High Throughput Preparation of Poly(Lactic-Co-Glycolic Acid) Nanoparticles Using Fiber Fluidic Reactor

Polymeric nanoparticles (NPs) have a variety of biomedical, biotechnology, agricultural and environmental applications. As such, a great need has risen for the fabrication of these NPs in large scales. In this study, we used a high throughput fiber reactor for the preparation of poly(lactic-co-glycolic acid) (PLGA) NPs via nanoprecipitation. The fiber reactor provided a high surface area for the controlled interaction of an organic phase containing the PLGA solution with an aqueous phase, containing poly(vinyl alcohol) (PVA) as a stabilizer. This interaction led to the self-assembly of the polymer into the form of NPs. We studied operational parameters to identify the factors that have the greatest influence on the properties of the resulting PLGA NPs. We found that the concentration of the PLGA solution is the factor that has the greatest effect on NP size, polydispersity index (PDI), and production rate. Increasing PLGA concentration increased NP sizes significantly, while at the same time decreasing the PDI value. The second factor that was found to affect NP properties was the concentration of PVA solution, which resulted in increased NP sizes and decreased production rates. Flowrates of the feed streams also affected NP size to a lesser extent, while changing the operational temperature did not change the product’s features. In general, the results demonstrate that fiber reactors are a suitable method for the large-scale, continuous preparation of polymeric NPs suitable for biomedical applications.


Mathematical proof for calculation of mixing time (τmix )
Assumptions: • Mixing is diffusion-based only.
• Diffusion coefficient equals 1.4 ˟ 10 cm 2 /s for acetone in water • Distribution of the two phases along each single fiber are as illustrated in Figure S1 • Acetone stream width equals water stream width and they both equal diffusion width • Fiber packing density is 8325 fibers/mm 2 • Fiber diameter is 8 μm Figure S1. Cross-section of one fiber and the streams that are flowing over the fiber.
First, we calculate the one-directional distance associated with diffusion of the polymer solution into the aqueous phase, Wd. To do so, we first calculate the area occupied by fibers in an area of 1 mm 2 : The void area in between fibers in a reactor area of 1 mm 2 is therefore: (1000 ) -418,460 = 581,540 Therefore, the void area per fiber is:

581,540 / 8325 fibers = 69.85 /fiber
From Figure S1, the area of one fiber and its void space can be described as: where rf is the fiber radius. Solving for the unknow variable, we find that Wd = 1.09 . In the second part of the derivation, we utilize Fick's second law of diffusion to find the time necessary to achieve full mixing of the polymer phase into the aqueous phase. According to the Fick's second law of diffusion: where C is volume fraction of acetone in the aqueous phase, which is a function of time (t) and distance (x), and D is the diffusion coefficient.
Boundary conditions are as follows: At x = 0, C = 1 (for all t at the interface of two phases) At t = 0, C = 0 (for all x in aqueous portion) B.C. S1 B.C. S2 Therefore, the equation is solved as follows: First, assume that

= 2√
Equation S2 Thus, we can rewrite equation 1 as And, the boundary conditions as: Equation S3 can be written as Then, Therefore, where cte1 is an integration constant. By rewriting the equation,

= .
Equation S8 According to definition of z in equation S4
( , ) Equation S13 erf(y) is defined by Then, Based on the second boundary condition (B.C. S2 and B.C. S4) Therefore, C(x,t) = 1 − erf(y) Equation S17 By substituting y from equation S2 in equation S17: To estimate the mixing time, the value of "C" is substituted with the final volume fraction of the two phases, "x" is substituted with the diffusion distance Wd, and the value of the diffusion coefficient is input to be able to solve for the time of mixing "t". For example, when C = 0.1, the mixing time will be 0.156 ms.