Absorption physical models

I Komiya, JY Park, A Kamani, NFH Ho, WI Higuchi. Physical model studies on the simultaneous fluid flow and absorption of steroids in the rat intestines. Int J Pharm 4 249-262, 1980. 

Ho, N. F., Higuchi, W. I., Quantitative interpretation of in vivo buccal absorption of n-alkanoic acids by the physical model approach, /. Pharm. Sci. 1971, 60, 537-541. 

A basic starting point in the development of predictive absorption models is to review the mathematical descriptions of rate and extent of dmg absorption. A physical model for simultaneous fluid flow and intestinal absorption that applies broadly to idealised simulation experiments, animal studies, and in vivo studies in humans has been described by Ho et al. [30] and is depicted in Figure 2.4. 

A physical model for simultaneous bulk fluid flow and absorption in the intestinal tract under steady-state conditions is presented in Figure 2.5. 

A better knowledge of force constants, the use of more detailed physical models, and the availability of large computers and of new methods of calculation has permitted the prediction, within close approximation, of the frequencies and, to a lesser degree, the intensities of absorptions of stereoregular polymers in ordered conformations (helix, zigzag, etc.). In this way data on molec-... 

The point of view based on a physical model started with the 1935 paper of Higbie [30], While the main problem treated by Higbie was that of the mass transfer from a bubble to a liquid, it appears that he had recognized the utility of his representation for both packed beds and turbulent motion. The basic idea is that an element of liquid remains in contact with the other phase for a time A and during this time, absorption takes place in that element as in the unsteady diffusion in a semiinfinite solid. The mass transfer coefficient k should therefore depend on the diffusion coefficient D and on the time A. Dimensional analysis leads in this case to the expression... 

Imagine light of irradiance P passing through an infinitesimally thin layer of solution whose thickness is dx. A physical model of the absorption process suggests that, within the infinitesimally thin layer, decrease in power (dP) ought to be proportional to the incident power (P), to the concentration of absorbing species (c), and to the thickness of the section (dx) ... 

Due to the complexity of most waste waters and unknown oxidation products, differences in lumped parameters such as COD or preferably DOC are used to quantify treatment success. A model to describe the oxidation process, including physical and chemical processes, based on a lumped parameter has been tried (Beltran et al., 1995). COD was used as a global parameter for all reactions of ozone with organic compounds in the chemical model. The physical model included the Henry s law constant, the kLa, mass transfer enhancement (i. e. the determination of the kinetic regime of ozone absorption) as well as the... 

Model-based nonlinear least-squares fitting is not the only method for the analysis of multiwavelength kinetics. Such data sets can be analyzed by so-called model-free or soft-modeling methods. These methods do not rely on a chemical model, but only on simple physical restrictions such as positiveness for concentrations and molar absorptivities. Soft-modeling methods are discussed in detail in Chapter 11 of this book. They can be a powerful alternative to hard-modeling methods described in this chapter. In particular, this is the case where there is no functional relationship that can describe the data quantitatively. These methods can also be invaluable aids in the development of the correct kinetic model that should be used to analyze the data by hard-modeling techniques. 

The gas-liquid and gas-solid reaction processes can be analyzed by several different physical models, namely film, penetration, surface renewal, Danckwerts, film-penetration, etc. These models are described by Danckwerts.39 Although each of these models gives a somewhat different physical picture of the reaction process, in many instances the final desired answer for the rate of absorption of gas in the presence of a liquid- or a solid-phase reaction is similar. Since film and penetration theories are most widely used, we review their applications here. 

The mechanism whereby drugs are absorbed from the GI tract is complex. Understanding the intestinal transport mechanism is crucial to the prediction of oral drug absorption. The physical model utilizes the basic principles of thermodynamics and mass transport. The physical model for the simultaneous passive and active membrane transport of drugs in the intestinal lumen is depicted in Fig. 7. The bulk aqueous solution with an aqueous boundary layer on the mucosal side is followed by a series of heterogeneous membranes consisting of parallel lipoidal and aqueous channel pathways for passive and active transport. Thereafter, a sink on the serosal side follows. 

As several researchers have shown empirically, the use of —log(reflectance) can provide, analogous to a transmittance measurement, a linear relationship between the transformed reflectance and concentration, if the matrix is not strongly absorbing as can be found for many samples studied by near-infrared spectroscopy. This issue is presented in detail below. A different approach based on a physical model was considered for UV/VIS measurements and later also applied within the mid-infrared. A theory was derived by Kubelka and Munk for a simple, onedimensional, two-flux model, although it must be noted that Arthur Schuster (1905) had already come up with a reflectance function for isotropic scattering. A detailed description of theoretical and practical aspects was given by Korttim. The optical absorption... 

Detailed experimental procedures for obtaining infrared spectra on humic and fulvic acids have been reported previously 9,22,25-26) and will be briefly described here. Infrared spectra were taken on the size-fractionated samples by using a Fourier transform infrared spectrometer (Mattson, Polaris) with a cooled Hg/Cd/Te detector. Dried humic and fulvic materials were studied by diffuse reflectance infrared spectroscopy (Spectra Tech DRIFT accessory) and reported in K-M units, as well as by transmission absorbance in a KBr pellet. Infrared absorption spectra were obtained directly on the aqueous size-fractioned concentrates with CIR (Spectra Tech CIRCLE accessory). Raman spectra were taken by using an argon ion laser (Spectra-Physics Model 2025-05), a triple-grating monochromator (Spex Triplemate Model 1877), and a photodiode array detector system (Princeton Applied Research Model 1420). All Raman and infrared spectra were taken at 2 cm resolution. 

Another situation where transformation of a descriptor, x is indicated is when it is known by some physical model how this descriptor is linked to more fundamental properties of the molecule. This may indicate some kind of mathematical transformation of the descriptor prior to autoscaling, e.g. In Xj, expfxj, l/ti- One example is spectral data, for which the wavelength, Xj, of an absorption by the reciprocal transformation l/Vj is transformed into a frequency measure which is proportional to the energy of excitation. 

Circular dichroism has been well understood and estabhshed in the ultra-violet, visible, near- and mid-infrared frequency range as an integral part of contemporary biophysics with numerous, excellent, turnkey instruments commercially available. However, there have been no documented measurements of terahertz circular dichroism. We have developed a simple physical model of circular dichroism in the terahertz frequency range, and build upon our broad band absorption spectrometer to explore the terahertz circular dichroism signatures of prototypical proteins in aqueous solutiom... 

We have developed a simple physical model suggesting that for most, if not all, chiral macromolecules, their terahertz absorption will be accompanied by terahertz circular dichroism. Ab initio methods have been used to successfully calculate the vibrational circular dichroism spectra of small molecules, however, these models have largely focused on spectra in the near-infrared, spectra dominated by bond stretching and bending, and the wagging of small... 

Cole et al. (2001) reviewed physical models for most stages of the microlithography process. For the curing stage, they state that there has been no recent development of cure models since the work of Dill (1975). Dill (1975) presented models that incorporate both light absorption and photopolymer cure kinetics modelling, as shown by the following equations ... 

It is not always easy to characterize the electronic and crystallographic structures of very small aggregates. Their size (a few nanometers) is due to the fact that as many atoms as possible must be active and therefore must be at the surface. Moreover, the analysis has to be done in situ, under the true reaction conditions, in order to build a physical model for the role of the catalyst. Then, many experimental techniques have been used, including most recently electron microscopy and X-ray absorption. We focus our attention here on the EXAFS (Extended X-ray Absorption Fine Structure) technique and its possibilities for the study of supported metal catalysts. Most of the examples come from a collaboration between LURE and some public CNRS laboratories (Strasbourg, Meudon) and a private one (IFF — Rueil Malmaison). We begin with some generalities about the technique and the type of catalysts studied, then move to several examples of application. 

X-ray absorption is not really a new technique since the first absorption spectra were obtained by Fricke, Hertz or Lindh at the beginning of the century, but the EXAFS technique appeared as a definite tool for experimentalists in the 1970s when, at the same time, synchrotron radiation and a new physical model became available. 

Design procedures of contactors for simultaneous gas absorption with chemical reaction require all the data -such as flooding, hold-up, ki a and k a and axial dispersion coefficients whenever they are relevant-which are normally required for the design of physical gas absorbers too. Further to these data, separate values of kL and a are also required in order to estimate the enhancement factor using one of the absorption-reaction models. 

The second one is the scaling length which depends on the absorbing property of the medium. The physical model of the medium assumes that total absorption is caused by N objects each having a cross-section (projected area) % also called specific absorbance. So, the ratio of lengths in the Lambert-Beer-Bouguer law must be understood as the ratio of the absorbing area upon the total area, which is also equal to a ratio of volumes ... 

Predicted by this physical model of the process and confirmed by experimental results, the mean roll distance (D) is governed by the material as well as process parameters. The material defines the extent of absorption at the given laser wavelength as well as the orientation of the macromolecules. The main laser parameter on the other hand is the number of laser pulses applied NP. As a matter of fact, the laser fluence, i.e. pulse energy per unit area, is of little influence. 

The FDTD numerical scheme presented here uses the uni-axial PML (UPML) developed by Sacks et al. [23] to truncate the absorptive host medium in the FDTD calculation. The UPML is a physical model based on an anisotropic, perfectly matched medium. For a single interface, the anisotropic medium is uni-axial and is composed of both electric permittivity and magnetic permeability tensors. 

Limitations in the model used for the detector response function and absorber transmission. The response of the detector varies with X-ray energy (and also depends on any absorbers used). This can be simulated using a simple physical model of the detector and parameterized expressions for X-ray absorption coefficient. However, for the highest accuracy it is necessary to analyse standard samples and derive a correction factor for each X-ray line of interest. 

---