal inflammation and contribute to dendritic cell activation and high levels of type 1 interferon. A number of central and peripheral B cell tolerance mechanisms designed to control the survival, differentiation and activation of autoreactive B cells are thought to be disturbed in patients with SLE. The characterization of DNA-reactive B cells has, however, been limited by their low frequency in peripheral blood. Using a tetrameric configuration of a peptide mimetope of DNA bound by pathogenic anti-DNA antibodies, we can identify B cells producing potentially pathogenic DNA-reactive antibodies. We, therefore, characterized the maturation and differentiation states of peptide, (ds) double stranded DNA cross-reactive B cells in the peripheral blood of lupus patients and correlated these with clinical disease activity. Flow cytometric analysis demonstrated a significantly higher frequency of tetramer-binding B cells in SLE patients compared to healthy controls. We demonstrated the existence of a novel tolerance checkpoint at the transition of antigen-naïve to antigen-experienced. We further demonstrate that patients with moderately active disease have more autoreactive B cells in both the antigen-naïve and antigen-experienced compartments consistent with greater impairment in B cell tolerance in both early and late checkpoints in these patients than in patients with quiescent disease. This methodology enables us to gain insight into the development and fate of DNA-reactive B cells in individual patients with SLE and paves the way ultimately to permit better and more customized therapies

Single Particle Analysis for High-Resolution 2D Electron Crystallography

Electron crystallography has been used for decades to determine three-dimensional structures of membrane proteins embedded in a lipid bilayer. However, high-resolution information could only be retrieved from samples where the 2D crystals were well ordered and perfectly flat. This is rarely the case in practice. We implemented in the FOCUS package a module to export transmission electron microscopy images of 2D crystals for 3D reconstruction by single particle algorithms. This approach allows for correcting local distortions of the 2D crystals, yielding much higher resolution reconstructions than otherwise expected from the observable diffraction spots. In addition, the single particle framework enables classification of heterogeneous structures coexisting within the 2D crystals. We provide here a detailed guide on single particle analysis of 2D crystal data based on the FOCUS and FREALIGN packages