Particle form factor, definition

In addition to electric charge between particles other factors are in some cases operative in preventing actual contact, thus the medium may be strongly adsorbed by the surface, and the thin film may not readily be displaced on collision of the two neutral particles, in other cases a tough elastic film may be formed, possessing definite mechanical strength and necessitating a violent impact to ensure rupture. 

An equivalent sphere is defined as the sphere with the same value of one of the above measures. The commonest referent is the volume-equivalent sphere, which many authors describe as the equivalent sphere without further definition. The particle shape factor is defined as the ratio of another measure from the above list to the corresponding value for the equivalent sphere. Of the many possible shape factors, those which have proved most useful are described below. All shape factors are open to the criticism that a range of bodies with different forms may have the same shape factor, but this is inevitable if regular or complex shapes are to be described by a single parameter. 

We will now briefly describe certain features of the optimization procedure. For simplicity, in this discussion we will use correlated gaussians without pre-exponential r factors. A general form of an n-particle correlated gaussian of this kind is the negative exponential of a positive definite quadratic form in 3n variables ... 

Another issue is reproducibility. The formulation may work perfectly in an in vitro test system, but the dosage form requires aerosolization, and lung deposition is a function of the characteristics of the aerosol (dose, mass concentration, droplet/particle size, etc.) and the nature of the inspiratory maneuver, a factor that the patient has control over. These factors can influence performance to a far greater extent than can be built into a particle, and thus the term controlled does not seem a defensible objective for pulmonary delivery. The vagaries of the deposition profile and of the amount that will deposit also imply that sustaining a certain drug concentration is a difficult proposition, but the loosest definition extended release, seems an acceptable goal within the boundaries set by the clearance mechanisms. 

The factors which lead to the formation of emulsions are not definitely known. The most permanent emulsions are formed when an insoluble oil is shaken with a solution which contains a substance that interacts with one of the constituents of the oil to produce a colloid. This occurs when an oil containing free fatty acids is shaken with an aqueous solution of an alkali. A layer of soap is formed around the particles of the oil, and it is probable that a layer of oil may surround the colloidal partides of soap. When a solution of egg albumin is shaken with olive oil, a layer of the coagulated protein is formed around the drops of the oil and emulsification takes place. 

For each set of initial conditions, Eqs. (4.1)-(4.3) can be solved to And X ", U ", and The initial conditions are randomly selected from known distribution functions, and we can assume that there is an infinite number of possible combinations. Each combination is called a realization of the granular flow, and the set of all possible realizations forms an ensemble. Note that, because the particles have finite size, they cannot be located at the same point thus X " 4 X for n 4 m. Also, the collision operator will generate chaotic trajectories and thus the particle positions will become uncorrelated after a relatively small number of collisions. In contrast, for particles suspended in a fluid the collisions are suppressed and correlations can be long-lived and of long range. We will make these concepts more precise when we introduce fluid-particle systems later. While the exact nature of the particle correlations is not a factor in the definition of the multi-particle joint PDF introduced below, it is important to keep in mind that they will have... 

The intrinsic properties are the amount of radioactivity and factors which give a measure of the risk for the worker (e.g. the radiotoxic properties of the particular nuclide as given by the ALI or DAC values). It is not possible to draw any definite conclusions about the hazard ft om a certain amount of a radiotoxic substance. The hazard risk may only be evaluated from its radiotoxicity value. For that purpose, it is also necessary to consider its chemical form and pathways to man, which are considered to be extensive properties. ALI values do take into account if the chemical form is "soluble" or "insoluble", but this is, of course, a rather crude subdivision. The DAC values consider the particle size and time of exposure to that particular air condition (e.g. in a factory). However, it does not consider the particular ways by which the substance is released to the environment (cf. 21.11.1). 

To increase the accuracy of the definition of factors fi in cases when the particles are located relatively far apart, one should take advantage of the method of reflections, which allows one to obtain an approximate solution in the form of a power series, r. In this way, terms of higher order are taken into account in Eqs. (12.49). Omitting simple but bulky calculations, accurate to terms of r , we obtain ... 

Column effects. In order to establish optimal operating conditions, it is useful to consider the effects of system parameters on the resolution characteristics of an HDC system. HDC has been described as a chromatographic method with very low capacity but very high efiBciency. For example, the calibration curves show that the spectrum of sizes from less than 100 nm to greater than 300 nm is encompassed in less than about 5% of the column void volume. On the other hand, the theoretical plate count corresponding to the marker peak is typically in the range of several thousand per foot. Comparisons in terms of the specific resolution factor, enable a more precise analysis, since both the separation factor and peak dispersion are included in its definition. A simple form for the specific resolution between two particle populations of diameter Dpi and Dp2 is [11]. 

A comparison of the expressions before. Equations 5.85 through 5.87 and Equations 5.99 through 5.101, for spherical and flake-formed geometries, shows that the particle geometry is of less importance for the effectiveness factor. Let us recall the definition of the Thiele modulus, as in Equation 5.68 ... 

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