Water-oil multilaminates

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. 

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... 

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

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]

In the chemical industry (on the mega- as well as the micro-scale) fine emulsions have many useful applications in, e.g., extraction processes or phase transfer catalysis. Additionally, they are of interest for the pharmaceutical and cosmetic industry for the preparation of creams and ointments. Micromixers based on the principle of multilamination have been found to be particularly suitable for the generation of emulsions with narrow size distributions [33]. Haverkamp et al. showed the use of micromixers for the production of fine emulsions with well-defined droplet diameters for dermal applications [38]. Bayer et al. [39] reported on a study of silicon oil and water emulsion in micromixers and compared the results with those obtained in a stirred tank. They found similar droplet size distributions for both systems. However, the specific energy required to achieve a certain Sauter mean diameter was 3-1 Ox larger for the macrotool at diameters exceeding 100 pm. In addition, the micromixer was able to produce distributions with a mean as low as 3 pm, whereas the turbine stirrer ended up with around 30 pm. Based on energy considerations, the intensification factor for the microstirrer appears to be 3-10. 

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