Temperature gradients rather

The short reaction time (1 min, 160 °C) in the benzoylation of anisole was probably a result of large temperature gradients rather than a nonthermal microwave effect. 

Thermal diffusion is a process in which solute is driven through solvent by the action of a temperature gradient rather than by a concentration (or chemical potential) gradient [46]. It is a natural outgrowth of the laws of irreversible thermodynamics (Section 3.2) in which all driving forces are expected to be associated with some transport of matter. 

In MD the driving force of the process, as in the OD operation, is the vapour pressure difference between the two solutions separated by the membrane however, unlike the OD process, this driving force is generated by a temperature gradient rather than a concentration gradient. In these conditions a water vapour transfer, from the warm side to the cold, occurs (Lawson and Lloyd, 1997). 

The original process of zone melting was developed at Bell Telephone Laboratories the basic principles of the methodology were published by W. G. Pfenn in July, 1952. The basic method was further developed to employ temperature gradients rather than the original hot-cold melt-freeze zones. The details of this methodology were published by Pfann in September, 1955. 

These equations, with six farther equations for the other components of a20 and au, when solved by the Burnett iteration procedure, yield the Navier-Stokes equations when solved simultaneously, however, there is no longer the simple dependence of the pressure tensor upon the velocity gradients, and of the heat flow upon the temperature gradient, but, rather, an interdependence of these relations. 

The solubility of the solute (in this case, quartz) is a function of both pressure and temperature. Pressure could be in theory be used as the controlling parameter rather than temperature. However, it is difficult to design an apparatus with a pressure gradient, whereas obtaining a temperature gradient is fairly easy. 

It appeared relevant to relate the heat released to the mean temperature within the board sample. Neglecting the rather small temperature gradient over the thickness of the hardboard samples (7), it was decided to relate the data to the temperature in the surface layer of the board Ts according to the expression ... 

The particle effectiveness factor 17 defined by equation 8.5-5 takes into account concentration and temperature gradients within the particle, but neglects any gradients from bulk fluid to the exterior surface of the particle. The overall effectiveness factor y)0 takes both into account, and is defined by reference to bulk gas conditions (cA, Tg) rather than conditions at the exterior of the particle (cAj, Ts) ... 

The flat crucible (Fig. 8 d) facilitates the spreading of the sample in the form of a thin layer. This kind of preparation is especially important for equilibrium studies and for reactions between the sample and the surrounding atmosphere. It also avoids any loss of substance during spontaneous decomposition reactions in high vacuum. The horizontal temperature gradient in these rather large crucibles (e.g. 20 mm diameter) must be taken into account and can be determined by a second thermocouple. 

The electrochemical etch-stop technology that produces the silicon island is rather complex, so that an etch stop directly on the dielectric layer would simplify the sensor fabrication (Sect. 4.1.2). The second device as presented in Fig. 4.6 was derived from the circular microhotplate design and features the same layout parameters of heaters and electrodes. It does, however, not feature any sihcon island. Due to the missing heat spreader, significant temperature gradients across the heated area are to be expected. Therefore, an array of temperature sensors was integrated on the hotplate to assess the temperature distribution. The temperature sensors (nominal resistance of 1 kfl) were placed in characteristic locations on the microhotplate, which were numbered Ti to T4. 

Energy efficiency. Temperature gradients are steady state and take place in space rather than in time, reducing the need for the expensive heating and cooling cycles common in batch equipment. 

The solution of Eq. (173) poses a rather formidable task in general. Thus the dispersed plug-flow model has not been as extensively studied as the axial-dispersed plug-flow model. Actually, if there are no initial radial gradients in C, the radial terms will be identically zero, and Eq. (173) will reduce to the simpler Eq. (167). Thus for a simple isothermal reactor, the dispersed plug flow model is not useful. Its greatest use is for either nonisothermal reactions with radial temperature gradients or tube wall catalysed reactions. Of course, if the reactants were not introduced uniformly across a plane the model could be used, but this would not be a common practice. Paneth and Herzfeld (P2) have used this model for a first order wall catalysed reaction. The boundary conditions used were the same as those discussed for tracer measurements for radial dispersion coefficients in Section II,C,3,b, except that at the wall. 

In the laboratory experiments, DOC monolith samples (length 7.5 cm, diameter 1.4 cm) with rather thin catalyst layer coating ( 25 pm) were employed to minimize the internal diffusion effects. The samples were placed into a thermostat to suppress the formation of temperature-gradients along the channels. In the course of each experiment, the temperature of the inlet gas and the monolith sample was increased at a constant rate of /min within the range of 300-800 K. The exhaust gases at the inlet of the converter were simulated by synthetic gas mixtures with defined compositions and flow rates (cf. individual figure captions all gas mixtures contained 6% C02 and 6% H20). 

Unless carried out very carefully, data from flow reactors may be influenced by experimental uncertainties. Potential problems with the flow reactor technique include imperfect mixing of reactants, radial gradients of concentration and temperature, and catalytic effects on reactor walls. Uncertainties in induction times, introduced by finite rate mixing of reactants, presence of impurities, or catalytic effects, may require interpretation of the data in terms of concentration gradients, rather than just exhaust composition [442]. 

For many applications low-temperature flexibility of the plasticized composition is also important. Plasticizers of low viscosity and low viscosity-temperature gradient are usually effective at low temperature. There is also a close relationship betv/een rate of oil extraction and low-temperature flexibility plasticizers effective at low temperature are usually rather readily extracted from the resin. Plasticizers containing linear alkyl chains are generally more effective at low temperature than those containing rings. Low-temperature performance is evaluated by measuremen t of stiffness in flexure or torsion or by measurement of second-order transition point, brittle point or peak dielectric loss factor. 

It is obvious that we must require that the partial pressure, rather than the concentration, be constant since under a temperature gradient the total pressure is conserved, whereas the sum of the concentrations varies in proportion to p, i.e., in proportion to 1/T. 

Thermal diffusion, also known as the Ludwig-Soret effect [1, 2], is the occurrence of mass transport driven by a temperature gradient in a multicomponent system. While the effect has been known since the last century, the investigation of the Ludwig-Soret effect in polymeric systems dates back to only the middle of this century, where Debye and Bueche employed a Clusius-Dickel thermogravi-tational column for polymer fractionation [3]. Langhammer [4] and recently Ecenarro [5, 6] utilized the same experimental technique, in which separation results from the interplay between thermal diffusion and convection. This results in a rather complicated experimental situation, which has been analyzed in detail by Tyrrell [7]. 

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