Similar Plates

A fuel cell has two basic elements a fuel delivery system and an electro-chemical cell that converts the delivered fuel into useful electricity. It is this unique combination that enables fuel cells to potentially offer the best features of both heat engines and batteries. Like batteries, the cell generates a dc electric output and is quiet, clean, and shape-flexible, and may be manufactured using similar plate and filmrolling processes. By contrast, the fuel delivery system ensures that fuel cells, like heat engines, can be... 

A metal plate ("driver ) of mild steel or brass was propelled explosively against a similar plate ("target ) on which was resting a sample layer of explosive backed by a further layer of an inert solid. When the driver plated velocity was sufficiently high, this process generated a steady "overdriven detonation wave in the explosive unless (or until) it was overtaken by the rarefaction from the rear of the driver plate. The shock transit times thru each layer of the system were measured to determine tne transmitted shock or detonation velocities. 

Similar plate-based systems have been reported in the literature21. The final goal of these efforts was to be able to synthesize several hundred compounds per day using microwave optimized reaction conditions. 

For vapor phase measurement of dry oil oxidation, the plate assembly shown in Figure 5 is used. The lower glass or terephtha-late plastic plate holds a disk of polyamide (1.2 x 0.1 cm) on which 1 pi of a suitable oil (linoleic acid, methyl linoleate, cottonseed oil) is deposited from a micropipette. A Buna "0" ring of 1.5-mm thickness is placed surrounding the spot and a similar plate with a polyamide disk is inverted over the ring forming a tight seal when clamped with "C" clamps. The plate assembly is placed in a 65°C draft oven with the receiver plate bottommost. 

An infinite plate with a temperature Kstrl and radiant efficiency j will transmit, independent of the distance, to a similar plate of frozen product with a temperature Kstr2 and a radiant efficiency e2 an amount of radiation energy. The surface heat flux q is ... 

Method 13 - A 1-5/8-inch diameter, 5-inch long uncased charge is fired on a 1-3/4-inch thick, 5-square inch cold-rolled steel plate, with one or more similar plates as backing. The charge is initiated with a No. 8 detonator and two 1-5/8-inch diameter, 30-g Tetryl boosters. Plate dent test value, or relative brisance =... 

Double-Layer Interaction Between Two Parallel Similar Plates... 

In this chapter, we give exact expressions and various approximate expressions for the force and potential energy of the electrical double-layer interaction between two parallel similar plates. Expressions for the double-layer interaction between two parallel plates are important not only for the interaction between plate-like particles but also for the interaction between two spheres or two cylinders, because the double-interaction between two spheres or two cylinders can be approximately calculated from the corresponding interaction between two parallel plates via Deijaguin s approximation, as shown in Chapter 12. We will discuss the case of two parallel dissimilar plates in Chapter 10. 

Consider two parallel similar plates 1 and 2 of thickness d separated by a distance h immersed in a liquid containing N ionic species with valence zt and bulk concentration (number density) nf i=, 2,. . . , N). Without loss of generality, we may assume that plates 1 and 2 are positively charged. We take an x-axis perpendicular to the plates with its origin at the right surface of plate 1, as in Fig. 9.1. From the symmetry of the system we need consider only the region —oo < x < h/2. We assume that the electric potential i/ (x) outside the plate (—oo < x < —d and 0 < x < hl2) obeys the following one-dimensional planar Poisson-Boltzmann equation ... 

DOUBLE-LAYER INTERACTION BETWEEN TWO PARALLEL SIMILAR PLATES... 

By substituting Eq. (9.63) into Eq. (9.27), we obtain the following expression P (h) for the interaction force at constant potential per unit area between two parallel similar plates 1 and 2 at separation h ... 

Honig and Mul [7] suggested that better approximations can be obtained if the interaction energy is expressed as a series of tanh(zei/ c/fcT) instead of i/ o and derived the interaction energy correct to tsDSi ze j/ JkT). The interaction energy V (h) per unit area correct to tanh zeij/o/kT) for the interaction between two parallel similar plates at constant surface potential separated by a distance in a symmetrical... 

We treat the interaction between two parallel similar plates placed at x = 0 and h (Fig. 9.6) (i.e., the plates are at separation h) for the case where i/tq remains constant during interaction. The boundary conditions are... 

In this section, we present a novel linearization method for simplifying the nonlinear Poisson-Boltzmann equation to derive an accurate analytic expression for the interaction energy between two parallel similar plates in a symmetrical electrolyte solution [13, 14]. This method is different from the usual linearization method (i.e., the Debye-Hiickel linearization approximation) in that the Poisson-Boltzmann equation in this method is linearized with respect to the deviation of the electric potential from the surface potential so that this approximation is good for small particle separations, while in the usual method, linearization is made with respect to the potential itself so that this approximation is good for low potentials. 

We first consider two interacting parallel similar plates 1 and 2 with constant surface potential at separation h in a symmetrical electrolyte solution of valence z and bulk concentration [13]. We assume that the surface potential ipo remains unchanged independent of h during interaction. We take an x-axis perpendicular to the plates with its origin 0 at the surface of plate 1 (Fig. 9.6). The Poisson-Boltzmann equation for the electric potential (which is a function of x only) relative to the... 

Note that Eq. (9.169) is only accurate near the plate surface, since Eq. (9.169) is obtained by linearizing the Poisson-Boltzmann equation with respect to Ay = y-yo-Now we calculate the double-layer free energy F (h) per unit area of two interacting parallel similar plates at separation h by Eq. (8.54),... 

This is the required expression for the interaction energy per unit area between two parallel similar plates with constant surface potential. Erom the nature of this linearization, the obtained potential distribution (9.177) is only accurate near the plate surface and thus the interaction energy expression (9.177) is also only accurate for small plate separations. Indeed, at h = 0, Eq. (9.177) gives the following correct expression, regardless of the value of yo,... 

FIGURE 9.7 Reduced potential energy V = K/64nkT)V of the double-layer interaction per unit area between two parallel similar plates with constant surface potential as a function of the reduced distance Kh between the plates for several values of the scaled unperturbed surface potential ya = ze j/olkT. Solid lines are exact values and dotted lines represent approximate results calculated by Eq. (9.177). The exact and approximate results for To = 1 agree with each other within the linewidth. (From Ref. 13.)... 

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