Spatial distribution of energy

In all of the above equations, is assumed to be constant and uniform throughout the flow field. In most items of bioprocess equipment, however, there is a spatial distribution of energy dissipation. The definition of an average or a maximum energy dissipation rate is notoriously difficult in the case of bioprocess equipment such as high pressure homogenisers, centrifuges, pumps and microfiltration units which all have complex flow fields. 

In the present approach a physically relevant expression for the local energy density is sometimes needed. In such a case we shall prefer the form (17) to that of Eq. (16). Thus there are situations where the moment has to be taken of the local energy density, with some space-dependent function /. Since wj and ws represent entirely different spatial distributions of energy, it is then observed that... 

The representation as a spatial distribution of energy deposition provides new possibilities in the analysis of the phenomenon. 

The ion track radius is also an important parameter in such reactions, reflecting the local spatial distribution of energy deposited by an incident ion and influencing the character of subsequent chemical reactions [8-12]. We recently reported on main-chain scission and crosslinking reactions in a variety of polymer systems and proposed chemical core sizes in ion tracks based on discussion of the non-homogeneous spatial distribution of reactions [9-15]. Intratrack crosslinking reactions are also of interest with respect to the potential for the direct formation of nano-structured materials, and materials exhibiting these reactions have been successfully visualized in recent years [11,13]. However, despite the extensive experimental and theoretical study undertaken to date, many factors in the relationship between the ion track structure and the chemical core radius remain unclear. This paper proposes a new formulation that determines the chemical core radius in an ion track based on the initial... 

Winterbon, K.B., Sigmund, P., Sanders, J.B. Spatial distribution of energy deposited by atomic particles in elastic collisions. Mat. Fys. Medd. Dan. Vidensk. Selsk. 37(14), 5. 

Figure 8.1.3 Spatial distribution of energy, cavitation, and effects in ultrasound fields.

The spatial distribution of energy in a sound field and the therefore distributed effective areas can be found by two different approaches. Measurement of the local parameters in a given reactor setup or modeling are suitable methods. 

Both photons and ions have In common that they Induce biological damage via emission of secondary electrons when penetrating matter. However, Ion beams show a quite distinct spatial distribution of energy deposition compared to photons on a microscopic as well as on a macroscopic scale. These differences are responsible also for their different biological action and will thus be described briefly here. 

Based on the analysis of chromosome aberrations, Neary [122] has developed one of the first models specifically based on lesion interaction. Estimates revealed that interaction should take place over distances of typically micrometers, so that the distribution of damage on a micrometer scale was thought to be of particular importance. Since the spatial distribution of damage cannot be investigated direct ly, the spatial distribution of energy deposition was taken as a measure reflecting the damage distribution. 

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