Adsorption transient time dependence

In a foam where the films ate iaterconnected the related time-dependent Marangoni effect is mote relevant. A similar restoring force to expansion results because of transient decreases ia surface concentration (iacteases ia surface tension) caused by the finite rate of surfactant adsorption at the surface. 

Transient technique — A technique whose response is time dependent and whose time dependence is of primary interest, e.g., -> chronoamperometry, -> cyclic voltammetry (where current is the transient), -> chronopotentiometry and -> coulostatic techniques (where voltage is the transient). A transient technique contrasts with steady-state techniques where the response is time independent [i]. Some good examples are cyclic voltammetry [i, ii] (fast scan cyclic voltammetry), the indirect-laser-induced-temperature-jump (ILIT) method [iii], coulostatics [i]. The faster the transient technique, the more susceptible it is to distortion by -> adsorption of the redox moiety. 

You saw how the equations governing energy transfer, mass transfer, and fluid flow were similar, and examples were given for one-drmensional problems. Examples included heat conduction, both steady and transient, reaction and diffusion in a catalyst pellet, flow in pipes and between flat plates of Newtonian or non-Newtonian fluids. The last two examples illustrated an adsorption column, in one case with a linear isotherm and slow mass transfer and in the other case with a nonlinear isotherm and fast mass transfer. Specific techniques you demonstrated included parametric solutions when the solution was desired for several values of one parameter, and the use of artificial diffusion to smooth time-dependent solutions which had steep fronts and large gradients. 

The above discussion accounts for the equilibrium state of a surface. However, when a new surface is formed (e.g., during drop formation), this equilibrium state will be reached after a transient time which ranges from milliseconds to hours, depending on the surfactant. The transient time is determined by the mobility of the molecules and their adsorption dynamics on the interface, which we discuss below. 

In a foam where the films are interconnected, the related time-dependent Marangoni effect is more relevant. A similar restoring force to expansion results because of transient decreases in surface concentration (increases in surface tension) caused by the finite rate of surfactant adsorption at the surface. Such nonequilibrium surface tension effects are best described in terms of dilatational moduli. The complex dilatational modulus e of a single surface is defined in the same way as the Gibbs elasticity as in equation (2) (the factor 2 is halved as only one surface is considered). 

Transient surface d)mamic properties of emulsifier adsorbed films also depend on emulsifier concentration in the bulk phase. As a general rule it was observed that the rate of tt or E change over time increases when the emulsifier concenfrafion in fhe bulk phase is increased. These data should be associated with emulsifier adsorption at the interface that is, emulsifier adsorption at the interface is facilitated at higher emulsifier concentrations in the bulk phase. 

Among the unit operations, adsorption may be considered a prototype for all fluid-solid separation operations. When it is conducted under countercurrent conditions, the calculation methods required are entirely analogous to those for countercurrent absorption or extraction (H3). Often, however, it is most economical to conduct adsorption in a semi continuous arrangement, in which the solid phase is present as a fixed bed of granular particles. The fluid phase passes through the interstices of this bed at a constant flow rate and for an extended period of time. The concentration gradients in the fluid and solid phases display a transient or unsteady-state behavior, and their evolution depends upon the pertinent material balances, rates, and equilibria. 

Thus, the most suitable route for obtaining information on the adsorption/desorption kinetics is from the short-time transient behavior. Under these conditions, surface diffusion effects are negligible and the short-time current response depends only on Ka, Kd, and A for a given tip/substrate separation. Provided that an independent measurement of A can be made, an absolute assignment of the interfacial kinetics is possible. Furthermore, analysis of the long-time current allows the importance, and magnitude, of surface diffusion to be determined. 

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