tailieunhanh - Heat and Mass Transfer Modeling and Simulation Part 12

Tham khảo tài liệu 'heat and mass transfer modeling and simulation part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Nonequilibrium Fluctuations in Micro-MHD Effects on Electrodeposition 211 T j for j r or f V 58 where as will be discussed later subscripts r and f imply rigid and free surfaces respectively. The signs and - are taken for the clockwise and counterclockwise rotations corresponding to the signs of the z-component of the vorticity ữ2j respectively when seeing the solution from electrode side. Then it follows that r R Dm 59 a0 and a1 are arbitrary coefficients. Formation of micro-mystery circle Occurrence of chirality As discussed initially micro-mystery circle is treated as a 2D nucleus arising from asymmetrical fluctuations. For asymmetrical fluctuation as discussed in the former sections due to much larger scale of length of asymmetrical fluctuation than that of symmetrical fluctuation not nucleation process on the electrode but electrochemical process in the electric double layer controls the total reaction. Therefore the same amplitude equations as Eqs. 49a and 49b are derived. The unstable condition for the micro-mystery circle formation is also the same as Eq. 49c which means that the micro-mystery circle formation in a vertical magnetic field follows the same unstable condition as the secondary nodule formation in a parallel magnetic field. Namely when proton adsorption occurs micromystery circle is self-organized. However the equations of the coefficients a0 and a1 are different from the same kind of equation Eq. 50a . Substituting for D r 0 t and 0 0 t from Eqs. 55a and 55b in Eq. 49a we have the coefficient equation for a rigid surface . t A R k al 60a and . 128k6 f - 128k5 ar 60b where ara zmFDmSaTraR 60c Sa Tra and R are the parameters expressing magnetic field rotation and mass transfer respectively. Here R is positive in Eq. 59 . To avoid the singular point of k in Eq. 60b the condition cữ rra _ S T 0 61 212 Heat and Mass Transfer - Modeling and Simulation is required. For the external magnetic flux density defined by B0 0 Sa is also .