Disk dispersal processes

The observations summarized in the previous sections indicate that most disks disperse their primordial dust and gas on a timescale shorter than lOMyr. Part of this primordial material may be incorporated into planets. However, planet formation is not the major disk-dispersal mechanism. In the case of our Solar System the mass of the planets amounts to less than one tenth of the minimum-mass solar nebula, which is the minimum disk mass required to reproduce the solar chemical composition (0.013-0.036M Hayashi et al. 1985 Desch 2007). With hydrogen and helium largely depleted in planets (see e.g. Weidenschilling 1977), 

Accretion. Viscous stresses and gravitational torques within the disk transport angular momentum to the outer regions allowing disk matter to flow inward and accrete onto the star. Because the source of viscosity is still not well understood (see also Chapter 4), it is common to describe the viscosity via a dimensionless parameter a (Shakura Syunyaev 1973). Using this simplification, the viscous dispersal timescale, i.e. the time for the disk to disperse via accretion, becomes inversely proportional to a and increases linearly with the radial distance from the star (Hartmann et al. 1998). While the inner-disk material accretes onto the star, material further out moves in and replenishes the inner disk. Thus, the disk-dispersal timescale from accretion alone is set by the timescale to disperse the mass at the outer disk. 

Stellar encounters. Since most stars form in clusters (see e.g. Lada Lada 2003) it is important to evaluate the effect of stellar encounters on the survival of protoplanetary disks. In the most destructive case the disk and the perturbing star move on coplanar orbits and in the same direction matter is removed from the disk as close in as one third of the periastron distance (Clarke Pringle 1993). Even for this most destructive case and for conditions typical to dense clusters like the Trapezium, Hollenbach et al. (2000) find that stellar encounters can only appreciably reduce the lifetime of the outer disk regions ( 100 AU). 

Photoevaporation. High-energy photons either from the central star or from nearby massive stars heat and ionize the disk surface. The main heating photons can come from the stellar chromosphere or from the shock at the base of the accretion and fie in the far-ultraviolet (FUV) (6-13.6 eV) and extreme ultraviolet (EUV) 

A comparison of disk-dispersal timescales, such as that presented in Fig. 1 of Hollenbach et al. (2000), suggests that viscous spreading and photoevaporafion are the major dispersal mechanisms. Models combining these two mechanisms were first developed by Clarke etal. (2001) and later refined by Alexander etal. (2006a,b). The evolution of an accreting and photoevaporating disk can be summarized as follows. In the first 106 7yr viscous evolution proceeds relatively unperturbed by photoevaporafion. Once the viscous accretion inflow rates fall below the photoevaporation rates a gap opens up close to rg and the inner disk rapidly ( 105 yr) drains onto the central star. At this point direct ionization of the disk inner edge (the flux is not anymore attenuated by the inner-disk atmosphere) disperses the 

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Of the stirrer types which set the liquid in a radial motion - or into a tangential flow in the case of high viscosities - only the turbine stirrer ) (so-called Rushton turbine , a disk 2d/3 in diameter supporting 6 blades each d/5 high and d/4 wide [474]) belongs to the high speed stirrers. It can be sensibly utilized only with low viscosity liquids and in baffled tanks. Its diameter ratio D/d is 3-5. The turbine stirrer causes high levels of shear and hence is well suited for dispersion processes. 

Liquid-liquid extraction is carried out either (1) in a series of well-mixed vessels or stages (well-mixed tanks or in plate column), or (2) in a continuous process, such as a spray column, packed column, or rotating disk column. If the process model is to be represented with integer variables, as in a staged process, MILNP (Glanz and Stichlmair, 1997) or one of the methods described in Chapters 9 and 10 can be employed. This example focuses on optimization in which the model is composed of two first-order, steady-state differential equations (a plug flow model). A similar treatment can be applied to an axial dispersion model. 

Rotary Atomization Spinning Disk 10-200 Spray drying. Aerial distribution of pesticides. Chemical processing Good mono-dispersity of droplets. Independent control of atomization quality and liquid flow rate Satellite droplets, 360° spray pattern... 

In industrial and laboratory settings the subdivision process more commonly involves the comminution of large particles or aggregates into smaller sizes, either dry with subsequent dispersion (size reduction to the order of a few pm) or directly in a slurry (size reduction to as small as a few tenths of pm). Examples of comminution machines include agitator ball mills, colloid mills, cutting mills, disk mills, homogenizers, jet mills, mechanical impact mills, ring-roller mills, and roll crushers. 

After a few million years of evolution, where most of the remaining disk mass is accreted to the T Tauri star, the residual disk is dispersed (see Chapter 8) and the star continues its further evolution to the main sequence as a Class III object. The processes going on in these disks, that are usually called protoplanetary during this final phase of protostar evolution, are the subject of the following chapters of this book. 

Observations of protoplanetary disks indicate that these objects remain optically thick for timescales of millions of years, meaning that a population of dust is sustained for that period of time (see Chapter 9 for a detailed discussion of disk lifetimes and dispersal mechanisms). As will be discussed in Chapter 10, the timescale for dust growth and incorporation into planetesimals is less than this time period. Additionally, the timescale for dust settling is much less than the age of these disks. However, the apparent contradictions between these timescales and the observations can be explained within the context of the processes described thus far. 

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