Parallel-plate

Derive the equation for the capillary rise between parallel plates, including the correction term for meniscus weight. Assume zero contact angle, a cylindrical meniscus, and neglect end effects. 

Derive, from simple considerations, the capillary rise between two parallel plates of infinite length inclined at an angle of d to each other, and meeting at the liquid surface, as illustrated in Fig. 11-23. Assume zero contact angle and a circular cross section for the meniscus. Remember that the area of the liquid surface changes with its position. 

In the case of a charged particle, the total charge is not known, but if the diffuse double layer up to the plane of shear may be regarded as the equivalent of a parallel-plate condenser, one may write... 

The measurement of the streaming potential developed when a solution flows through two parallel plates [74-76] allows the characterization of macroscopic surfaces such as mica. 

A number of more or less equivalent derivations of the electrocapillary Eq. V-49 have been given, and these have been reviewed by Grahame [113]. Lippmann based his derivation on the supposition that the interface was analogous to a parallel-plate condenser, so that the reversible work dG, associated with changes in area and in charge, was given by... 

Since we have parallel-plate geometry, the viscosity of the liquid layer is given by... 

As illustrated in Fig. XU-13, a drop of water is placed between two large parallel plates it wets both surfaces. Both the capillary constant a and d in the figure are much greater than the plate separation x. Derive an equation for the force between the two plates and calculate the value for a 1-cm drop of water at 20°C, with x = 0.5, 1, and 2 mm. 

Figure Bl.6.2 Electron analysers consisting of a pair of capacitor plates of various configurations (a) the parallel-plate analyser, (b) the 127° cylindrical analyser and (c) the 180° spherical analyser. Trajectories for electrons of different energies are shown.

The electrostatic sector consists of two curved parallel plates between which is applied a potential difference producing an electric field of strengtir E. Transmission of an ion tlirough the sector is governed by the following relationship... 

Wlien an electrical coimection is made between two metal surfaces, a contact potential difference arises from the transfer of electrons from the metal of lower work function to the second metal until their Femii levels line up. The difference in contact potential between the two metals is just equal to the difference in their respective work fiinctions. In the absence of an applied emf, there is electric field between two parallel metal plates arranged as a capacitor. If a potential is applied, the field can be eliminated and at this point tire potential equals the contact potential difference of tlie two metal plates. If one plate of known work fiinction is used as a reference electrode, the work function of the second plate can be detennined by measuring tliis applied potential between the plates [ ]. One can detemiine the zero-electric-field condition between the two parallel plates by measuring directly the tendency for charge to flow through the external circuit. This is called the static capacitor method [59]. 

Figure C2.2.9. Polygonal domains of focal conics in a smectic A phase confined between parallel plates.

We consider a co-extrusion die consisting of an outer circular distribution channel of rectangular cross-section, connected to an extrusion slot, which is a slowly tapering narrow passage between two flat, non-parallel plates. The polymer melt is fed through an inlet into the distribution channel and flows into... 

For this purpose we compare a parallel plate capacitor under vacuum and one containing a dielectric, as shown in Figs. 10.4a and b, respectively. The plates of the capacitor carry equal but opposite charges Q which can be described as aA, where o is the surface charge density and A is the area of the plates. In this case, the field between the plates is given by... 

Figure 10.4 Parallel-plate capacitor with surface charge density a. (a) The field is Eo with no dielectric present, (b) The field is reduced to E by a dielectric which acquires a surface charge of its own,...

Two parallel plates of conducting material separated by an insulation material, called the dielectric, constitutes an electrical condenser. The two plates may be electrically charged by connecting them to a source of direct current potential. The amount of electrical energy that can be stored in this manner is called the capacitance of the condenser, and is a function of the voltage, area of the plates, thickness of the dielectric, and the characteristic property of the dielectric material called dielectric constant. 

Fig. 22. Shear viscosity Tj and first normal stress difference (7) vs shear rate 7 for a low density polyethylene at 150°C (149), where (Q) — parallel plate ...

Parallel Plate Viscometer. In parallel plate viscometers (164) the gap width usually is larger and can be varied freely. This is an advantage when measuring suspensions or dispersions with large particles or with a tendency to fly out of the gap. The wide gap means that there is less sensitivity to... 

Dyna.mic Viscometer. A dynamic viscometer is a special type of rotational viscometer used for characterising viscoelastic fluids. It measures elastic as weU as viscous behavior by determining the response to both steady-state and oscillatory shear. The geometry may be cone—plate, parallel plates, or concentric cylinders parallel plates have several advantages, as noted above. 

The Ravenfield model BS viscometer is a wide shear rate range iastmment with several possible measurement systems cone—plate, parallel plates, concentric cylinders, and taper plug. The last gives shear rates of up to 10 , and the cone—plate of up to 8 x lO". The viscosity range is... 

The RMS-800 provides steady-shear rotational rates from 10 to 100 rad/s and oscillatory frequencies from 10 to 100 rad/s. An autotension device compensates for expansion or contraction. With the standard 25- and 50-mm parallel plates, the viscosity range is 50-10 mPa-s, and the shear modulus range is 8 x 10 to 10 N/m. These ranges can be expanded with nonstandard plates, cones, and a Couette system. The temperature range is 20-350°C (-150 0 optional). 

A nonaHoyed carbon steel having 0.76% carbon, the eutectoid composition, consists of austenite above its lowest stable temperature, 727°C (the eutectoid temperature). On reasonably slow cooling from above 727°C, transformation of the austenite occurs above about 550°C to a series of parallel plates of a plus cementite known as peadite. The spacing of these plates depends on the temperature of transformation, from 1000 to 2000 nm at about 700°C and below 100 nm at 550°C. The corresponding BrineU hardnesses (BHN), which correspond approximately to tensile strengths, are about BHN... 

Plasmas can be used in CVD reactors to activate and partially decompose the precursor species and perhaps form new chemical species. This allows deposition at a temperature lower than thermal CVD. The process is called plasma-enhanced CVD (PECVD) (12). The plasmas are generated by direct-current, radio-frequency (r-f), or electron-cyclotron-resonance (ECR) techniques. Eigure 15 shows a parallel-plate CVD reactor that uses r-f power to generate the plasma. This type of PECVD reactor is in common use in the semiconductor industry to deposit siUcon nitride, Si N and glass (PSG) encapsulating layers a few micrometers-thick at deposition rates of 5—100 nm /min. 

Fig. 15. Parallel-plate PECVD reactor, where typical parameters are radio frequency at 50 kH2 to 13.56 MH2 temperature, 25—700°C pressure, 13—270 Pa...

A number of viscometers have been developed for securing viscosity data at temperatures as low as 0 °C (58,59). The most popular instmments in current use are the cone plate (ASTM D3205), parallel plate, and capillary instmments (ASTM D2171 and ASTM D2170). The cone plate can be used for the deterniination of viscosities in the range of 10 to over 10 Pa-s (10 P) at temperatures of 0—70°C and at shear rates from 10 to 10 5 . Capillary viscometers are commonly used for the deterniination of viscosities at 60 —135°C. 

Mass Transport. Probably the most iavestigated physical phenomenon ia an electrode process is mass transfer ia the form of a limiting current. A limiting current density is that which is controlled by reactant supply to the electrode surface and not the appHed electrode potential (42). For a simple analysis usiag the limiting current characteristics of various correlations for flow conditions ia a parallel plate cell, see Reference 43. 

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