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While the transport by the liquid recirculation can be accounted for by an advection term, the mixing induced by the bubbles is a diffusive process, the effective diffusivity of which has been measured in a homogeneous bubble column by Alméras et al. (2015).
If the species are coupled by a diffusive process in the molecular diffusion regime, special multi-component phenomena may arise.
The motions of water molecules in liquid are described in terms of a jump diffusion mechanism and a rotational diffusive process, together with an intermolecular vibration and a hindered rotation.
By directly measuring the distribution of the cross-sectional averaged concentration along the axial direction, concentration dispersion can be modelled as a diffusive process with a constant apparent diffusivity (the dispersion coefficient).
Moreover, in the low-frequency regions, the disturbance is mainly dominant by mechanical process of transportation of energy and at high-frequency regions it is significantly dominated by a close to diffusive process (heat conduction or mass diffusion).
The activation enthalpy of diffusion is therefore reduced compared with a purely diffusive process.
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The interest in studying the fractional diffusion in modeling diffusive processes has a wide literature, especially studying the long-range diffusive interaction in porous medium type propagation and infinitesimal generators of stable Lévy processes [4, 5].
Considering that body weight change mimics molecular diffusion, and that diffusive processes are involved in body weight changes at the cellular level, this behavioral activity can be described by Equation 6.
We have found that diffusion-driven flow can be harnessed as a remarkable means of propulsion, acting as a diffusion-engine that extracts energy from microscale diffusive processes to propel macroscale objects.
Two diffusive processes were detected.
Two diffusive processes were observed.
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