Motion, laws pressure gradient force

Solving this flow model for the velocity the pressure is calculated from the ideal gas law. The temperature therein is obtained from the heat balance and the mixture density is estimated from the sum of the species densities. It is noted that the viscous velocity is normally computed from the pressure gradient by use of a phenomenologically derived constitutive correlation, known as Darcy s law, which is based on laminar shear flow theory [139]. Laminar shear flow theory assumes no slip condition at the solid wall, inducing viscous shear in the fluid. Knudsen diffusion and slip flow at the solid matrix separate the gas flow behavior from Darcy-type flow. Whenever the mean free path of the gas molecules approaches the dimensions of pore diameter, the individual gas molecules are in motion at the interface and contribute an additional flux. This phenomena is called slip flow. In slip flow, the layer of gas next to the surface is in motion with respect to the solid surface. Strictly, the Darcy s law is valid only when the flow regime is laminar and dominated by viscous forces. The theoretical foundation of the dusty gas model considers that the model is applied to a transition regime between Knudsen and continuum bulk diffusion. To estimate the combined flux, the model is based on the assumption that the combined flux can be expressed as a linear sum of the Knudsen flux and the convective flux due to laminar flow. 

The second force component, the dielectric boundary pressure, results from the tendency of a high dielectric medium to displace a low dielectric constant medium if an electrical field is present. This force is always directed along the gradient of the dielectric constant, which means that it constitutes a pure pressure at the solute-solvent interface. The dielectric boundary pressure is the force component that balances the reaction field component of the qE force. For example, in the case of an isolated charge inside a low dielectric cavity, the dielectric boundary pressure provides the equal and opposite force to the qE force urging the charge toward the solvent. It is therefore evident that the dielectric boundary force is quantitatively as important as the reaction field force and that its neglect will lead to a violation of Newton s third law of motion. 

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