Gradient profiles propagation

Isothermal frontal polymerization (IFP) is a self-sustaining, directional polymerization that can be used to produce gradient refractive index materials. Accurate detection of frontal properties has been difficult due to the concentration gradient that forms from the diffusion and subsequent polymerization of the monomer solution into the polymer seed. A laser technique that detects tiny differences in refractive indices has been modified to detect the various regions in propagating fronts. Propagation distances and gradient profiles have been determined both mathematically and experimentally at various initiator concentrations and cure temperatures for IFP systems of methyl methacrylate with poly(methyl methacrylate) seeds and wilh the thermal initiator 2,2 -azobisisobutryonitrile. 

In order for the front to occur, the gel effect must take place and occurs when the viscosity reaches a critical value causing the rate of polymerization to dramatically increase. This point of conversion was plotted wrt time to show the propagation, and LSODA was the software used to generate the numerical solutions. The gradient profile of the monomer concentration, dM/dy, was calculated using finite differences. 

To determine propagation distances and gradient profiles, the captured images (e.g. Figure 8A) were assigned x- and y-data points using the software UN-SCAN-IT (e.g. Figure 8B), and the data was then analyzed in a spreadsheet... 

FP has two essential features - a sharp concentration gradient and a temperature gradient that propagates through the unstirred medium. Figure 4.1 shows a typical temperature profile. 

Figure 2-8. A sketch of the profiles of constant hydrostatic pressure near the nose of a gravity current. Because of the horizontal gradients of hydrostatic pressure within the nose region, it will propagate to the right, displacing the exterior fluid as it goes.

The problem is to determine the velocity distribution in the fluid as a function of time. In this problem, the fluid motion is due entirely to the motion of the boundary - the only pressure gradient is hydrostatic, and this does not affect the velocity parallel to the plate surface. At the initial instant, the velocity profile appears as a step with magnitude Uat the plate surface and magnitude arbitrarily close to zero everywhere else, as sketched in Fig. 3 11. As time increases, however, the effect of the plate motion propagates farther and farther out into the fluid as momentum is transferred normal to the plate by molecular diffusion and a series of velocity profiles is achieved similar to those sketched in Fig. 3-11. In this section, the details of this motion are analyzed, and, in the process, the concept of self-similar solutions that we shall use extensively in later chapters is introduced. 

Figure 5.14 Film shape with S = 10 and M = -10 fixed for several values of time t (shown in the npper right). A wave driven hy snrface tension gradients propagates up the film. Thinning proportional to and concave-out profiles above the propagating wave indicate a mobile surface below the wave, t thinning and the downward parabolic shape indicate a rigid surface.

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