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The thickness of the material boundary layer that absorbs a specific element depends on the concentration and the partition coefficient of the specific element.

In this calculation result, the Pb concentration in the hydrated material boundary layer is 0.3 ppm, in which the most Pb-enriched phase is garnet (1.1 ppm Pb).

It is noted for clarity that the material boundary layer is saturated with aqueous fluid at a depth range between 150 and 200 km, where both the hydrated material boundary layer (Figure 2a) and the aqueous fluid phase (Figure 2b) coexist.

Similarly, fluid mobile elements (e.g., Rb, Th, Sr) are expelled from the slab and are absorbed into the material boundary layer to be dragged down to the deep mantle.

As a result, virtually, all of the Pb is absorbed into the solid before it reaches the melting region (hence, no positive Pb spike is seen in Figure 3) and is dragged down to the deep mantle with the descending material boundary layer (Figure 4a).

An additional calculation in the Additional file 1: Figure S2 incorporates subducted sediments into the model that contains more Pb than the altered oceanic crust and again shows that virtually all the Pb expelled from the slab is absorbed into the solid material boundary layer before it reaches the melting region.

Similar(54)

Velocity profiles measured using the delay line transducer, were initially distorted due to the effect of finite sample volume characteristics and propagation through the delay line material boundary layers.

These material boundary layers absorb the fluid-mobile elements, resulting in no relative enrichment of elements, which characterizes the arc magmas, for the model melt (Figure 3).

The effects of lateral mass flux, Rayleigh number, wall inclination angle, wall temperature distribution, porosity and conductivity variation of the porous material on boundary layer thickness and heat-transfer characteristics at the surface are presented.

Using the so-called residual-based gradient plasticity theory, the state equations and the higher order boundary conditions are derived quite naturally for both the bulk material and the boundary layer.

A phenomenological constitutive model is envisioned, in which the bulk material and the boundary layer obey (rate independent associative) coupled plasticity evolution laws, with kinematic hardening laws of differential nature for the bulk material, but of nondifferential nature for the layer.

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