Chapter 7 - Non-linear steady states

Abstract

This chapter discusses the form of nonlinear flux equations for electro-osmosis and streaming current, mass and heat flux in thermal diffusion, and chemical reactions from experimental and theoretical angle. Steady state corresponding to the situation when linear phenomenological relations hold is also discussed. It also discusses theoretical interpretation of second-order coefficients in terms of double layer theory. Specific features of nonlinear steady states beyond linear steady state can be summarized in seven steps that include: (i) Linear nonequilibrium thermodynamics is useful for identifying fluxes and forces, which continue to be valid for a wide nonlinear range. It is a good tool for extrapolation of concepts to nonlinear region. (ii) Nonlinear flux equations involve higher powers of gradients but ORR between first-order coefficients is satisfied. (iii) The theorem of minimum entropy production for the linear steady state does not hold in the nonlinear range. (iv) Nonlinear steady states are usually stable. In some cases, bistability (multistability) may appear with and without hysteresis. (v) Nonlinear steady states can conveniently be experimentally investigated in the case of electro-kinetic phenomena and chemical reactions. (vi) In cases such as above, nonlinearity also depends on structure factors (e.g., Helmholtz double layer) and nonlinear kinetics. (vii) In case of thermal diffusion in gases, nonlinear flux equations of mass and heat transport involve space derivatives of gradient, but higher powers of gradients of single force do not occur, although ORR is satisfied between first-order coefficients.