Particle model basic

Several mathematical models are available for predicting the dissolution of particles of mixed size. Some are more complex than others and require lengthy calculations. The size of polydisperse drug particles can be represented with a distribution function. During the milling of solids, the distribution of particle sizes most often results in a log-normal distribution. A log-normal distribution is positively skewed such that there can exist a significant tail on the distribution, hence a number of large particles. The basic equation commonly used to describe the particle distribution is the log-normal function,... 

It is extremely difficult to model macroscopic transport of mass, energy, and momentum in porous media commonly encountered in various fields of science and engineering based on microscopic transport models that account for variation of velocity and temperature as well as other quantities of interest past individual solid particles. The basic idea of porous media theory, therefore, is to volume average the quantities of interest and develop field equations based on these average quantities. 

We consider methods for investigating the interactions between aerosol particles and molecules and how to calculate properties of molecules interacting with aerosol particles. The basic models include a heterogeneous dielectric media approach and a quantum mechanical-classical mechanical approach. Both models describe the electronic structure of the molecule at the level of correlated electronic approaches or density functional theory approximations. 

One of the most basic features of the helium spectrum is its organization into an infinite sequence of ionization thresholds. This feature is not the result of intricate computations. It is already apparent on the level of the independent particle model of the helium atom (see Section 10.1). All predictions on the quantum manifestations of chaos have to... 

To describe the combined bulk and Knudsen diffusion flrrxes the dusty gas model can be used [44] [64] [48] [49]. The dusty gas model basically represents an extension of the Maxwell-Stefan bulk diffusion model where a description of the Knudsen diffusion mechanisms is included. In order to include the Knudsen molecule - wall collision mechanism in the Maxwell-Stefan model originally derived considering bulk gas molecule-molecule collisions only, the wall (medium) molecules are treated as an additional pseudo component in the gas mixture. The pore wall medium is approximated as consisting of giant molecules, called dust, which are uniformly distributed in space and held stationary by an external clamping force. This implies that both the diffusive ffrrx and the concentration gradient with respect to the dust particles vanish. 

The deformation behaviors have been interpreted in terms of the two basic models(11), (i) the deformed two-phase model in which the interparticle distances and the particles, initially giving rise to Debye s hard-sphere type scattering(1U), are affinely deformed under constant volumes (designated as "deformed hard-particles") and (ii) the deformed core-shell particle model in which a spherical core-shell particle is affinely deformed under constant volume into an ellipsoidal core-shell particle. 

However, there is a basic difficulty with all hard particle models. Their properties are essentially athermal and depend entirely on the density. Thus if one defines a quantity... 

The basic particle model poses challenges. To the eye, matter appears to be continuous and imagination is needed to think in terms of extremely small, discrete particles. Initially, some students may construct an image of particles embedded in continuous matter. Unfortunately, textbooks sometimes show such images and talk about particles in a solid/liquid/gas, which could lead students astray. Here, the particles are not the substance, they are extra to it. Ideas of particle movement are consistent with this model since movement will be determined by the state of the continuous matter (for example, particles can move arovmd in a liquid). Identifying the particles with the substance helps to avoid such misconceptions, for example, sugar particles , water particles and oxygen particles . 

Assuming students do not already hold the concept of a substance, melting behaviour is an accessible first step. Melting at a precise temperature indicates a pure sample of a substance and the temperature identifies which substance. The basic particle model can then be introduced to explain melting and why different substances have different melting points. Once established for the solid and liquid states, the model is used to predict the gas state (and boiling). This approach recognises that students will not know what a gas is and, importantly, demonstrates the predictive function of scientific models. 

Particle theory involves a number of ideas which work together to form a model. The minimum core for a basic particle model is ... 

Dissolving provides a context to strengthen and develop students understanding of the basic particle model, but also to recognise its limitations. 

From everyday experience, students wiU know that water evaporates at temperatures well below boiling point. The basic particle model can deal with the overall disappearance - water particles become mixed in among air particles - but it cannot explain how this can happen. Moreover, to explain boiling we said particles were... 

Gas state pressure is readily tackled by the basic particle model. Bombarding particles exert a force on the walls of their container. The total force on an area depends on how strong the collisions are and the number of collisions at any one time. For a given sample of... 

The basic assumption of the independent-particle model is that the valence nucleon(s) move in an average field produced by the inert core nucleons. 

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