We have reanalysed the problem of growth of a dense product rim on a sphere of parent phase. To decouple the problem of calculating deformation from rheology, we assume spherical symmetry, and incompressible phases. Within the product, the radial deviatoric strain and its time-derivative prove to be of opposite sign: strain is compressive, but the strain rate is tensile. Further, the radial deviatoric strain in the new product adjacent to the interface is invariant in time. Propagation of the phase interface is determined by a competition between two mechanisms: as an element of material is transformed, its shear strain energy is increased; and the core pressure performs work compressing it. For elastic phases, this competition results in metastability. Within a certain pressure range, either phase can occur alone, but the two phases can not coexist. Because this result is inconsistent with experiments by Kawazoe et al. (2010) in which a rim of high-pressure phase (wadsleyite) coexists with a central core of low-pressure phase (olivine), we then incorporate plastic flow. Assuming perfect plasticity, we show that for a given applied pressure exceeding the coexistence pressure, a rim of product can now nucleate if the excess pressure δ. p exceeds a critical value depending on yield stress. Increasing δ. p above this value allows product to grow into the parent phase. There are now two possibilities, depending on the value of δ. p. Growth may eventually cease to produce a state in which the product rim is in equilibrium with a parent core; or growth may follow a more complicated path: within a range of excess pressures, the growth rate can decrease strongly from its initial value to produce a quasi-equilibrium state, before increasing again to a rate similar to that at which transformation began. We interpret these results to mean that if δ. p is increased slowly in a series of experiments with constant yield stress, the sample passes through a series of equilibria until δ. p is large enough for the second type of growth to be possible transformation is then completed rapidly on the timescale set by interface kinetics. This result may be relevant to the problem of deep earthquakes. Lastly, using existing experiments in which a wadsleyite rim grows on an olivine sphere, we apply the theory to estimate the yield strength of wadsleyite: our estimates are consistent with measurements by independent methods. © 2014 Elsevier B.V.

Motivated by experiments showing that a sessile drop of volatile perfectly wetting liquid initially advances over the substrate, but then reverses, we formulate the problem describing the contact region at reversal. Assuming a separation of scales, so that the radial extent of this region is small compared with the instantaneous radius a of the apparent contact line, we show that the time scale characterizing the contact region is small compared with that on which the bulk drop is evolving. As a result, the contact region is governed by a boundary-value problem, rather than an initial-value problem: the contact region has no memory, and all its properties are determined by conditions at the instant of reversal. We conclude that the apparent contact angle θ is a function of the instantaneous drop radius a, as found in the experiments. We then non-dimensionalize the boundary-value problem, and find that its solution depends on one parameter 葦, a dimensionless surface tension. According to this formulation, the apparent contact angle is well-defined: at the outer edge of the contact region, the film slope approaches a limit that is independent of the curvature of bulk drop. In this, it differs from the dynamic contact angle observed during spreading of non-volatile drops. Next, we analyse the boundary-value problem assuming 葦 to be small. Though, for arbitrary 葦, determining θ requires solving the steady diffusion equation for the vapour, there is, for small 葦, a further separation of scales within the contact region. As a result, θ is now determined by solving an ordinary differential equation. We predict that θ varies as a-1/6, as found experimentally for small drops (a < 1 mm). For these drops, predicted and measured angles agree to within 10-30 %. Because the discrepancy increases with a, but 葦 is a decreasing function of a, we infer that some process occurring outside the contact region is required to explain the observed behaviour of larger drops having a > 1 mm.

In a polymorphic change in which the phases differ only by a reversible difference in specific volume, kinematics requires a unit mass to suffer deviatoric strain in the instant it is transformed. Unlike the Eshelby stress–free strain, this strain is a property of the motion. Its existence must be considered when formulating the constitutive relation for the product of an incoherent transformation. To show this, two models are compared: in both, the (Nabarro) condition of vanishing shear stress is imposed at the incoherent interface; they differ only in the treatment of the deviatoric strain at issue. In the existing model, deviatoric stress within a unit mass of product is determined by total deviatoric strain from its initial state as parent phase. In the new model, lattice reconstruction is assumed to erase all memory within the unit mass of deviatoric strain suffered before, or during, its transformation. The existing model is not consistent with experiments on the olivine spinel–phase change in single crystals. It predicts that when the pressure applied exceeds a critical value, samples should transform completely at almost constant rate; instead, growth is seen to slow, and may even cease. The new model predicts this. Without adjustable constants, fair agreement is obtained with experiments on samples having 75–200 ppmw of water. Because elastic deformation by itself can explain those observations, the very thin rims seen on even drier samples suggest that water may be essential to lattice reconstruction in this phase change.

We consider the evaporating meniscus of a perfectly wetting liquid in a channel whose superheated walls are at common temperature. Heat flows by pure conduction from the walls to the phase interface; there, evaporation induces a small-scale liquid flow concentrated near the contact lines. Liquid is continually fed to the channel, so that the interface is stationary, but distorted by the pressure differences caused by the small-scale flow. To determine the heat flow, we make a systematic analysis of this free-boundary problem in the limit of vanishing capillary number based on the velocity of the induced flow. Because surface tension is then large, the induced flow can distort the phase interface only in a small inner region near the contact lines; the effect is to create an apparent contact angle Θ depending on capillary number. Though, in general, there can be significant heat flow within that small inner region, the presence of an additional small parameter in the problem implies that, in practice, heat flow is significant only within the large outer region where the interface shape is determined by hydrostatics and Θ. We derive a formula for the heat flow, and show that the channel geometry affects the heat flow only through the value of the interface curvature at the contact line. Consequently, the heat flow relation for a channel can be applied to other geometries.

Deviatoric stress generated within subducting slabs by the olivine-spinel transformation has been modeled by assuming the phases to be simply connected rather than comprising a mixture in which one phase is embedded within another. Here, we use a simplified model to explain how transformation strain is incorporated into a continuum model, and we then use the simplified model to explain quantitatively the origin of the unreasonably large deviatoric stresses predicted by existing slab models. We review experiments on the transformation of single-crystal samples and argue that they are consistent with the occurrence, at the grain scale, of deviatoric stresses comparable with those predicted (erroneously) to exist at the slab scale by those slab models. Using a simple example, we show that although large deviatoric stresses can exist at the grain scale, their average over a sample containing many grains can be hydrostatic. This leads us to the problem of modeling the microscale structure. We outline the thermodynamics needed for such nonhydrostatic systems, and we illustrate their use and implications with examples.

We study the evaporating meniscus of a perfectly wetting liquid formed in the gap between two horizontal flat plates. The plates are at the same temperature as the surroundings, and the pure liquid evaporates into a binary mixture of its own vapor and an inert component. Though the identical problem for a capillary has been studied since the work of Stefan, except for the work by Derjaguin et al. (1965), the interface has been treated as a plane surface having a known contact angle of 90°. Here, by contrast, the interface location is determined as part of the solution to a free boundary problem coupling viscous flow in the liquid to diffusive transport in the gas. We make the following simplifying assumptions: (a) liquid and vapor at the interface are in local thermodynamic equilibrium, and (b) the system is effectively isothermal. Given (a) and (b), the vapor partial pressure is related to the liquid pressure by the Kelvin equation. Though the hydrostatic contact angle is zero for a completely wetting system, the stationary evaporating meniscus exhibits an apparent contact angle; Θ is determined chiefly by a capillary number Ca = μℓ V s/γ based on surface tension γ, liquid viscosity μℓ, and a velocity scale V s set by evaporation. Though microphysics must be included in the free boundary problem in order to resolve a hydrodynamic singularity at the contact line, Θ is insensitive to the microphysical details. © 2014 Copyright Taylor & Francis Group, LLC.