The Lucas-Washburn equation is commonly used to predict the distance (L) that a liquid travels through paper. This equation establishes that L2 is linear with time and inversely proportional to the viscosity of the liquid. However, there is currently no theoretical equation connecting the viscosity of a solution to its concentration. In this study, the imbibition flow of a sucrose solution was measured along the length of a horizontal strip of filter paper, featuring a printed, thermometer-shaped hydrophobic boundary. A sample (38 μL) was dispensed onto the bulb area, and the solution's flow was visually tracked using a red dye added to the sample. The imbibition length (L) was measured by a vernier caliper at 10.0 min after the sample addition. An empirical equation, based on literature values of the viscosity (η) and concentration (C) of sucrose solutions, was proposed. By integrating this empirical equation with the Lucas-Washburn equation, the following equation was derived: L = a⋅exp{-(bC + cC2)}, where 'a', 'b' and 'c' are parameters. This equation was fitted to the dataset of L and C, covering C values from 0 to 60 % w/w standard sucrose solutions, resulting in a coefficient of determination of 0.9987. The plot of L against C was observed to closely follow a linear line, with a fitting providing a coefficient of determination of 0.9986. The sucrose contents in samples, such as soft drinks, syrups, and sugarcanes, determined using the imbibition length method and conventional refractometry, were in statistical agreement via the paired t-test at the 95 % confidence level. This method is simple, instrument-free, requiring only a small amount of safe red food dye, and can be conducted on-site.
Keywords: Beverages; Distance-based readout; Imbibition; Microfluidic paper-based analytical device; Sucrose; Viscosity.
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