Fluid Motion Induced by Gravitational Differentiation of Immiscible Two Phases: Basic Equations and Linear Analyses

Abstract

Fluid motion caused by flotation of fine immiscible particles is investigated. Fine immiscible particles can be formed by several mechanisms in the Earth's outer core. For example, light materials may exsolve from cooling iron melt. Light-material-rich blobs may be formed through a boundary layer instability, even if light materials are thermodynamically miscible with molten iron. Governing equations for two-phase flow composed of fine particles and ambient fluids are derived from the conservation laws of mass and momentum. The stationary state without macroscopic fluid motion is neutrally stable to an infinitesimal disturbance. Transient fluid motion is induced by a horizontal disturbance of particle concentration. The resultant fluid motion can be classified into three types. One is a circulative motion driven by the buoyancy of fine particles and the others are non-circulative flows caused by “apparent compressibility” of two-phase flow. If we took into account effects of nonlinear advection, the buoyancy-driven flow would be self-sustaining. The relationship between the flow types and values of nondimensional parameters are investigated. The parameter range where the buoyancy-driven motion is observed is approximately given by G > 3Q2 and G > 30Q. G and Q are the nondimensional parameters defined as G ≡ ρδH3g/η2 and Q ≡ Δvz ρH/η, where ρ, η, δ, H, Δvz and g are the density and viscosity of mixture, the difference of intrinsic density between particles and the ambient fluid, the depth of the fluid layer, the ascending velocity of particles relative to the motion of ambient fluid, and the gravitational acceleration, respectively. The lower the relative velocity of ascending particles is, the more effectively the circulative motion occurs. The values of physical parameters estimated for the outer core fall in the range in which a buoyancy-driven motion should be observed.