Multilamination

Coffee vacuum-packed in flexible, bag-in-box packages has gained wide acceptance in Europe. The inner liner, usually a plastic-laminated foil, is formed into a hard brick shape during the vacuum process (30). In the United States, a printed multilaminated flexible stmcture is used to form the brick pack which is sold as is at retail. These types of packages provide a barrier to moisture and oxygen similar to that of a metal can. 

Figure 1.2 Normal and focused multilamination flow patterns, slug flow composed of gas/liquid segments (Taylor flow ), and ordered foam flow ( hexagon flow ) (from top to bottom).

Figure 2.10 Multilamination flow oriented along the computational grid (left) and forming a tilted angle with the grid cells (right).

Figure 2.45 Design of a multilamination mixer with hydrodynamic focusing (upper left) and flow pattern in such a mixer for a total volume flow of 10 ml h of water (lower left), taken from [141. The right side of the figure shows the orientation of liquid lamellae over a cross-section of the constriction for different Reynolds numbers [142].

Figure 2.61 Formation of water droplets in silicone oil in a multilamination micro mixer.

Details on microfabrication and on the internals in the stacked plates have not been substantially disclosed so far. Accordingly, no information on the mechanisms of mass and heat transfer was reported. In one version, geometrically focused multilamination is used for mixing liquid streams [55]. 

In transmission mode a spatial resolution of about 15-20 pm can be achieved with infrared microscopes [32]. This is generally sufficient to properly identify such as small impurities, inclusions, gels or single components of multilaminate foils. Similar to Raman spectroscopy, line profiles or maps over larger sample areas can be performed. 

Interaction of permeation with decomposition. The effects of detoxifying reactions can be considered using the multilaminate model and assuming that first order reaction takes place only in the aqueous phase with a rate constant K which... 

Figure 3. Effect of partition coefficient (P) on availance within a multilaminate septum in which detoxifying reactions occur with rate constants (k) = 1 and (k) = 0.04. Redrawn from Hartley and Graham-Bryce (13).

Peterson, T., and Dreyer, S. Factors influencing delivery from multilaminate transdermal patch systems. Int. Symp. Contr. Rel. Bioact. Mater. 21 477—478, 1994. 

Figure 4 Micromixers, (a) Interdigital structure of a multilamination micromixer. (b) Principle of split-and-recombine static micromixers. (Source IMM.)...

Fig. 4. Concepts to achieve multilamination Direct subdivision by splitting of a main stream and indirect methods by splitting, drilling or bending based on separation-reunification mechanisms...

In this paper, solutions to three important heterogeneous diffusion problems are presented, and their implications for transport in biological systems are discussed. While the detailed methods of solutions and subtleties are presented in other papers (2-6), the asymptotic solutions are easily described, and they define the important physics of diffusion for most of the ranges of interest. In particular, a) nonsteady-state diffusion through oil-water multilaminates (2,3) b) desorption from oil-water multilaminates (4) and... 

Nonsteady-state diffusion through oil-water multilaminates has been used extensively as a model for the optimal biological response of a series of congeners with respect to partition coefficient (3,7, 8). Actual solution of this model reveals the deficiencies of multilaminates as a model for biological transport, but it does show the extraordinary separation factors of these multilaminates in the nonsteady-state regime. 

The second diffusion problem, desorption from oil-water multilaminates, is considered as a model for (a) controlled release from liposomes and lipid multilayers and (b) for transport through biological laminates such as stratum corneum. In contrast to nonsteady-state transport across multilaminates, desorption from laminates depends only on the outermost layers. 

Nonsteady-State Permeation Through Oil-Water Multilaminates... 

The remarkable capability of oil-water multilaminates to separate permeants in the nonsteady state can be best demonstrated by studying the asymptotic solutions of the simultaneous diffusion equations (.2,3). An alternating series of n oil and n-1 water laminates (Figure 1) separate a well-stirred, infinite aqueous source compartment of solute concentration C and an aqueous receptor compartment of zero solute concentration.0 Within the ith membrane phase, the solute concentration, obeys Fick s second law,... 

The solution to this series of diffusion equations demonstrates (Figure 2) the extraordinary capability of these oil-water multilaminates to separate permeants based on partition coefficient. Let PMA be the partition coefficient for maximum transport. For P MAX t le total transport CR(t) depends exponentially on, the number of oil layers for p>>pjIAX> cR(t) depends exponentially on n-1, the number of water laminates. 

To understand the origin of this exponential separation, let us study the concentration profiles at times shorter than the lag time. For small partition coefficients, (P P ), the lag time for a single oil laminate is short compared to tne time to change the concentration of the surrounding water phases. Consequently, one expects (a) the concentration profiles across each oil barrier to resemble steady state, (i.e., the concentration should be a linear function of distance,) and (b) the concentration in each water phase should almost be constant. In Figure 3, a typical concentration profile for an n=2 oil-water multilaminate is shown to demonstrate these two features. 

The assumption of a steady-state profile in the oil laminates and small concentration drops in the water layers may be used to derive asymptotic solutions for the permeation problem. It may be shown that (2) for P P y and t[Pg.36]

Figure 1. Model for permeation through oil-water multilaminate of 2n-l membranes. (Reproduced with permission from Ref. 3. Copyright 1984 American Pharmaceutical Association.)...

Figure 3. Concentration profile across oil-water multilaminate for n=2, P=10-4, and t=71390 s. (Reproduced with permission from Ref. 2. Copyright 1983 Elsevier.)...

Desorption from an oil-water multilaminate should be an accurate model for controlled release from liposomes and lipid multilayers and may be helpful to understand transport through naturally occurring biological laminates such as stratum corneum. Asymptotic solutions based upon simple assumptions about the concentration profile may also be used to understand the desorption properties. 

The model for desorption from an oil-water multilaminate is shown in Figure 5. Only the boundary and initial conditions change from the earlier diffusion problem. Both source and receptor compartments are now maintained under sink conditions. At time zero, each oil layer contains initial concentration PC of solute and the concentration of each aqueous layer is C. To determine the amount... 

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