Time scale, convection

The scan rate, u = EIAt, plays a very important role in sweep voltannnetry as it defines the time scale of the experiment and is typically in the range 5 mV s to 100 V s for nonnal macroelectrodes, although sweep rates of 10 V s are possible with microelectrodes (see later). The short time scales in which the experiments are carried out are the cause for the prevalence of non-steady-state diflfiision and the peak-shaped response. Wlien the scan rate is slow enough to maintain steady-state diflfiision, the concentration profiles with time are linear within the Nemst diflfiision layer which is fixed by natural convection, and the current-potential response reaches a plateau steady-state current. On reducing the time scale, the diflfiision layer caimot relax to its equilibrium state, the diffusion layer is thiimer and hence the currents in the non-steady-state will be higher. 

In this expression, w is a typical velocity scale and d a typical length scale, for example the diameter of a micro charmel. The Peclet number represents the ratio of the diffusive and the convective time-scales, i.e. flows with large Peclet numbers are dominated by convection. 

Second, sensors are often intended for a single use, or for usage over periods of one week or less, and enzymes are capable of excellent performance over these time scales, provided that they are maintained in a nfild environment at moderate temperature and with minimal physical stress. Stabilization of enzymes on conducting surfaces over longer periods of time presents a considerable challenge, since enzymes may be subject to denaturation or inactivation. In addition, the need to feed reactants to the biofuel cell means that convection and therefore viscous shear are often present in working fuel cells. Application of shear to a soft material such as a protein-based film can lead to accelerated degradation due to shear stress [Binyamin and Heller, 1999]. However, enzymes on surfaces have been demonstrated to be stable for several months (see below). 

Note that as Re/, goes to infinity with Sc constant, both the turbulent energy spectrum and the scalar energy spectrum will be dominated by the energy-containing and inertial/inertial-convective sub-ranges. Thus, in this limit, the characteristic time scale for scalar variance dissipation defined by (3.55) becomes... 

Krt < k scalar spectral transport time scale defined in terms of the velocity spectrum (e.g., rst). 

As discussed in Chapter 7, when modeling inhomogeneous flows the value of At must be chosen also to be smaller than the minimum convective and diffusive time scales of the flow. 

The case of convective conditions is a special one in determining atmospheric dispersion (Section VII,D). Since under convective conditions the most energetic eddies in the mixed layer scale with Zi, the time scale relevant to dispersion is zj/w,. This time scale is therefore roughly the time needed after release for material to become well mixed through the... 

Molar conductivity measurements are equally applicable to both solid and liquid electrolytes. In contrast, the measurement of current flowing through an electrochemical cell on a time scale of minutes or hours while the cell is perturbed by a constant dc potential is only of value for solid solvents (Bruce and Vincent, 1987) where convection is absent. Because of the unique aspects of dc polarisation in a solid solvent this topic is treated in some detail in this chapter. Let us begin by considering a cell of the form ... 

In general, for a compound to reach the upper troposphere in sufficient concentrations to impact the chemistry, it must not react rapidly in the lower troposphere. However, more reactive compounds can be rapidly transported (on the time scale of a few minutes) from the surface to the upper troposphere through convective events (e.g., thunderstorms) (e.g., Gidel, 1983 Chatfield and Crutzen, 1984 Chatfield and Alkezweeny, 1990 Pickering et al., 1992 Wang et al., 1995 Kley et al., 1996 Mahlman, 1997 Kley, 1997 Jaegle et al., 1998a Talbot et al., 1998). As a result, some compounds with relatively short tropospheric lifetimes can be carried into the upper troposphere and act as free radical sources. 

The Peclet number compares the effect of imposed shear (known as the convective effect) with the effect of diffusion of the particles. The imposed shear has the effect of altering the local distribution of the particles, whereas the diffusion (or Brownian motion) of the particles tries to restore the equilibrium structure. In a quiescent colloidal dispersion the particles move continuously in a random manner due to Brownian motion. The thermal motion establishes an equilibrium statistical distribution that depends on the volume fraction and interparticle potentials. Using the Einstein-Smoluchowski relation for the time scale of the motion, with the Stokes-Einstein equation for the diffusion coefficient, one can write the time taken for a particle to diffuse a distance equal to its radius R, as... 

This characterizes the time taken for the restoration of the equilibrium microstructure after a disturbance caused, for example, by convective motion, i.e., this is the relaxation time of the microstructure. The time scale of shear flow is given by the reciprocal of the shear rate, 7. The dimensionless group formed by the ratio (tD ff/tShear) is the Peclet number... 

These measures of solute segregation are closely related to the spatial and temporal patterns of the flow in the melt. Most of the theories that will be discussed are appropriate for laminar convection of varying strength and spatial structure. Intense laminar convection is rarely seen in the low-Prandtl-number melts typical of semiconductor materials. Instead, nonlinear flow transitions usually lead to time-periodic and chaotic fluctuations in the velocity and temperature fields and induce melting and accelerated crystal growth on the typically short time scale (order of 1 s) of the fluctuations. 

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