# Paper on a disc: balancing the capillary-driven flow with a centrifugal force

Entry by Yuhang Jin, AP225 Fall 2011

## Reference

Hyundoo Hwang, Seung-Hoon Kim, Tae-Hyeong Kim, Je-Kyun Parkb and Yoon-Kyoung Cho, *Lab Chip*, 2011, **11**, 3404.

## Keywords

paper microfluidics, capillary-driven flow, centrifugal forces

## Introduction

Paper microfluidic devices allow passive transport of fluids through capillary force, and carry intrinsic advantages such as low-cost, flexible, and simple fabrication and easiness to store, transport, and dispose. Liquid transport in paper depends on the structure and material of the pre-manufactured paper, and controlling the flow in a continuous and active manner appears rather difficult. This paper presents a novel concept for active control of the flow in paper using a centrifugal force by integrating a paper strip into a disc-shaped centrifugal microfluidic platform and rotating it with various spin speeds. The flow in the paper under different strength of the centrifugal force is characterized. The paper demonstrates the ability to control the flow rate in a programmable manner as well as reverse the flow direction.

## Theory, experiments and results

The wicking distance *h*, shown in Fig. 1, obeys the Darcy's law:

<math>\frac{\mbox{d}h}{\mbox{d}t}=\frac{\kappa}{\eta}\frac{\Delta P}{h}</math>,

where *κ* is the permeability of the paper and *h* is the fluid viscosity. The net driving pressure is given by

<math>\Delta P=\Delta P_c-\rho\omega^2(R_0-\frac{h}{2})</math>.

The theoretical value of the equilibrium wicking distance is given by assuming d*h*/d*t*=0 as below:

<math>h_0=R_0-\sqrt{R_0^2-\frac{2\Delta P}{\rho\omega^2}}</math>.

Hence, the equilibrium wicking distance might significantly decrease as *ω* increases.

Temporal change of the wicking distance of water in the paper against the rotating speed is shown in Fig. 2. As *ω* increases, the flow rate of the fluid absorbed by the capillary effect decreases. These results were consistent with our expectations on the basis of the theoretical model discussed above.

The flow rate can also be actively controlled by using a programmable centrifugal microfluidic system, as illustrated in Fig. 3. A spin program continuously rotates the disc with varied spin speed to maintain a constant flow rate.