Influence Of Viscosity Contrast Research Articles

Dynamics of core-mantle separation: Influence of viscosity contrast and metal/silicate partition coefficients on the chemical equilibrium

The composition of the Earth's core and mantle is set by the chemical equilibrium between metals and silicates during core/mantle segregation. The metallic core separated from the mantle by gravitational descent in the form of diapirs in a magma ocean, and therefore the dynamics of the diapir's downward movement has an influence on the chemical equilibrium. In this study, we characterize the descent of metallic droplets into a molten silicate using numerical models. By varying the silicate and metal viscosities (between 0.1 and 1000 Pa·s for each phase) as well as the partition coefficient between metal and silicate (Dmet/sil, varying between 1 and 1000), we obtained quantifying parametrizing equations for the degree of equilibrium between molten metal and molten silicate, in a regime characterized by low We (We < 10) and low Re (10−3 < Re<102). We showed that the main parameters controlling the equilibrium for a siderophile element are the viscosity of the silicate and the partition coefficient. We applied our parameterization for Ni and Co in the context of late accretion on Earth so as to quantify the variation of the Ni/Co ratio after a large impact as a function of the magma ocean viscosity, for an iron-rain scenario of metal/silicate segregation. Using previous models (Canup, 2004) of the Moon–forming impact, we showed that the Moon formation had an effect on the current Ni/Co ratio. Depending on the radius of Theia's core and the viscosity of the magma ocean produced after the impact between the proto-Earth and Theia, the Moon formation could account for 0.45% to 3% of the current Ni/Co ratio for magma ocean viscosities of 0.1 to 100 Pa·s, respectively.

Influence of viscosity contrast on buoyantly unstable miscible fluids in porous media

The influence of viscosity contrast on buoyantly unstable miscible fluids in a porous medium is investigated through a linear stability analysis (LSA) as well as direct numerical simulations (DNS). The linear stability method implemented in this paper is based on an initial value approach, which helps to capture the onset of instability more accurately than the quasi-steady-state analysis. In the absence of displacement, we show that viscosity contrast delays the onset of instability in buoyantly unstable miscible fluids. Further, it is observed that by suitably choosing the viscosity contrast and injection velocity a gravitationally unstable miscible interface can be stabilized completely. Through LSA we draw a phase diagram, which shows three distinct stability regions in a parameter space spanned by the displacement velocity and the viscosity contrast. DNS are performed corresponding to parameters from each regime and the results obtained are in accordance with the linear stability results. Moreover, the conversion from one dimensionless formulation to another and its importance when comparing the different type of flow problem associated with each dimensionless formulation are discussed. We also calculate${\it\epsilon}$-pseudo-spectra of the time dependent linearized operator to investigate the response to external excitation.

Effect of Strong Sample Solvent on the Solute Dynamics for More or Less Viscous Sample: A Comparative Study

The flow dynamics of the adsorbed solute is studied under the influence of viscosity contrast between the localised solvent and the displacing fluid. This viscosity contrast leads to viscous fingering at either of the interfaces of the solvent. Alongside, the solute dynamics is getting affected by its solvent modulated adsorption also. To explore the effect of this physico-chemical phenomena on the broadening of the multiphase solute, we present a comparative study of unstable frontal and rear interface of sample having eluting strength larger than the displacing fluid. The study showed that viscous fingering at the frontal interface of the sample solvent combined with the solvent strength, intensifies the band broadening of the solute zone. Whereas, it counteracts when the viscous fingering is at the rear interfce of the sample solvent. A comparative study is performed to analyze the degree of mixing which shows that the less viscous sample leads to faster mixing of adsorbed solute in comparison to the more viscous one.

The influence of viscosity contrast on the strain pattern and magnitude within and around dense blocks sinking through Newtonian rock salt

Dense inclusions in salt cover a wide range of materials and therefore material properties, depending on their origin. We have modelled the deformation associated with gravity-driven sinking of horizontal, initially rectangular blocks of dense material through Newtonian salt. Our two-dimensional Finite Differences models analyse the influence and interaction of two parameters: (1) the size, i.e. the aspect ratio (AR), of the block and (2) the viscosity contrast between the salt and the more viscous block over four orders of magnitude. The results demonstrate that during gravity-driven sinking the blocks are folded and sheared. The strain magnitude within the block increases with increasing block AR and decreases with increasing viscosity contrast. Sinking velocities of the blocks are in the range of <2 and >6 mm a −1 and are a function of block and salt deformation that depend on the block mass and AR, as well as on the viscosity contrast. Salt deformation is characterised by the development of an array of characteristic structures that include folds and shear zones, as well as a zone characterised by extreme vertical stretching above the block, termed entrainment channel. Strain in the salt is locally more than two orders of magnitude higher than in the block and increases with increasing block AR and viscosity contrast. Salt deformation is distributed in closely spaced high- and low-strain zones concentrated in the block vicinity and the entrainment channel.

Influence of viscosity contrast and anisotropy on strain accommodation in competent layers

Folds with different values of viscosity contrast and anisotropy have been simulated using the finite-difference code FLAC™. The kinematical analysis of these folds has enabled conclusions to be reached about strain accommodation mechanisms. The sequence of strain patterns in all the folds analysed only differs in the intensities of the different mechanisms involved, which depend on the mechanical properties of the folds. The order of the different strain patterns in the sequence is the same, regardless of the anisotropy and viscosity contrast. Strain accommodation in folds follows the patterns of tangential longitudinal strain, flexural flow and layer shortening. Nevertheless, no combination of these strain patterns can explain the shape of the folded layer at the inflection point and the high strain intensity values in the inner arc. These problems can only be solved by considering a variant of longitudinal tangential strain that is less intense than has classically been thought and combined with a heterogeneous distribution of flexural flow and layer shortening across the layer. The dependence of the different folding mechanisms on the mechanical properties has been used to devise a graphical method for estimating viscosity contrast and anisotropy from the intensities of the strain patterns in the sequence.

Numerical study of pattern formation in miscible rotating Hele-Shaw flows

The dynamics of the diffusing interface separating two miscible fluids in a rotating Hele-Shaw cell is studied by intensive and highly accurate numerical simulations. We perform numerical experiments in a wide range of parameters, focusing on the influence of viscosity contrast and Korteweg stresses on the shape of the interfacial patterns. A great variety of morphological behaviors is systematically introduced, and a wealth of interesting phenomena related to finger competition dynamics, filament stretching, and interface pinch off are reveal. Our simulations exhibit miscible patterns that bear a strong resemblance to their immiscible counterparts for larger Korteweg stresses. The quantitative equivalence between such stresses and the usual immiscible surface tension is studied. The concept of an effective interfacial tension is considered, allowing the direct and precise calculation of the important fingering properties under miscible circumstances. Our results show excellent agreement with existing experiments and simulations for corresponding immiscible displacements. This agreement refers to a striking similarity between miscible and immiscible pattern morphologies, and also to an accurate prediction for the typical number of miscible fingering structures formed. Our findings suggest that the effective interfacial tension is both qualitatively and quantitatively equivalent to its immiscible counterpart.