Descending fronts

FIGURE 11.4 Temperature profile of the descending front in tri (ethylene glycol) dimethacrylate (TGDMA) and tricaprylmethylammonium persulfate as an initiator. Front velocity was ll.Omm/min. 

Let us first consider the liquid/solid case. Neglecting heat loss, the descending front is always stable because it corresponds to heating a fluid from above. The front is always flat. If the front is ascending, convection may occur depending on the parameters of the system. 

Bowden et al. experimentally confirmed that the first mode is an antisymmetric one, followed by an axisymmetric one (32). Figure 2 shows a flat descending front as well as axisymmetric and antisymmetric modes of ascending fronts. Figure 3 shows the stability diagram in the viscosity-front velocity plane. Most importantly, they confirmed that the stability of the fluid was a fiinction not only of the viscosity but also of the front velocity. This means that the front dynamics affects the fluids dynamics, unlike with pH fronts and chemical waves in the BZ reaction in which the front velocity does not play a role in the stability of the fluid (33-38). 

If the reactor is not vertical, there is no longer a question of stability - there is always convection. Bazile et al. studied descending fronts of acrylamide/bisacrylamide polymerization in DMSO as a function of tube orientation (39). The fronts remained nearly perpendicular to the vertical but the velocity projected along the axis of the tube increased with a 1/cos 0 dependence. 

Figure 4. Rayleigh-Taylor instability with a descending front of butyl acrylate...

The first experimental confirmation that gravity plays a role in spin modes in a liquid/solid system came in the study of descending fronts in which the viscosity was significantly increased with silica gel (55). Masere et al. found... 

In Figure 9.4, the front profiles in several tubes are shown. There is a clear transition from antisymmetric to axisymmetric convection for ascending fronts with increasing tube diameter. Descending fronts are flat, as predicted. From these experiments, the critical radius was determined to be 0.055 0.005 cm, corresponding to a value of S of 77 21, in agreement with the theoretical value. Pojman el al. (1991b) had predicted a critical radius of 0.06 cm. 

Figure 9.9 A descending front in the chlorate-sulfite system. Descending fingers are suppressed by the large thermal gradient.

Figure 11.9 A descending front of methacrylic acid polymerization (with benzoyl peroxide initiator). Descending fingers of polymerizing material occur under some conditions.

Natural convection plays an important role in FP. Since the reaction is exothermic, then in the case of an ascending front the cold monomer is heated from below. If the monomer is liquid, it can cause the convective instability. Convection increases the heat transfer from the reaction zone and can lead to extinction. This is why descending fronts were studied in [1-4,9-11]. 

We mention also one more experimental observation concerning the interaction of reaction fronts and natural convection. If a planar descending front forming a solid product is considered, then the natural convection should not occur (see Section 2). However, if there is a heat loss through the side wall of the tube, the front is no longer planar. It becomes more advanced in the center. In this case the action of gravity can cause convective motion of the liquid under the front. This phenomenon was observed also in numerical simulations [12]. 

Unlike the case of FP forming a solid product, here the convective instability can also occur for descending fronts [23,24]. We note finally that natural... 

The first experimental confirmation that gravity plays a role on spin modes in a liquid/sohd system came from the study of descending fronts in which the viscosity was significantly increased with sihca gel. Masere et al. [101] found that silica gel significantly altered the spin behavior, as predicted by Garbey et al. [77]. Pojman et al. made a similar observation in square reactors [103]. Pojman et al. studied the dependence of spin modes on viscosity with the FP of HDDA with persulfate initiator [106]. They found that the number of spins was independent of the viscosity until a critical viscosity was reached, at which point the spins vanished. 

Figure 3. Rayleigh-Taylor instability with descending front of butyl acrylate polymerization. Although the polymer product is hot (> 200 °C) it still is about 20% more dense than the monomer below it.

Descending fronts with thermosets are generally immune to convective instabilities but thermoplastics exhibit the Rayleigh-Taylor instability (Figure 3)... 

Frontal polymerization can be achieved with a variety of monomers and has been studied with thermosets and thermoplastics. Examples include n-butyl acrylate, benzyl acrylate, styrene, dodecyl acrylate and hexyl acrylate. If the front is ascending, the monomer inmiediately above the front is lower in density because of the temperature gradient than the bulk monomer and so simple convection can occur for a thermoset (/P) or a thermoplastic. 20) A descending front with a thermoset is stable but a thermoplastic is unstable because even though the polymer is very hot, it is more dense than the unreacted monomer. This leads to the Rayleigh-Taylor instability. 16,21)... 

Figure 7 A descending front of triethylene glycol dimethacrylate polymerization with benzoyl peroxide as the initiator.

Let us first consider the liquid-solid case. Negleaing heat loss, the descending front is always stable because it... 

Figure 26 The dependence of the front shape for descending fronts of acrylamide polymerization in DMSO with persuifate initiator. Adapted from Bazile, M., Jr. Nichols, H. A. Pojman, J. A. Volpert, V. J. Polym. Sci. Part A Polym. Chem. 2002, 40,3504-3508. ...

---