Moving interface problems

Transcendental equations, such as for A in Eq. 20.10, appear frequently in moving interface problems and can be solved using numerical methods. 

Li Z (1997) Immersed interface methods for moving interface problems. Numerical Algorithms 14 269-293... 

Steven G (1982) Internally Discontinuous Finite elements for moving interface problems. Int J Numer Methods Eng 18 (4), 569-582... 

Normally, it is not possible to obtain analytical solutions for this transport problem and so we cannot a priori calculate the reaction path. Kirkaldy [J. S. Kirkaldy, D. J. Young (1985)] did pioneering work on metal systems, based on investigations by C. Wagner and the later work of Mullins and Sekerka. They used the diffusion path concept to formulate a number of stability rules. These rules can explain the facts and are predictive within certain limits if applied properly. One of Kirkaldy s results is this. The moving interface in a ternary system is morphologically stable if... 

In the moving-boundary problems treated above, it was assumed that the interface retained its basic initial shape as it moved. It is important to realize that such problems are a subset of a much wider class of problems known as free-boundary problems, in which the boundary is allowed to change its shape as a function of time [2]. A mathematically correct solution for the motion of a boundary of a fixed ideal shape is no guarantee that it is physically realistic. 

Whilst the object of this chapter has been to show the extent and type of HPLC technique that is used today in today s environmental laboratories, there are a number of less routine techniques that may or may not have an impact on routine environmental monitoring. One of the most potentially important of these is the use of LC-MS. The problems associated with using LC-MS for trace analysis are twofold one is the usual LC-MS problem of interfacing the second is that of sensitivity of detector. The interfacing problem may well continue to have partial (compared with GC-MS interfacing) solutions such as FAB, and thermospray, etc. However, even given the advances arising from electrospray interfaces the answer may well be to move away from LC-MS to supercritical fluids and SFC-MS. 

Pore Mouth (or Shell Progressive) Poisoning This mechanism occurs when the poisoning of a pore surface begins at the mouth of the pore and moves gradmuly inward. This is a moving boundary problem, and the pseudo-steady-state assumption is made that the boundary moves slowly compared with diffusion of poison and reactants and reaction on the active surface. P is the fraction of the pore that is deactivated. The poison diffuses through the dead zone and deposits at the interface between the dead and active zones. The reactants diffuse across the dead zone without reaction, followed by diffusion-reaction in the active zone. 

In both, layer and suspension crystallization solid material forms from the melt starting with a nucleus through which a solid/liquid interface is created. As crystallization proceeds the mass of solidified substance steadily increases which causes the interface to move. The impurity components remaining in the melt thereby enrich in front of the solid/liquid interface, forming a concentration boundary layer. The concentration profile in this boundary layer changes as the interface advances which is in literature referred to as moving boundary problem. ... 

Now let us see what this model gives us in terms of F t) or (/) responses. T o solve this equation (which, incidentally, is no longer of the form of an initial-value problem but is a boundary-value problem), it is convenient to make a change of variables. We let V represent the position of the moving interface represented by all elements of fluid introduced into the reactor at some given time, analogous to the downstream volume y used in Chapter 4. In terms of the length variable, this transformation is... 

Farkas et al. [19,20] studied heat transfer in larger items of food, which retain a moist core after frying, e.g., french fries. They considered the food as a semi-infinite slab and the movement of the crust/core interface as a moving boundary problem. The properties of the crust were considered to be uniquely different from those of the core and separate mathematical expressions were developed to describe heat transfer in each region. The crust region was assumed to contain a negligible amount of water and the conductive heat transfer coefficients of each region were considered constant. 

Eulerian methods perform weU for a variety of moving boundary problems. However, in these problems, particularly when surface forces are to be included in the flow calculations, the interface is diffused and occupies a few grid cells in practical calculations. This is undesirable in many problems both from an accuracy and physical realizability/modeling standpoint. 

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