Reference plane

Diffusivity measures the tendency for a concentration gradient to dissipate to form a molar flux. The proportionality constant between the flux and the potential is called the diffusivity and is expressed in m /s. If a binary mixture of components A and B is considered, the molar flux of component A with respect to a reference plane through which the exchange is equimolar, is expressed as a function of the diffusivity and of the concentration gradient with respect to aji axis Ox perpendicular to the reference plane by the fpllqvving relatipn 6 /... 

Let us consider a diffuser G Figure la) which is illuminated with an He-Ne laser. The illuminated area is limited with a rectangular aperture A. The observation plane IToiTl, ), parallel to the reference plane n(x,y), is located at a distance D from it. 

The stereochemistry is usually expressed in structure diagrams by wedged and hashed bonds. A wedge indicates that the substituent is in ont of a reference plane and a hashed bond indicates that the substituent is pointing away om the viewer (behind the reference plane). This projection is applied both to tetrahe-... 

However, care has to be taken to keep this graphical 3D information in 2D structure diagrams unambiguous. Since the reference plane can be chosen arbitrarily, there exist different possible ways of displaying the stereochemistry (Figure 2-68). 

For compounds containing only double-bonded atoms, the reference plane contains the double-bonded atoms and is perpendicular to the plane containing these atoms and those directly attached to them. It is customary to draw the formulas so that the reference plane is perpendicular to that of... 

The 1,2,4-trioxolane ring prefers a half-chair conformation (131) the C—O—C portion of the ring forms the reference plane, and alkyl substituents prefer the equatorial positions. 

To determine the deterioration in component performance and efficiency, the values must be corrected to a reference plane. These corrected measurements will be referenced to different reference planes depending upon the point, which is being investigated. Corrected values can further be adjusted to a transposed design value to properly evaluate the deterioration of any given component. Transposed data points are very dependent on the characteristics of the components performance curves. To determine the characteristics of these curves, raw data points must be corrected and then plotted against representative nondimensional parameters. It is for this reason that we must evaluate the turbine train while its characteristics have not been altered due to component deterioration. If component data were available from the manufacturer, the task would be greatly reduced. 

As previously proposed, tpiz) is defined as the probability of an asperity having a height z above a reference plane. Assuming the presence of N asperities per unit area, the probability that n of these would contact a smooth surface having a separation distance d is given by... 

A typical plan view of a 4-loop PWR is shown in Figure 5.1-4, At first glance, the iurangement appears to be symmetrical about reference planes A and B, but the symmetry about plane B is less than it is about plane A. 

Bulging or caving of a duct The maximum deflection that occurs in the sides of a duct due to negative (caving) or positive (bulging) pressure differences. The reference plane is that existing with no pressure difference. 

Deflection of a joint The largest deformation of a joint subjected to a positive or negative pressure, given by the measured difference in distance from a reference plane outside the joint to the joint with and without pressure. 

Wind shear The change in the wind velocity and direction with height above some reference plane. 

A relatively simple approach suggests itself if the interfaces are known to be almost flat. In that case, the interface position can be described by a single-valued function z(x,y), where (A,y) are cartesian coordinates on a flat parallel reference plane. The functional (21) can be approximated by... 

In the relative velocity system of Fig. 1-4, a rectangular coordinate system is set up as follows the i3 axis is the line antiparallel to g, through the origin the ix axis is the line in the reference plane from which e is measured the i2 axis is in the reference plane, perpendicular... 

Fig. 3. Schematic beam path of a phase-measurement interference microscope (PMIM, Fizeau optics). The beam partially reflected at the reference plane and at the sample surface interfere with each other while the reference plane is moved by the piezoelectric transducer for automatic phase determination. A reflectivity of at least 1% is required for the sample surface...

The variants are distinguished by the locants of those ring atoms that lie outside a reference plane (defined below) and are listed for some examples in Table 1. The locants of ring atoms that lie on the side of the reference plane from which numbering appears clockwise (i.e. the upper side in the normal Haworth representation of furanoses and pyranoses) are written as superscripts and precede the letter those that lie on the other side are written as subscripts and follow the letter. Heteroatoms (e.g. O, S) are indicated by their subscript or superscript atomic symbols. Table 1 gives the notations and Chart III some examples. 

Chairs. The reference plane is defined by two parallel ring sides, so chosen that the lowest-numbered carbon atom in the ring is exoplanar (examples 5 and 6). 

Envelopes. The reference plane is defined by the five adjacent coplanar atoms (example 12). 

Conformation Atoms of reference plane Above plane Below plane... 

Chart III. Drawings of the conformations listed in Table 1. The reference plane... 

Twists. The reference plane is defined by three adjacent ring-atoms, so chosen that the exoplanar atoms lie on opposite sides of the plane (examples 3 and 4). 

The conformational symbols for enantiomers are different. It is therefore important to state in the context whether the d or the L form is under consideration. Enantiomers have the same reference plane (see 2-Caib-7.3), and it should be noted that the mirror image of a-D-glucose-4Ci is a-L-glucose-C4. 

While the choice of a reference plane is usually simple for heat and electricity flow, this is not the case for diffusion in liquid mixtures. 

For illustration, consider the simplest type of diffusion, described by the partial differential equation (2.5.3), also called linear diffusion. The system will be represented by an infinite tube closed at one end (for x = 0) and initially filled with a solution with concentration c°. Diffusion is produced by very fast removal (e.g. by precipitation or an electrode reaction) of the dissolved substance at the x = 0 plane (the reference plane). The initial concentration c° is retained at large distances from this reference plane (x— < >). The initial condition is thus... 

The material flux through the reference plane is given by the concentration gradient for x = 0. In the present case the concentration gradient is... 

Another example is linear diffusion, with a prescribed concentration gradient at the reference plane, i.e. a prescribed material flux through the reference plane. This type of diffusion transport is important mainly for electrode processes (see Section 5.4). The point of interest in this case is the concentration at the reference plane. In the simplest case, the material flux is constant, so that the boundary condition for x = 0 (Eq. 2.5.5) can be replaced by... 

The error function complement erfcy is defined by the relationship erfcy = 1 — erf y. The concentration at the reference plane c is... 

Clearly, the concentration at the reference plane decreases to zero after... 

Assume that both the initial substances and the products of the electrode reaction are soluble either in the solution or in the electrode. The system will be restricted to two substances whose electrode reaction is described by Eq. (5.2.1). The solution will contain a sufficient concentration of indifferent electrolyte so that migration can be neglected. The surface of the electrode is identified with the reference plane, defined in Section 2.5.1. In this plane a definite amount of the oxidized component, corresponding to the material flux J0x and equivalent to the current density j, is formed or... 

---