# Fluid Dynamics Optimization of Microfluidic Diffusion Systems for Assessment of Transdermal Drug Delivery: An Experimental and Simulation Study

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Caffeine Cream Formulation

#### 2.2. Viscosity and Particle Size Distribution of Caffeine Cream

#### 2.3. Devices for Penetration Studies

_{2}, all substances were acquired from Sigma-Hungary Kft., Budapest, Hungary). The perfusion flow rate was 4 µL/min, 40 μL/min, and 100 μL/min, respectively. Samples were collected every 30 min for 5 h.

#### 2.4. Diffusion Platforms

#### 2.5. Bioanalysis

#### 2.6. Statistical Methods

#### 2.7. Computational Fluid Dynamics in Single-Channel Microfluidic Diffusion Chamber (sMDC)

#### 2.7.1. Computational Fluid Dynamics in Single-Channel Microfluidic Diffusion Chamber (sMDC)

_{i}is the mass fraction of the i

^{th}species and $\overrightarrow{{J}_{i}}$ is the diffusion flux of the i

^{th}species, which is given by

^{th}species.

#### 2.7.2. Numerical Method

#### 2.7.3. Parameters Used

^{−4}, 10

^{−6}, 10

^{−8}), with a Darcy number of 10

^{−8}or higher preventing PPF penetration into the membranes, allowing only diffusion and leading to a converged solution. Therefore, Darcy numbers of 10

^{−8}and higher were utilized.

^{−5}or 10

^{−6}) of caffeine in the flow during steady state, the viscosity of the mixture remained nearly constant near the value of PPF. Thus, the viscosity of caffeine did not have a significant effect on the simulations.

#### 2.7.4. Simulations

## 3. Results

#### 3.1. Viscosity and Particle Size Distribution

#### 3.2. Diffusion of Caffeine through Polyester (PET) Membrane, Cellulose Acetate (CA) Membrane, Excised Rat Skin, and Alginate Scaffold

#### 3.3. Computational Fluid Dynamics (CFD)

#### 3.4. Shear Stress Profiles of Membranes

#### 3.5. Velocity Profiles

#### 3.6. Velocity Contours

#### 3.7. Caffeine Progression

#### 3.8. Three-Dimensional Simulations

## 4. Discussion and Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Diffusion systems: (

**A**) single-channel microfluidic device (sMDC), (

**B**) multichannel microfluidic device (mMDC), (

**C**) LiveBox2.

**Figure 2.**Scanning electron micrographs of the diffusion platforms, which were integrated into the microfluidic diffusion chambers: (

**A**) polyester (PET) membrane, (

**B**) cellulose acetate (CA) membrane, (

**C**) excised rat skin, (

**D**,

**E**) alginate scaffold, surface view (

**D**) and cross-sectional view (

**E**), respectively.

**Figure 3.**(

**A**,

**B**) Schematic of the problem, (

**C**) Representation of fluid and porous regions in the computational domain, (

**D**) Coarse mesh (uniform mesh), (

**E**) Fine mesh (finer in the critical regions). A finer version of this mesh was used for simulations.

**Figure 4.**Particle size distribution (

**A**), particle size (

**B**) (at d0.1, d0.5, and d0.9 values), and (

**C**) double logarithmic plot of shear viscosity against shear rate of 2% caffeine-containing cream indicating shear-thinning behavior. Means +/− SEM, n = 9.

**Figure 5.**Cumulative mass–time profiles of caffeine permeation through polyester (PET) membrane in (

**A**) sMDC, (

**B**) mMDC, and (

**C**) LiveBox2 systems with a flow rate of 4 µL/min, 40 µL/min, and 100 µL/min, respectively, and (

**D**) area under the cumulative mass–time curves (AUC). * p < 0.05, *** p < 0.001. All data are means +/− SEM, n = 3.

**Figure 6.**Cumulative mass–time profiles of caffeine permeation through cellulose-acetate membrane in (

**A**) sMDC, (

**B**) mMDC, and (

**C**) LiveBox2 at a flow rate of 4 µL/min, 40 µL/min, and 100 µL/min, respectively, and (

**D**) area under the cumulative mass–time curves (AUC). * p < 0.05, *** p < 0.001. All data are means +/− SEM, n = 3.

**Figure 7.**Cumulative mass–time profiles of caffeine permeation through ex vivo rat skin in (

**A**) sMDC, (

**B**) mMDC, and (

**C**) LiveBox2 at a flow rate of 4 µL/min, 40 µL/min, and 100 µL/min, respectively, and (

**D**) area under the cumulative mass–time curves (AUC). * p < 0.05, *** p < 0.001. All data are means +/− SEM, n = 3.

**Figure 8.**Cumulative mass–time profiles of caffeine permeation through alginate scaffold in (

**A**) sMDC, (

**B**) mMDC, and (

**C**) LiveBox2 at a flow rate of 4 µL/min, 40 µL/min, and 100 µL/min, respectively, and (

**D**) area under the cumulative mass–time curves (AUC). * p < 0.05, *** p < 0.001. All data are means +/− SEM, n = 3.

**Figure 9.**Shear stress contours from top to bottom in order of membrane thickness: (

**A**) PET (Da = 10

^{−8}, porosity = 0.03 [25]), (

**B**) cellulose acetate (h = 0.2 mm, Da = 10

^{−11}, porosity = 0.3 [22,23]), (

**C**) rat skin (h = 0.59 mm, Da = 10

^{−8}, porosity = 0.03 (assumed)), and (

**D**) alginate scaffold (h = 1.77 mm, Da = 10

^{−10}, porosity = 0.4 [22,23]). A flow rate of 40 µL/min was selected as the most effective flow for caffeine diffusion.

**Figure 10.**Shear stress at the membrane surface exposed to perfusion flow for (

**A**) PET, (

**B**) CA, (

**C**) rat skin, and (

**D**) alginate scaffold at flow rates of 4 μL/min, 40 μL/min, and 100 μL/min, respectively.

**Figure 11.**Velocity contours at (

**A**) 4 μL/min, (

**B**) 40 μL/min, and (

**C**)100 μL/min, in thickness order from top to bottom: alginate, rat skin, CA, and PET membranes in sMDC.

**Figure 12.**(

**A**) Caffeine progression in excised rat skin at time t = 0, 30, 180, 450, 900, 1800, and 2700 s at a flow rate of 4 μL/min. (

**B**) Caffeine progression in excised rat skin at time t = 0, 30, 180, 450, 900, 1800, and 2700 s at a flow rate of 40 μL/min. (

**C**) Caffeine progression in excised rat skin at time t = 0, 30, 180, 450, 900, 1800, and 2700 s at a flow rate of 100 μL/min.

**Figure 13.**PPF velocity streamlines below alginate scaffold in sMDC device at Q = 4 μL/min: (

**A**) top view; (

**B**) magnified top view near the alginate scaffold; (

**C**) front view; time t = 0, 30, 180, 450, 900, 1800, and 2700 s at a flow rate of 40 μL/min; and (

**D**,

**E**) view at the inlet and outlet.

**Figure 14.**Shear stress below alginate scaffold in sMDC device at Q = 4 μL/min: (

**A**) front view; (

**B**) magnified front view near the alginate membrane; (

**C**) bottom view; (

**D**) shear stress at alginate exposed to the flow of PPF.

Excipient | Concentration (%) | Function | Supplier |
---|---|---|---|

Paraffin oil | 7.7 | lipophilic base | Hungaropharma Zrt. Budapest, Hungary |

Polyoxyethylene sorbitan monostearate (polysorbate 60) | 1.8 | hydrophilic emulsifying agent | Hungaropharma Zrt. Budapest, Hungary |

White petrolatum | 12.0 | lipophilic base | Hungaropharma Zrt. Budapest, Hungary |

Cetostearyl alcohol | 5.5 | lipophilic emulsifying agent | Molar Chemicals Kft, Halásztelek, Hungary |

Propylene glycol | 14.6 | antimicrobial agent preservative, stabilizer | Hungaropharma Zrt. Budapest, Hungary |

Purified water | 56.4 | hydrophilic phase |

**Table 2.**Technical details of the different diffusion systems. sMDC: single-channel microfluidic diffusion cell, mMDC: multichannel microfluidic diffusion cell.

Diffusion Surface | Material of the Frame | Material of the Receptor Chamber | |
---|---|---|---|

sMDC | 0.283 cm^{2} | aluminum | polydimethylsiloxane |

mMDC | 0.503 cm^{2} | poly(methyl methacrylate) | polydimethylsiloxane |

Livebox2 | 1.767 cm^{2} | Medical-grade silicon (platinic silicon) | acrylonitrile butadiene styrene and delrin |

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## Share and Cite

**MDPI and ACS Style**

Kocsis, D.; Dhinakaran, S.; Pandey, D.; Laki, A.J.; Laki, M.; Sztankovics, D.; Lengyel, M.; Vrábel, J.; Naszlady, M.B.; Sebestyén, A.;
et al. Fluid Dynamics Optimization of Microfluidic Diffusion Systems for Assessment of Transdermal Drug Delivery: An Experimental and Simulation Study. *Sci. Pharm.* **2024**, *92*, 35.
https://doi.org/10.3390/scipharm92020035

**AMA Style**

Kocsis D, Dhinakaran S, Pandey D, Laki AJ, Laki M, Sztankovics D, Lengyel M, Vrábel J, Naszlady MB, Sebestyén A,
et al. Fluid Dynamics Optimization of Microfluidic Diffusion Systems for Assessment of Transdermal Drug Delivery: An Experimental and Simulation Study. *Scientia Pharmaceutica*. 2024; 92(2):35.
https://doi.org/10.3390/scipharm92020035

**Chicago/Turabian Style**

Kocsis, Dorottya, Shanmugam Dhinakaran, Divyam Pandey, András József Laki, Mária Laki, Dániel Sztankovics, Miléna Lengyel, Judit Vrábel, Márton Bese Naszlady, Anna Sebestyén,
and et al. 2024. "Fluid Dynamics Optimization of Microfluidic Diffusion Systems for Assessment of Transdermal Drug Delivery: An Experimental and Simulation Study" *Scientia Pharmaceutica* 92, no. 2: 35.
https://doi.org/10.3390/scipharm92020035