# Capillarity Induced Negative Pressure of Water Plugs in Nanochannels

Original entry: Nan Niu, APPHY 226, Spring 2009

*By Niels R. Tas, Petra Mela, Tobias Kramer, J. W. Berenschot, and Albert van den Berg*

## Abstract

This is a very interesting article. In this article, the authors focused on fluidic behavior in the nano-scale and discovered interesting phenomeons. From conducting experiment, the authors found evidence that water plugs in hydrophilic nanochannels can be at significant negative pressure due to tensile capillary forces. All in all, the negative pressure of water plugs in nanochannels induces bending of the thin channel capping layer, which results in a visible curvature of the liquid meniscus. The authors did detailed analysis of the meniscus curvature and calculated the amount of bending of the channel to determine the negative pressure of the liquid. In their experiment, for water plugs in silicon oxide nanochannels of 108 nm height, a negative pressure of 17 ± 10 bar was found. Last but not least, the authors used scaling analysis of capillarity induced negative pressure, and showed that absence of cavitation is also expected at other channel heights.

## Experiment

With the advancement in fabrication technology, scientists can now make devices in the nano-scale. This allowed scientists to study fluidic science in the nano-scale. Nanofluidics is the study of fluid behavior in nanoconfinement. The authors insisted that the extremely large surface-to-volume ratios leading to the prominence of surface forces is indeed the essence of nanofluidic. Here, the authors gave a few examples to illustrate his statements. First, Dujardin studied carbon nanotubes and showed that they can be filled by low surface tension substances. On a larger scale, capillarity was studied, measured, and determined. The authors discussed the results and showed that the Young-Laplace equation is valid on 100 nm length scale, and that on this scale the surface tension of water is equal to its macroscopic value. In their experiments, the authors used nanochannels to study capillarity and used surface tension effects to manipulate aqueous solutions on a picoliter scale. In their study of capillarity, the authors observed a peculiar shape of the meniscus of water plugs in nanochannels shown in figure 1, which is an optical micrograph of the water plug in the 10 um wide nanochannel during drying. The channel ends on the right, where a remnant of the sacrificial polysilicon can be seen. Water vapor exits on the left, where the channel is open. Figure 2 is an artist impression of the shape of the meniscus as related to the bending of the channel capping. In figure 2, part of the capping has been left out to show the meniscus more clearly. The authors used hydrophilic silicon oxide nanochannels with an approximate height of 100 nm as shown in figure 3 and filled them with water in order to obtain these water plugs. The excess water was removed from the channel entrance. Furthermore, to estimate the pressure of the water plug in figure 1, the authors made detailed analysis of the meniscus curvature. The interesting fact is that the tensile capillary forces are so strong on this scale that the water plugs are at a significant negative pressure. As the authors' analysis is based on application of the Young-Laplace equation:

- <math>P_{LV} = \gamma \cdot(\frac{1}{r_{1}}+\frac{1}{r_{2}})</math>

Figure 4 gives two useful equation. From figure 4a, the authors obtained the relation:

- <math>\frac{1}{r_{1c}}+\frac{1}{r_{2c}} = \frac{1}{r_{1e}}+\frac{1}{r_{2e}}</math>

Figure 4b relates the curvature in the xz-plane to the channel heights h_{c} and h_{e} at positions c and e:

- <math>r_{2c,e} = \frac{-h_{c,e}}{2cos\theta}</math>

Figure 5 shows a representation of the water plug in a flat hydrophilic channel, where h is the channel height and \theta is the contact angle. The tensile capillary forces F_{cap} result in a lowering of the pressure of the water plug.