Stake s law


Thus in the case of ions, measurements of this type are generally used to obtain values of the mobility and, through Stoke s law or related equations, an estimate of the effective ionic size.  [c.184]

Because the drop in energy of the molecule that occurs on emitting a fluorescent photon is generally less than the energy of the absorbed photon, the wavelength of the fluorescent light is almost invariably longer than the wavelength of the exciting light. This is Stoke s law, and appHes in almost all cases of fluorescence.  [c.300]

For dilute systems, Stoke s law is applicable to particle settling. References cited at the end of this chapter provide design and sizing information.  [c.392]

The next correction is for the effect that specific gravity of the solids and liquid have on the separation. Since the cyclone does not actually achieve a size separation but rather a mass separation, the specific gravity of the particle is extremely important in determining the separation. It is especially meaningful in applications where the mineral has a higher specific gravity than the gangue material which allows better liberation of mineral particles at a coarser overall separation size. Stoke s law can be applied to determine particle diameters which would produce the same terminal settling velocity for a particle of known specific gravity in a liquid of known specific gravity as compared to a particle of 2.65 specific gravity in water. This relationship can be calculated using the following equation.  [c.425]

The second important mechanism in filtration is that of settling. From Stoke s law of laminar particle settling, the settling velocity of a particle is given by  [c.251]

Smart Walking Jumping directly into a high temperature structure is not the only way to use the conformational space information from the J-Walker. Instead, the structure can be first relaxed before being jumped into.[58] Approximate minimization with a steepest descent method (or conjugate gradient method) will generate structures close to the local minimum. These relaxed configurations will significantly decrease the potential energy, and thus increase the jump success ratio dramatically. Each minimized structure is then regarded as one of the possible trial moves at low temperature and are accepted or rejected with acceptance probability function, that generates a Boltzmann distribution at the low temperature. Unlike the J-Walking acceptance probability, this scheme, which is called Smart Walking[58] (or S-Walking), will dramatically increase the jump success ratio from one basin to another. It also enables the system to explore more phase space and undergo more efficient barrier-crossings. This S-walking method avoids the linear increase of CPU time and memory usage required by the multiple-stage J-Walking method, because it is not necessary to use multiple stages for most systems, even though it would be very easy to implement a multi-stage S-Walking procedure. S-Walking preserves detailed balance approximately  [c.314]

Although many different electrochemical methods of analysis are possible (Figure 11.1) there are only three basic experimental designs (1) measuring the potential under static conditions of no current flow (2) measuring the potential while controlling the current and (3) measuring the current while controlling the potential. Each of these experimental designs, however, is based on Ohm s law that a current, i, passing through an electric circuit of resistance, R, generates a potential, E thus  [c.463]

Stieg, S. A Low-Noise Simplex Optimization Experiment,  [c.700]

Let us recall the dependence of solutions to dynamical and quasi-static problems on the time parameter t. Then Hooke s law (1.3) takes the form  [c.3]

Power Supplies and Controls. Induction heating furnace loads rarely can be connected directiy to the user s electric power distribution system. If the load is to operate at the supply frequency, a transformer is used to provide the proper load voltage as weU as isolation from the supply system. Adjustment of the load voltage can be achieved by means of a tapped transformer or by use of a solid-state switch. The low power factor of an induction load can be corrected by installing a capacitor bank in the primary or secondary circuit.  [c.127]

Faraday s Law appHes to the anode as wed as to the cathode ie, the total reaction at the anode is proportional to the current, and much like the cathode, the anode efficiency varies with the current density. As the current on the anode is iacreased, the anode efficiency decreases, slightly at first, until it reaches a poiat at which the anode metal caimot dissolve fast enough through the anode film. The first stage of dissolution for the soluble anode is the oxidation of the metal fodowed by dissolution of the oxide. When the oxide dissolution rate is less than the oxidation rate, polarization of the anode takes place. The oxide film builds up ia sufficieat thickness to form an iasulating coating, and the current decreases rapidly. The thick anode films can dislodge at  [c.146]

Ethanol s use as a chemical iatemiediate (Table 8) suffered considerably from its replacement ia the production of acetaldehyde, butyraldehyde, acetic acid, and ethyUiexanol. The switch from the ethanol route to those products has depressed demand for ethanol by more than 300 x 10 L (80 x 10 gal) siace 1970. This decrease reflects newer technologies for the manufacture of acetaldehyde and acetic acid, which is the largest use for acetaldehyde, by direct routes usiag ethylene, butane (173), and methanol. Oxo processes (qv) such as Union Carbide s Low Pressure Oxo process for the production of butanol and ethyUiexanol have totaUy replaced the processes based on acetaldehyde. For example, U.S. consumption of ethanol for acetaldehyde manufacture declined steadily from 50% ia 1962 to 37% ia 1964 and none ia 1990. Butadiene was made from ethanol on a large scale duriag World War II, but this route is no longer competitive with butadiene derived from petroleum operations.  [c.415]

Although many different electrochemical methods of analysis are possible (Figure 11.1) there are only three basic experimental designs (1) measuring the potential under static conditions of no current flow (2) measuring the potential while controlling the current and (3) measuring the current while controlling the potential. Each of these experimental designs, however, is based on Ohm s law that a current, i, passing through an electric circuit of resistance, R, generates a potential, E thus  [c.463]

Stieg, S. A Low-Noise Simplex Optimization Experiment,  [c.700]

It follows that die separation of cadmium must be carried out in a distillation column, where zinc can be condensed at the lower temperamre of each stage, and cadmium is preferentially evaporated. Because of the fact that cadmium-zinc alloys show a positive departure from Raoult s law, the activity coefficient of cadmium increases in dilute solution as the temperature decreases in the upper levels of the still. The separation is thus more complete as the temperature decreases.  [c.357]

Paschen s law states that the sparking voltage is a function of gas density and gap length alone. The law is usually followed for gas pressures up to a few atmospheres with small dependenee on temperamre. The sparking voltage in a unifonn electric field can be expressed in terms of breakdown voltage or breakdown field. It should be noted that corona and brush discharges may occur at voltages considerably less than the sparking voltage. At atmospheric pressure, the breakdown field of air varies continuously from 45 kV/cm at a gap of 1 mm to 26 kV/cm at a gap of 10 cm. An average value of 30 kV/cm, corresponding to a gap of 2 cm, is often used as the approximate breakdown field of air. Atmospheric air, dry air, nitrogen, carbon monoxide, acetone vapor, and methane all have roughly the same breakdown field. Oxygen and carbon dioxide have 85-90% of the value while hydrogen has about half the value and rare gases such as helium about one-tenth of the value. Eor organic compounds in an homologous series, such as methane through octane, the breakdown field usually increases with increased molecular weight with little effect due to branching. The presence of double and triple bonds also increases breakdown field relative to aliphatic hydrocarbons. When hydrogen in a molecule is replaced by a halogen the breakdown voltage is usually increased an example is carbon tetrachloride, which has a breakdown field about 170% that of methane or air. Sulfur hexafluoride has been used industrially to prevent charge loss via static discharge, having about 240% the breakdown field of air. The effect of halogens is due to their high electronegativity, facilitating electron attachment to form relatively massive negative ions. Oxygen and water are also electronegative, but less so than halogens their effect on breakdown field on addition to dry air is  [c.37]

A heat exchanger tube rupture occurs in two stages Stage 1 The tube breaks and high-pressure fluid displaces the low-pressure fluid out the exchanger s low-pressure side. High-pressure fluid does not flow through the connecting low-pressure piping. Stage 2 High-pressure fluid flows out through the low-pressure piping. Stage 2 consists of fully developed, often bwo-phase flow of low- and high-pressure fluid from the heat exchanger through downstream piping.  [c.48]

Between 1831 and 1834, using a voltaic pile, Faraday discovered the inductive effects of the electromagnet — the basic principle underlying the operation of electrical machinery — and experimentally quantified the direct proportionality between electrical current and the rates of electrochemical reactions (Faraday s Law). Working with voltaic piles, a great battery of eight Leyden jars charged with static electricity, and using data obtained on other devices by other investigators, Faraday established that electricity was universal and not dependent on its source. During the course of this intense activity, he also invented both the direct and alternating current dynamos.  [c.232]

Figure 8-9. Acetone (1)-chloroform (2) system at 760 mm Hg. Maximum boiling azeotrope formed by negative deviations from Raoult s Law (dashed lines). Used by permission, Smith, B.D., Design of EquiUbnum Stage Processes, McGraw-Hill, New York, (1963), all rights reserved. Figure 8-9. Acetone (1)-chloroform (2) system at 760 mm Hg. Maximum boiling azeotrope formed by negative deviations from Raoult s Law (dashed lines). Used by permission, Smith, B.D., Design of EquiUbnum Stage Processes, McGraw-Hill, New York, (1963), all rights reserved.
Constant molal overflow from stage to stage (theoretical) for simple ideal systems following Raoult s Law. More complicated techniques apply for nonideal systems.  [c.15]

Mate et al [111], who pioneered LFM, used their instrument to show atomic-scale structure in the frictional force between a tungsten tip and surface graphite atoms. In fact, what these authors observed was stick-slip behaviour an effect nonnally associated with macroscopic phenomena, such as the vibration induced in a violin string by the bow, or the squealing of an automobile s brakes. They also found that the frictional coefficient varied slightly with applied load, i.e. a deviation from Amontons law. The same group went on to study mica surfaces [124], where a similar stick-slip behaviour was observed, the frictional coefficient varying with the unit cell periodicity of the mica cleavage plane (figure B 1.19.34). Flu et al [176] examined mica surfaces by LFM using silicon nitride tips, and found that above  [c.1710]

Increase the bond length of the molecule by 0.001 A and recalculate the energy at this fixed value. Fixing a bond length at the value given in the second entr y of the fifth line of the input file (preventing optimization to the equilibrium bond length) is brought about by changing the switch from 1 to 0 in the fourth entry of that line. Leaving a blank in place of 1 would accomplish the same purpose, but it is good practice to enter 0 as a placeholder. Increase the bond length from 1.100 to 1.110 in steps of 0.001 A. Plot the energy E, calculated by MNDO, as a function of bond length r. What is the mathematical function you observe Is this consistent with what you know about the hamionic oscillator According to MNDO, is it reasonable to regard the N—N bond as a harmonic (Hooke s law) spring Print out the input data to your E vs. r plot and use the file to answer the questions below.  [c.284]

The most popular HRSG for use with these machines is a vertical, assisted-circulation design featuring a built-in stack and low groundspace requirements. More recently, an L-shaped HRSG has been developed to reduce the hot flue-gas temperature abmpfly after the gas turbine s exhaust diffuser by locating both the reheater and HP and IP superheaters in the horizontal inlet section to the HRSG. This design reportedly simplifies and reduces the cost of the exhaust duct and expansion joint design. Like most popular designs, the L-shaped HRSG incorporates prefabricated tube bundles packaged and shipped to ease on-site constmction. For this design, a typical three-pressure HRSG having reheat capabiUty requires about 30 separate tube bundles.  [c.16]

Rathbun-Babb suggested that Darkens equation could be improved by raising the thermodynamic correciion factor Pa Io power, n, less than unity. They looked at systems exhibiting negative deviations from Raoult s law and found n = 0.3. Furthermore, for polar-nonpolar mixtures, they found n = 0.6. In a separate study, Siddiqi and Lucas followed those suggestions and found an average absolute error of 3.3 percent for nonpolar-uoupolar mixtures, 11.0 percent for polar-nonpolar mixtures, and 14.6 percent for polar-polar mixtures. Siddiqi et al. examined a few other mixtures ana found that n = was proba-blv best. Thus, this approach is, at best, highly dependent on the type o(components being considered.  [c.598]

The term static bead generally denotes the pressure in a fluid due to the head of fluid above the point in question. Its magnitude is given by the apphcation of Newton s law (force = mass X acceleration). In the case of bquids (constant density), the static headp/, Pa (lbf/ft ) is given by  [c.889]

Two principles are utilized in the design of static samplers—diffusion and permeation (6, 7). Samplers based on the diffusion principle depend on the molecular interactions of N2, O2, and trace pollutant gases. If a concentration gradient can be established for the trace pollutant gas, under certain conditions the movement of the gas will be proportional to the concentration gradient (Tick s law of diffusion), and a sampler can be designed to take advantage of this technique. Figure 13-4 illustrates this principle. The sampler has a well-defined inlet, generally with a cylindrical shape, through which the pollutant gas must diffuse. At the end of the tube, a collechon medium removes the pollutant gas for subsequent analysis and  [c.189]

There are two main disadvantages to this technique. Firstly, the sample is placed in a static sample bucket , and so there is no possibility of stirring. Equilibrium is thus reached solely by diffusion of the gas into the IL sample. For the more viscous samples this can require equilibration times of as much as several hours. Secondly, the weight gain must be corrected for the buoyancy of the sample in order to determine the actual gas solubility. While the mass is measured accurately, the density of the sample must also be known accurately for the buoyancy correction. This is a particularly important problem for low-solubility gases, where the buoyancy correction is a large percentage of the weight gain. For example, the density of an IL must be known to at least + 0.5 % if one wishes to measure the solubility of gases with FLenry s law constants greater than 2000 bar accurately. A detailed description of a FFiden Analytical (IGA003) microbalance and its use for the measurement of gas solubilities in ILs can be found elsewhere [1].  [c.85]

The solubilities of the various gases in [BMIM][PFg] suggests that this IL should be an excellent candidate for a wide variety of industrially important gas separations. There is also the possibility of performing higher-temperature gas separations, thanks to the high thermal stability of the ILs. For supported liquid membranes this would require the use of ceramic or metallic membranes rather than polymeric ones. Both water vapor and CO2 should be removed easily from natural gas since the ratios of Henry s law constants at 25 °C are -9950 and 32, respectively. It should be possible to scrub CO2 from stack gases composed of N2 and O2. Since we know of no measurements of H2S, SO, or NO solubility in [BMIM][PFg], we do not loiow if it would be possible to remove these contaminants as well. Nonetheless, there appears to be ample opportunity for use of ILs for gas separations on the basis of the widely varying gas solubilities measured thus far.  [c.91]

Imagine an electric circuit consisting of abatteiy, a switch, and a coil ofwire (Figure 1). There is no electric current in the coil when the switch is open. Wlien the switch is closed, a current is initiated and a magnetic field is produced in the region around the wire. This is an example of the Oersted effect. As long as the magnetic field is changing, voltage is induced in the coil according to an example of Faraday s law. The induced voltage provides opposition to the current established by the battery, this opposition is the essence of Lenz s law. Eventually the current will stabilize at a constant value and a constant magnetic field is established. Electric forces provided by the battery do work to establish the magnetic field and tins work gives rise to energy stored in the magnetic field. The energy can be recovered when the switch is opened and the current eventually falls to zero. The amount of energy stored in the magnetic field depends on the electric current and a property of the coil called the inductance. Inductance depends on the construction of the coil and the medium in which the coil is placed. Formally, the magnetic energy is given by E = (1/2) LT, where L  [c.1099]

Figure 8-5. Chloroform (l)-methanol (2) system at 50°C. Azeotrope formed by positive deviations from Raoult s Law (dashed lines). Data of Sesonke, dissertation, University of Delaware, used by permission. Smith, B.D., Design of Equilibrium Stage Processes, McGraw-Hill New York, (1963), all rights reserved. Figure 8-5. Chloroform (l)-methanol (2) system at 50°C. Azeotrope formed by positive deviations from Raoult s Law (dashed lines). Data of Sesonke, dissertation, University of Delaware, used by permission. Smith, B.D., Design of Equilibrium Stage Processes, McGraw-Hill New York, (1963), all rights reserved.
Figure 8-6. Acetone (1)-Chloroform (2) system at 50°C. Azeotrope formed by negative deviations from Raoult s Law (dashed lines). Data of Sesonke, dissertation. University of Delaware, used by permission. Smith, B.D., Design of Equilibrium Stage Processes, McGraw-Hill New York (1963), all rights reserved. Figure 8-6. Acetone (1)-Chloroform (2) system at 50°C. Azeotrope formed by negative deviations from Raoult s Law (dashed lines). Data of Sesonke, dissertation. University of Delaware, used by permission. Smith, B.D., Design of Equilibrium Stage Processes, McGraw-Hill New York (1963), all rights reserved.
Review the system illustrated in Figure 40.8. Chamber A is under pressure and is connected by a tube to chamber B, which is also under pressure. The pressure in chamber A is static pressure of lOOpsi. The pressure at some point (X) along the connecting tube consists of a velocity pressure of lOpsi exerted in a direction parallel to the line of flow, plus the unused static pressure of 90psi. The static pressure (90psi) follows Pascal s law and exerts equal pressure in all directions. As the fluid enters chamber B, it slows down and its velocity is reduced. As a volume of liquid moves from a small, confined space into a larger area, the fluid will expand to fill the greater volume. The result of this expansion is a reduction of velocity and a momentary reduction in pressure.  [c.592]

The potential advantages of LPG concern essentially the environmental aspects. LPG s are simple mixtures of 3- and 4-carbon-atom hydrocarbons with few contaminants (very low sulfur content). LPG s contain no noxious additives such as lead and their exhaust emissions have little or no toxicity because aromatics are absent. This type of fuel also benefits often enough from a lower taxation. In spite of that, the use of LPG motor fuel remains static in France, if not on a slightly downward trend. There are several reasons for this situation little interest from automobile manufacturers, reluctance on the part of automobile customers, competition in the refining industry for other uses of and fractions, (alkylation, etherification, direct addition into the gasoline pool). However, in 1993 this subject seems to have received more interest (Hublin et al., 1993).  [c.230]

CO. + CO. = CO. with wavevector = -k. + k. + k. = k.. Their fidl degeneracy is evident since all four fields carry the same frequency (apart from sign). Resonances appear in the electric susceptibilities when, by choice of incident colours and their signs, one or more of their energy denominators (s in iiumber at. sth order) approaches a very small value because the appropriate algebraic colour combination matches material energy gaps. All Raman spectroscopies must, by definition, contain at least one low frequency resonance. When using only optical frequencies, this can only be achieved by having two fields acting conjugately and possessing a difference frequency that matches the material resonance. Further, they must act in the first two steps along the path to the third order polarization of the sample. These first two steps together prepare the Raman resonant material coherence and can be referred to as the doorway stage of the Raman 4WM event.  [c.1185]


See pages that mention the term Stake s law : [c.183]    [c.1340]    [c.1831]    [c.151]    [c.181]    [c.164]    [c.7]    [c.108]    [c.77]    [c.592]    [c.409]    [c.595]    [c.1574]   
Handbook of water and wastewater treatment technologies (2002) -- [ c.273 , c.274 ]