An analysis of convection in a mushy layer with a deformable permeable interface

We study the dynamics of a mushy layer in directional solidification for the case of a thin near-eutectic mush with a deformable and permeable mush–liquid interface. We examine the onset of convection using linear stability analysis, and the weakly nonlinear growth of liquid inclusions that signal the onset of chimneys. This analysis is compared to past analyses in which the mush–liquid interface is replaced by a rigid impermeable lid. We find qualitative agreement between the two models, but the rigid-lid approximation gives substantially different quantitative behaviour. In linear theory, the rigid-lid approximation leads to an over-estimate of the critical Rayleigh number and wavenumber of the instability. The condition for the onset of oscillatory instability is also changed by a factor of about 5 in composition number C. In the weakly nonlinear theory, the location of the onset of liquid inclusions is near the undisturbed front for the free-boundary analysis, whereas it lies at the centre of the mushy layer when the rigid-lid approximation is used. For hexagonal patterns, the boundary between regions of parameter space in which up and down hexagons are stable, shifts as a result of coupling between the liquid and mush regions

Electromigration of Single-Layer Clusters

Single-layer atom or vacancy clusters in the presence of electromigration are studied theoretically assuming an isotropic medium. A variety of distinctive behaviors distinguish the response in the three standard limiting cases of periphery diffusion (PD), terrace diffusion (TD), and evaporation-condensation (EC). A general model provides power laws describing the size dependence of the drift velocity in these limits, consistent with established results in the case of PD. The validity of the widely used quasistatic limit is calculated. Atom and vacancy clusters drift in opposite directions in the PD limit but in the same direction otherwise. In absence of PD, linear stability analysis reveals a new type of morphological instability, not leading to island break-down. For strong electromigration, Monte Carlo simulations show that clusters then destabilize into slits, in contrast to splitting in the PD limit. Electromigration affects the diffusion coefficient of the cluster and morphological fluctuations, the latter diverging at the instability threshold. An instrinsic attachment-detachment bias displays the same scaling signature as PD in the drift velocity.Comment: 11 pages, 4 figure

Phase-Field Approach for Faceted Solidification

We extend the phase-field approach to model the solidification of faceted materials. Our approach consists of using an approximate gamma-plot with rounded cusps that can approach arbitrarily closely the true gamma-plot with sharp cusps that correspond to faceted orientations. The phase-field equations are solved in the thin-interface limit with local equilibrium at the solid-liquid interface [A. Karma and W.-J. Rappel, Phys. Rev. E53, R3017 (1996)]. The convergence of our approach is first demonstrated for equilibrium shapes. The growth of faceted needle crystals in an undercooled melt is then studied as a function of undercooling and the cusp amplitude delta for a gamma-plot of the form 1+delta(|sin(theta)|+|cos(theta)|). The phase-field results are consistent with the scaling law "Lambda inversely proportional to the square root of V" observed experimentally, where Lambda is the facet length and V is the growth rate. In addition, the variation of V and Lambda with delta is found to be reasonably well predicted by an approximate sharp-interface analytical theory that includes capillary effects and assumes circular and parabolic forms for the front and trailing rough parts of the needle crystal, respectively.Comment: 1O pages, 2 tables, 17 figure

Contribution of plasma cells and B cells to hidradenitis suppurativa pathogenesis

Hidradenitis suppurativa (HS) is a debilitating chronic inflammatory skin disease characterized by chronic abscess formation and development of multiple draining sinus tracts in the groin, axillae, and perineum. Using proteomic and transcriptomic approaches, we characterized the inflammatory responses in HS in depth, revealing immune responses centered on IFN-γ, IL-36, and TNF, with lesser contribution from IL-17A. We further identified B cells and plasma cells, with associated increases in immunoglobulin production and complement activation, as pivotal players in HS pathogenesis, with Bruton’s tyrosine kinase (BTK) and spleen tyrosine kinase (SYK) pathway activation as a central signal transduction network in HS. These data provide preclinical evidence to accelerate the path toward clinical trials targeting BTK and SYK signaling in moderate-to-severe HS

Localisation of convection in mushy layers by weak background flow

It is known that freckles form at the sidewalls of directionally solidified materials. We present a weakly nonlinear analysis of the effects of a weak and slowly varying background flow formed by non-axial thermal gradients on convection near onset in a mushy layer. We find that in the two-dimensional case, the onset of mush convection occurs away from the walls. However if three-dimensional disturbances are allowed, the onset occurs near the walls of the container confining the mush. We derive amplitude equations governing this behaviour and simulate their evolution numerically

Convection in a mushy zone forced by sidewall heat losses

We calculate the convective state due to weak sidewall heat losses in a mushy zone during the steady directional solidification of a binary alloy. The configuration consists of a warm liquid region and a cold solid region separated by a mixed phase region, the mushy zone, which is modeled as a reactive porous matrix. The structure of the convection that arises from horizontal temperature gradients, induced by the heat losses at the sidewalls, is characterized by a set of nondimensional parameters that describe the effects of latent heat, composition, permeability, and thermal and solutal buoyancy. We observe a wide range of behaviors and show that, as the critical Rayleigh number for convection in a horizontally uniform mush is reached, we begin to see the precursors of chimneys near the cooled boundaries. The strength of the cooling plays an important role in determining the strength and degree of localization of the convection near the boundary. We find, in common with other authors, that upflow, in this case caused by lighter fluid being released at the cooled sidewalls, leads to regions of dissolution, which are precursors to chimney formation. Although a treatment of the stability of the steady convective states presented is not considered, we identify the effects of the different physical parameters on the steady states