Bakker equation

The quantity pT can be regarded as the tangential pressure , acting in a plane parallel to the interface and tending to decrease an interfacial area. Taking into account that the difference between pT and p is significant only within the discontinuity surface, the Bakker equation can be written as... 

The definition of surface tension y for a spherical interface can be defined by the Bakker equation (after Ono Kondo 1960 and Buff 1955)... 

Using quasi-thermodynamic treatment, according to which to the evaluation of the material density in the interfacial zone, the macromolecule orientation and length, alongside of co-ordinates axes, is neglected, according to the Bakker equation [1231] it can be written ... 

Venneker et al. (2002) extended the GHOST approach due to Bakker and Van den Akker (1994b) by replacing the single transport equation for the... 

Consequently, Bakker (1996) described the concentration evolution of a single layer subjected to the vorticity field of a single CSV by means of a onedimensional differential equation where both the nondimensional time and the nondimensional spatial coordinate contain the exponential shrinking rate. In this respect, the CSV approach differs from the various Bourne models in which the successive generation of several multiple-layer stacks is required and vortex age is a crucial element. 

Van der Waals, whose theory has been further developed by Hulshoff and by Bakker, went one step further than Gibbs by assuming that there exists a perfectly continuous transition from one medium to the other at the boundary. This assumption limits him to the consideration of one particular case that of a liquid in contact with its own saturated vapour, and mathematical treatment becomes possible by the further assumption that the Van der Waals equation (see Chapter II.) holds good throughout the system. The conditions of equilibrium thus become dynamical, as opposed to the statical equilibrium of Laplace s theory. Van der Waals arrives at the following principal results (i) that a surface tension exists at the boundary liquid-saturated vapour and that it is of the same order of magnitude as that found by Laplace s theory (2) that the surface tension... 

The Nicolsky-Eisenman equation (15-8) is predicated on equal charges for the primary (A) and interfering (X) ions [E. Bakker, R. Meruva, E. Pretsch, and M. Meyerhoff, Selectivity of Polymer Membrane-Based Ion-Selective Electrodes, Anal. Chem. 1994, 66, 3021]. Recipes for measuring selectivity... 

Increasing errors with increasing salinities (see patterns in the discussion above) were observed in earlier work (e.g., Englezos and Hall 1994 Bakker et al. 1996). Equation 3.36 is the model used in this work to estimate equi-... 

In this beam-sweeping scheme the effective spatial distribution of the ions sampled is defined by the characteristics of the sweeping action and the detector slit parameters [20]. Maintaining the fast rise time of the deflection pulse is critical in maintaining spatially small ion packets at the detector surface, and thus adequate resolution. The overall resolution for the differential impulse-sweeping mode in Fig. 12.3 can be estimated with the following equation developed by Bakker [20] ... 

Although Gossart claimed that y was the same for substances of the same chemical class (alcohols, acids, esters, some chlorine derivatives), this was not found by Hock. Cantor found that y/a=7/3=2-33, where a=coefficient of expansion Bakker found the ratio 3 6 to 3 7 at the m.p. (except for water and allyl alcohol), and gave the equation y=2a+M5rc, where Tc=cntical temperature. Creighton found that surface tension followed Ramsay and Young s equation ( 8.VIII K) ... 

If 1 jvg is neglected in comparison with 1 jvi, the law of rectilinear diameter of Cailletet and Mathias ( 5.VIIB) gives llvi=A—BTy where A and B are constants, and r=abs. temp. Hence, from Bakker s equation ( 4.VIIIL), l. =alvi, it foUows that l —a A—BT), where a is van der Waals s constant. From Stefan s equation ( 6.VIII G),... 

A formula for the latent heat of evaporation based on the Stefan relation with internal pressure ( 6.VIII G) was deduced from the van der Waals equation by Bakker. The internal pressure is K=alv and the work spent in expanding continuously ( 9.VTI C) from the liquid volume vi to the vapour volume Vg is equal to the internal latent heat ... 

Macleodi tried to improve Bakker s equation by introducing a variable van der Waals b ( 13.VIIC) and put (P=p+a/ 2) ... 

Kapieijn F., Bakker W.J.W., Zheng G., Poppe J. and Moulijn J.A., Permeation and separation of light hydrocarbons through a silicalite-1 membrane Application of the generalized Max-well-Stefan equations, Cherru Eng. J. 57 145 (1995). 

Let also calculate the power requirement. Equation 24 in Bakker and Gates (1995) gives an equation for Np as a function or Nrc and the system geometry. 

Bakker, Smith, and Myers combined the results of Nienow and those of Warmoeskerken and Smith to establish an equation for the determination of the transition point at which the gas becomes completely dispersed in the liquid (in the regions both below and above the impeller). For flat-blade disk turbines, the expression that they found... 

Correlations have also been developed for Pq. Bakker, Smith, and Myers report the following equation for a single gassed impeller ... 

Recently, Bittorf and Kresta have successfully correlated the cloud height data of Bujalski et al. and Hicks, Myers, and Bakker with the following equation for purely axial impellers ... 

The application of CFD in the modeling of solid-liquid mixing is fairly recent. In 1994, Bakker et al. developed a two-dimensional computational approach to predict the particle concentration distribution in stirred vessels. In their model, the velocity field of the liquid phase is first simulated taking into account the flow turbulence. Then, using a finite volume approach, the diffusion-sedimentation equation along with the convective terms is solved, which includes Ds, a... 

In the following kinetic analysis of the cure of TGDDM with DDS at elevated temperatures, the equations are developed from both DSC and MR data (in some circumstances collected simultaneously (de Bakker et al, 1993)), and enable quantitative estimation of the reactive-group profile at any time during isothermal (and in some cases temperature-ramped) cure. 

We mentioned that selectivity coefficients determined using the Nicolsky equation often vary, depending on relative concentrations and measurement conditions, and the equation does not dpply if the response is non-Nemstian (often the case with secondary ions). The matched potential method is an attempt to deal with this. Bakker and co-workers introduced a new formulism that provides a.clear interpretation of the matched potential method, elegantly deriving an equation based on ion exchange in which the last term in Equation 13.49 becomes where... 

Sanfeld (1968) generalised Bakker s equation to a plane layer with an electric field normal to the interface... 

Because exhaustive experimental testing of every dryer model would be extremely expensive, simulation techniques based on a representation of a drying process (or a dryer) by a series of mathematical equations have been developed by Bakker-Arkema et al. [29,31-33]. 

He showed how the use of double logarithmic plots of the recovery strain against time, obtained for different stress levels, could be related to one another by shift factors the shift factors then could be related simply to gi and. The technique of step loading combined with Equation (10.22) has been used also by Crook [18] and Lai and Bakker [19]. Schapery s model has been applied to nitrocellulose, fibre-reinforced phenolic resin and pol3dsobutylene [17], polycarbonate [18] and high-density polyethylene [19]. 

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