Force field, external convective diffusion

Diffusion, which occurrs in essentially all matter, is one of the most ubiquitous phenomena in nature. It is the process of transport of materials driven by an external force field and the gradients of pressure, temperature, and concentration. It is the net transport of material that occurs within a single phase in the absence of mixing either by mechanical means or by convection. The rates of different technical as well as many physical, chemical, and biological processes are directly influenced by diffusive mass transfer, and also the efficiency and quality of processes are governed by diffusion [1]. 

The basic concept of diffusion refers to the net transport of material within a single phase in the absence of mixing (by mechanical means or by convection). Both experiment and theory have shown that diffusion can result from pressure gradients (pressure diffusion), temperature gradients (thermal diffusion), external force fields (forced diffusion), and concentration gradients. Only the last type is considered in this book that is, the discussion is limited to diffusion caused by the concentration difference between two points in a stagnant solution. This process, called molecular diffusion, is described by Pick s laws. His first law relates the flux of a chemical to the concentration gradient ... 

CONVECTIVE DIFFUSION IN AN EXTERNAL FORCE FIELD ELECTRICAL PRECIPITATION... 

Let us consider a flat y=0) interface gas-liquid and suppose that a gas is fixed and a liquid, including a dissolved surface-active substance with bulk concentration Cq, is moving parallel to the phase boundary (towards the x-axis). Furthermore, assume that the convective diffusion is a decelerated stage coming up to the phase boundary of the surface-active substance. In case of a low Reynolds numbers without any external field, Eq. (13) for the balance of tangential forces at the phase boundary becomes more simple ... 

The external electric field is in the direction of the pore axis. The particle is driven to move by the imposed electric field, the electroosmotic flow, and the Brownian force due to thermal fluctuation of the solvent molecules. Unlike the usual electroosmotic flow in an open slit, the fluid velocity profile is no longer uniform because a pressure gradient is built up due to the presence of the closed end. The probability of the particle position is obtained by solving the Fokker-Planck equation. The penetration depth is found to be dependent upon the Peclet number, which is a measure of significance of the convective electroosmotic flow relative to the Brownian diffusion, and the Damkohler number, which is a ratio of the characteristic diffusion-to-deposition times. 

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