scholarly journals Non-Arrhenian Temperature-Dependent Viscosity of Alkali(ne) Carbonate Melts at Mantle Pressures

2021 ◽  
Vol 9 ◽  
Author(s):  
Xenia Ritter ◽  
Bertrand Guillot ◽  
Nicolas Sator ◽  
Elsa Desmaele ◽  
Malcolm Massuyeau ◽  
...  

The viscosity of carbonate melts is a fundamental parameter to constrain their migration and ascent rates through the mantle and ultimately, their role as carbon conveyors within the deep carbon cycle. Yet, data on the viscosity of carbonate melts have remained scarce due to experimental limitations and the lack of appropriate theoretical descriptions for molten carbonates. Here, we report the viscosity of K2Mg(CO3)2 and K2Ca(CO3)2 melts up to 13 GPa and 2,000 K by means of classical molecular dynamics (MD) simulations using optimized force fields and provide first evidence for non-Arrhenian temperature-dependent viscosity of molten carbonates at mantle pressures. The viscosity of K2Mg(CO3)2 and K2Ca(CO3)2 melts ranges respectively between 0.0056–0.0875 Pa s and 0.0046–0.0650 Pa s in the investigated pressure-temperature interval. Alkali(ne) carbonate melts, i.e. mixed alkali and alkaline earth carbonate melts -K2Mg(CO3)2 and K2Ca(CO3)2− display higher viscosity than alkaline earth carbonate melts -CaCO3 and MgCO3− at similar conditions, possibly reflecting the change in charge distribution upon addition of potassium. The non-Arrhenian temperature-dependence of the viscosity is accurately described by the Vogel-Fulcher-Tammann model with activation energies Ea for viscous flow that decrease with temperature at all investigated pressures, e.g. from ∼100 kJ/mol to ∼30 kJ/mol between 1,300 and 2,000 K at 3 GPa. Pressure is found to have a much more moderate effect on the viscosity of alkali(ne) carbonate melts, with activation volumes Va that decrease from 4.5 to 1.9 cm3/mol between 1,300 and 2,000 K. The non-Arrhenian temperature-viscosity relationship reported here could be exhibited by other carbonate melt compositions as observed for a broad range of silicate melt compositions and it should be thus considered when modeling the mobility of carbonate melts in the upper mantle.

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1300
Author(s):  
Evgenii S. Baranovskii ◽  
Vyacheslav V. Provotorov ◽  
Mikhail A. Artemov ◽  
Alexey P. Zhabko

This paper deals with a 3D mathematical model for the non-isothermal steady-state flow of an incompressible fluid with temperature-dependent viscosity in a pipeline network. Using the pressure and heat flux boundary conditions, as well as the conjugation conditions to satisfy the mass balance in interior junctions of the network, we propose the weak formulation of the nonlinear boundary value problem that arises in the framework of this model. The main result of our work is an existence theorem (in the class of weak solutions) for large data. The proof of this theorem is based on a combination of the Galerkin approximation scheme with one result from the field of topological degrees for odd mappings defined on symmetric domains.


Author(s):  
G. N. Sekhar ◽  
G. Jayalatha

A linear stability analysis of convection in viscoelastic liquids with temperature-dependent viscosity is studied using normal modes and Galerkin method. Stationary convection is shown to be the preferred mode of instability when the ratio of strain retardation parameter to stress relaxation parameter (elasticity ratio) is greater than unity. When the ratio is less than unity the possibility of oscillatory convection is shown to arise. Oscillatory convection is studied numerically for Rivlin-Ericksen, Walters B′, Maxwell and Jeffreys liquids by considering free-free and rigid-free isothermal/adiabatic boundaries. It is found that there is a tight coupling between the Rayleigh and Marangoni numbers, with an increase in one resulting in a decrease in the other. The effect of variable viscosity parameter is shown to destabilize the system. The problem reveals the stabilizing nature of strain retardation parameter and destabilizing nature of stress relaxation parameter, on the onset of convection. The Maxwell liquids are found to be more unstable than the one subscribing to Jeffreys description whereas the Rivlin-Ericksen and Walters B′ liquids are comparatively more stable. Rigid-free adiabatic boundary combination is found to give rise to a most stable system, whereas the free isothermal free adiabatic combination gives rise to a most unstable system. The problem has applications in non-isothermal systems having viscoelastic liquids as working media.


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