# Wicking in Paper Strips under Consideration of Liquid Absorption Capacity

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Model

_{R}is the voltage difference across the resistance R, V

_{C}is the voltage difference across the capacitance C. Rearranging Equation (1) into the function of charge Q is described as:

^{−19}Coulomb), v is velocity (m/s), A

_{c}is cross-sectional area (m

^{2}), n is charge density (1/m

^{3}). Given $q=ne$ (Coulomb/m

^{3}), which is charge with unit volume, this parameter is equivalent to the density of the fluid. Integrating current over time results in the total charge flow:

^{3}), Ac is cross-sectional area and R(t) is the fluidic resistance function. Given $-b\times M\left(t\right)=-\frac{1}{C}{\displaystyle \int}\frac{1}{R\left(t\right)}dt$, the unknown coefficients a and b can be determined experimentally with the fitting equation:

_{abs}(µL) is the ability to store liquid per surface area A

_{S}(cm

^{2}) of paper strip

## 3. Materials and Method

#### 3.1. Materials and Instrumentation

#### 3.2. Paper Strip Preparation

#### 3.3. Experiment Setup and Data Acquisition

#### 3.4. Fitting Curve Settings

^{−8}and 0.1 for minimum and maximum changes, respectively. The maximum iteration and termination tolerance are set at 10

^{6}and 10

^{−10}respectively, to make sure that fitting solution converges and fits with the smallest tolerance. Table 1 shows the starting point of iteration, the upper and the lower boundary used for fitting. After fitting with MATLAB, all coefficients in Equation (7) are experimentally determined. The exponential functions have several local solution points. Although curve fitting is performed with many initial boundaries, the result of fitting did not show any significant difference (S.D. is around 0.1% of average values). Therefore, all results were reported as average values. Table 2 lists the values used in the calculation. For Washburn model, the experimental data of the liquid front were fitted as a square root function of time:

#### 3.5. Direct Measurement for Liquid Absorption Capacity

## 4. Result and Discussion

#### 4.1. Fitting for Cellulose Fiber Paper

^{8}and 7.53 × 10

^{−8}, respectively. The fitting procedure was performed for the case of non-laminated cellulose paper. One-side laminated CFSP was subsequently investigated. The average coefficient a and b for one-side laminated CFSP are 1.12 × 10

^{8}and 6.31 × 10

^{−8}, respectively. Finally, two-side laminated CFSP was investigated. The two-side lamination helps to improve the strength of the test strip and prevents evaporation. The average coefficients a and b for two-side laminated CFSP are 1.12 × 10

^{8}and 6.51 × 10

^{−8}, respectively. Thus, our model agrees well with experimental data of all conditions: non-laminated, one-side and two-side laminated CFSP, Figure 6. The characteristic of wicking speed and material is represented by the coefficient d in the model, which is 0.4. It is dictated by the power law resulting in the steep curve in the early period. As a result, this model fits experimental data better than the Washburn model.

#### 4.2. Fitting for Nitrocellulose Paper

^{8}and 2.95 × 10

^{−8}, respectively. For laminated NC, the average coefficient a and b are 1.05 × 10

^{8}and 2.68 × 10

^{−8}, respectively. As a result, the model in both conditions is in good agreement with both experimental conditions: non-laminated NC and laminated NC as shown in Figure 7. As the coefficient d is 0.5, this model provides a similar relationship between liquid front distance and the square root of time as Washburn model. As a result, both CFSP and NC materials agree well with conventional Washburn model.

#### 4.3. Absorption Capacity

^{2}which is lower than other cases, which are one-side laminated (76.7 µL/cm

^{2}) and non-laminated (79.3 µL/cm

^{2}). For NC cases (Figure 8b), laminated NC (6.42 µL/cm

^{2}) also provide lower absorption capacity than non-laminated NC (10.1 µL/cm

^{2}). As a result, laminated film was melted and permeated into paper matrix resulting in reduced space in the paper matrix. Furthermore, our model with fitting coefficients can also predict the absorption capacity. We obtained the absorption capacity from the model through coefficient a and Equations (9) and (10). The absorption capacity estimated with the model has the same order of magnitude as those from direct weighting and from the literature, Table 7. The C

_{abs}of non-laminated CFSP and NC papers provides 5.77% and 18.9% error respectively compared to the absorption capacity from direct weighting experiment. However, the absorption capacity of both CFSP and NC cases from direct weighting experiment are not statistically different from the model under p value of <0.01. The discrepancy may come from the environment factors such as temperature or humidity, which affect the ability of the paper to store liquid. Thus, we conclude that our model can predict the absorption capacity and can be further used for predicting capillary pressure in each material as discussed later in Section 4.5.

#### 4.4. Fluidic Resistance Function

#### 4.5. Capillary Pressure

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## References

- Eaidkong, T.; Mungkarndee, R.; Phollookin, C.; Tumcharern, G.; Sukwattanasinitt, M.; Wacharasindhu, S. Polydiacetylene paper-based colorimetric sensor array for vapor phase detection and identification of volatile organic compounds. J. Mater. Chem.
**2012**, 22, 5970–5977. [Google Scholar] [CrossRef] - Hossain, S.M.Z.; Brennan, J.D. β-Galactosidase-Based Colorimetric Paper Sensor for Determination of Heavy Metals. Anal. Chem.
**2011**, 83, 8772–8778. [Google Scholar] [CrossRef] - Jokerst, J.C.; Adkins, J.A.; Bisha, B.; Mentele, M.M.; Goodridge, L.D.; Henry, C.S. Development of a Paper-Based Analytical Device for Colorimetric Detection of Select Foodborne Pathogens. Anal. Chem.
**2012**, 84, 2900–2907. [Google Scholar] [CrossRef] - Vella, S.J.; Beattie, P.; Cademartiri, R.; Laromaine, A.; Martinez, A.W.; Phillips, S.T.; Mirica, K.A.; Whitesides, G.M. Measuring Markers of Liver Function Using a Micropatterned Paper Device Designed for Blood from a Fingerstick. Anal. Chem.
**2012**, 84, 2883–2891. [Google Scholar] [CrossRef] [Green Version] - Sajid, M.; Kawde, A.-N.; Daud, M. Designs, formats and applications of lateral flow assay: A literature review. J. Saudi Chem. Soc.
**2015**, 19, 689–705. [Google Scholar] [CrossRef] [Green Version] - Wong, R.; Tse, H. Lateral Flow Immunoassay, 1st ed.; Humana Press: Totowa, NJ, USA, 2009. [Google Scholar] [CrossRef]
- Kasetsirikul, S.; Shiddiky, M.J.A.; Nguyen, N.-T. Challenges and perspectives in the development of paper-based lateral flow assays. Microfluid Nanofluidics
**2020**, 24, 17. [Google Scholar] [CrossRef] - Dungchai, W.; Chailapakul, O.; Henry, C.S. Use of multiple colorimetric indicators for paper-based microfluidic devices. Anal. Chim. Acta
**2010**, 674, 227–233. [Google Scholar] [CrossRef] - Avoundjian, A.; Jalali-Heravi, M.; Gomez, F.A. Use of chemometrics to optimize a glucose assay on a paper microfluidic platform. Anal. Bioanal. Chem.
**2017**, 409, 2697–2703. [Google Scholar] [CrossRef] - Hamedpour, V.; Oliveri, P.; Leardi, R.; Citterio, D. Chemometric challenges in development of paper-based analytical devices: Optimization and image processing. Anal. Chim. Acta
**2020**, 1101, 1–8. [Google Scholar] [CrossRef] - Jalali-Heravi, M.; Arrastia, M.; Gomez, F.A. How Can Chemometrics Improve Microfluidic Research? Anal. Chem.
**2015**, 87, 3544–3555. [Google Scholar] [CrossRef] - Scampicchio, M.; Mannino, S.; Zima, J.; Wang, J. Chemometrics on Microchips: Towards the Classification of Wines. Electroanalysis
**2005**, 17, 1215–1221. [Google Scholar] [CrossRef] - Shariati-Rad, M.; Irandoust, M.; Mohammadi, S. Multivariate analysis of digital images of a paper sensor by partial least squares for determination of nitrite. Chemom. Intell. Lab. Syst.
**2016**, 158, 48–53. [Google Scholar] [CrossRef] - Liu, Z.; He, X.; Han, J.; Zhang, X.; Li, F.; Li, A.; Qu, Z.; Xu, F. Liquid wicking behavior in paper-like materials: Mathematical models and their emerging biomedical applications. Microfluid Nanofluidics
**2018**, 22, 132. [Google Scholar] [CrossRef] - Liu, Z.; Hu, J.; Zhao, Y.; Qu, Z.; Xu, F. Experimental and numerical studies on liquid wicking into filter papers for paper-based diagnostics. Appl. Therm. Eng.
**2015**, 88, 280–287. [Google Scholar] [CrossRef] - Jahanshahi-Anbuhi, S.; Chavan, P.; Sicard, C.; Leung, V.; Hossain, S.M.Z.; Pelton, R.; Brennan, J.D.; Filipe, C.D.M. Creating fast flow channels in paper fluidic devices to control timing of sequential reactions. Lab. A Chip
**2012**, 12, 5079–5085. [Google Scholar] [CrossRef] - Hong, S.; Kim, W. Dynamics of water imbibition through paper channels with wax boundaries. Microfluid Nanofluidics
**2015**, 19, 845–853. [Google Scholar] [CrossRef] - Lioumbas, J.S.; Zamanis, A.; Karapantsios, T.D. Towards a wicking rapid test for rejection assessment of reused fried oils: Results and analysis for extra virgin olive oil. J. Food Eng.
**2013**, 119, 260–270. [Google Scholar] [CrossRef] - Ponomarenko, A.; QuÉRÉ, D.; Clanet, C. A universal law for capillary rise in corners. J. Fluid Mech.
**2011**, 666, 146–154. [Google Scholar] [CrossRef] [Green Version] - Washburn, E.W. The Dynamics of Capillary Flow. Phys. Rev.
**1921**, 17, 273–283. [Google Scholar] [CrossRef] - Elizalde, E.; Urteaga, R.; Berli, C.L.A. Rational design of capillary-driven flows for paper-based microfluidics. Lab. A Chip
**2015**, 15, 2173–2180. [Google Scholar] [CrossRef] - Fu, E.; Ramsey, S.A.; Kauffman, P.; Lutz, B.; Yager, P. Transport in two-dimensional paper networks. Microfluid Nanofluidics
**2011**, 10, 29–35. [Google Scholar] [CrossRef] [Green Version] - Parolo, C.; Medina-Sánchez, M.; de la Escosura-Muñiz, A.; Merkoçi, A. Simple paper architecture modifications lead to enhanced sensitivity in nanoparticle based lateral flow immunoassays. Lab. A Chip
**2013**, 13, 386–390. [Google Scholar] [CrossRef] [Green Version] - Richards, L.A. CAPILLARY CONDUCTION OF LIQUIDS THROUGH POROUS MEDIUMS. Physics
**1931**, 1, 318–333. [Google Scholar] [CrossRef] - Whitaker, S. Flow in porous media I: A theoretical derivation of Darcy’s law. Transp. Porous Media
**1986**, 1, 3–25. [Google Scholar] [CrossRef] - Ge, W.-K.; Lu, G.; Xu, X.; Wang, X.-D. Droplet spreading and permeating on the hybrid-wettability porous substrates: A lattice Boltzmann method study. Open Phys.
**2016**, 14, 483. [Google Scholar] - Hyväluoma, J.; Raiskinmäki, P.; Jäsberg, A.; Koponen, A.; Kataja, M.; Timonen, J. Simulation of liquid penetration in paper. Phys. Rev. E
**2006**, 73, 036705. [Google Scholar] [CrossRef] - Sadeghi, M.A.; Aghighi, M.; Barralet, J.; Gostick, J.T. Pore network modeling of reaction-diffusion in hierarchical porous particles: The effects of microstructure. Chem. Eng. J.
**2017**, 330, 1002–1011. [Google Scholar] [CrossRef] [Green Version] - Tang, R.; Yang, H.; Gong, Y.; Liu, Z.; Li, X.; Wen, T.; Qu, Z.; Zhang, S.; Mei, Q.; Xu, F. Improved Analytical Sensitivity of Lateral Flow Assay using Sponge for HBV Nucleic Acid Detection. Sci. Rep.
**2017**, 7, 1360. [Google Scholar] [CrossRef] [Green Version] - Toley, B.J.; McKenzie, B.; Liang, T.; Buser, J.R.; Yager, P.; Fu, E. Tunable-delay shunts for paper microfluidic devices. Anal. Chem.
**2013**, 85, 11545–11552. [Google Scholar] [CrossRef] [Green Version] - Fries, N. Capillary Transport Processes in Porous Materials–Experiment and Model. Ph.D. Thesis, Universität Bremen, Göttingen, Germany, 2010. [Google Scholar]
- Li, X.; Zwanenburg, P.; Liu, X. Magnetic timing valves for fluid control in paper-based microfluidics. Lab. A Chip
**2013**, 13, 2609–2614. [Google Scholar] [CrossRef]

**Figure 1.**The equivalent circuit comparison between electrical circuit and fluidic circuit and parameter equivalence table including unit analysis.

**Figure 2.**The ability to store liquid in paper matrix was observed (

**a**) the sequential observed photos depicted the progress of liquid front after removing the liquid reservoir (

**b**) the comparison of experimental data between with liquid reservoir and without liquid reservoir. (

**c**) schematic diagram of an equivalent circuit for wicking in a paper strip with liquid reservoir.

**Figure 3.**Paper types used in the experiment: (

**a**) non-laminated CFSP, (

**b**) one-side laminated CFSP, (

**c**) both-side laminated CFSP, (

**d**) nitrocellulose (NC) membrane, (

**e**) laminated nitrocellulose membrane.

**Figure 6.**Comparison between our model and experiment data (

**a**) non-laminated CFSP, (

**b**) one-side laminated CFSP and (

**c**) two-side laminated CFSP.

**Figure 7.**Comparison between our model and experiment data for (

**a**) non-laminated NC paper and (

**b**) laminated NC paper.

**Figure 8.**Comparison between our model and experiment data for (

**a**) non-laminated NC paper and (

**b**) laminated NC paper. Sample n = 3 for independent experiments.

**Figure 9.**The fluidic resistance over time: (

**a**) Non-laminated CFSP with various widths of paper strips (

**b**) for one-side laminated CFSP; (

**c**) Two-side laminated CFSP; (

**d**) Various laminated conditions under the same width 4 mm of paper strips.

**Figure 10.**The fluidic resistance over time: (

**a**) Non-laminated NC with various widths of paper strips (

**b**) Laminated NC (

**c**) Various laminated conditions under the same width of paper strips.

Coefficient | Starting Points | Lower Boundary | Upper Boundary |
---|---|---|---|

a | 1 × 10^{8}–1 × 10^{9} | 1 × 10^{8} | 1 × 10^{9} |

b | 0.001–0.999 | 0 | 1 |

d | 0.001–0.999 | 0 | 1 |

Parameter | Value |
---|---|

Vs-Pressure-Capillary pressure in CFSP | 3000 Pa [30] |

Vs-Pressure-Capillary pressure in Nitrocellulose (FF80HP) | 13,000 Pa [30] |

Vs-Pressure-Capillary pressure in Nitrocellulose (FF170HP) | 2879 Pa * |

Adsorption capacity in CFSP | 79.29 µL/cm^{2} [30] |

Adsorption capacity in Nitrocellulose (FF170HP) | 10.06 µL/cm^{2} [30] |

Viscosity | 8.94 × 10^{−}^{4} Pa.s |

Density | 1000 kg/m^{3} |

Non-Laminated CFSP Size | a | b | d |
---|---|---|---|

2 mm | 1.02 × 10^{8} | 8.14 × 10^{−}^{8} | 0.40 |

4 mm | 1.03 × 10^{8} | 8.63 × 10^{−}^{8} | 0.39 |

6 mm | 1.02 × 10^{8} | 8.69 × 10^{−}^{8} | 0.39 |

Materials | Coefficient p for Washburn Relation | |||
---|---|---|---|---|

Width 2 mm | Width 4 mm | Width 6 mm | Average | |

Non-laminated CFSP | 6.05 | 6.14 | 6.25 | 6.15 |

One-side laminated CFSP | 4.47 | 4.86 | 4.96 | 4.76 |

Two-side laminated CFSP | 5.08 | 4.93 | 5.08 | 5.03 |

Non-Laminated NC Size | a | b | d |
---|---|---|---|

2 mm | 1.02 × 10^{8} | 3.03 × 10^{−}^{8} | 0.50 |

4 mm | 1.02 × 10^{8} | 3.41 × 10^{−}^{8} | 0.48 |

6 mm | 1.01 × 10^{8} | 3.00 × 10^{−}^{8} | 0.52 |

Materials | Coefficient p for Washburn Relation | |||
---|---|---|---|---|

Width 2 mm | Width 4 mm | Width 6 mm | Average | |

Nitrocellulose membrane | 3.08 | 3.18 | 3.12 | 3.12 |

Laminated nitrocellulose membrane | 2.75 | 2.94 | 2.80 | 2.83 |

**Table 7.**Absorption capacity result from the model and direct weighting experiment comparing to literature.

Non-Laminated CFSP (µL/cm^{2}) | Nitrocellulose Membrane (µL/cm^{2}) | |
---|---|---|

Absorption capacity from the model | 75.0 | 8.14 |

Absorption capacity from the direct weighting experiment | 79.3 | 10.07 |

Absorption capacity from literature | 83 [30] | 10 [30] |

Materials | Absorption Capacity (µL/cm^{2}) | Coefficient a | Capillary Pressure (Pa) |
---|---|---|---|

Non-laminated CFSP | 79.3 ± 1.60 | 1.14 × 10^{8} | 2586 |

One-side laminated CFSP | 76.7 ± 3.49 | 1.12 × 10^{8} | 2881 |

Two-side laminated CFSP | 65.2 ± 2.93 | 1.12 × 10^{8} | 3522 |

Nitrocellulose membrane | 10.1 ± 1.85 | 1.06 × 10^{8} | 2345 |

Laminated nitrocellulose membrane | 6.42 ± 0.25 | 1.06 × 10^{8} | 3636 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kasetsirikul, S.; Shiddiky, M.J.A.; Nguyen, N.-T.
Wicking in Paper Strips under Consideration of Liquid Absorption Capacity. *Chemosensors* **2020**, *8*, 65.
https://doi.org/10.3390/chemosensors8030065

**AMA Style**

Kasetsirikul S, Shiddiky MJA, Nguyen N-T.
Wicking in Paper Strips under Consideration of Liquid Absorption Capacity. *Chemosensors*. 2020; 8(3):65.
https://doi.org/10.3390/chemosensors8030065

**Chicago/Turabian Style**

Kasetsirikul, Surasak, Muhammad J. A. Shiddiky, and Nam-Trung Nguyen.
2020. "Wicking in Paper Strips under Consideration of Liquid Absorption Capacity" *Chemosensors* 8, no. 3: 65.
https://doi.org/10.3390/chemosensors8030065