How Small Is Too Small for the Capillarity Theory?

Abstract

We perform molecular dynamics (MD) simulations of nanoscale water capillary bridges (WCBs) expanding between two parallel walls and determine the smallest separation between the walls above which the capillarity theory (CT) remains valid. We consider silica-based walls with tuned surface partial charges that expand from hydrophobic to hydrophilic. We find that the CT is valid (i.e., it predicts successfully the WCB geometry and forces induced on the walls) for, approximately, wall separations h ≥ h 0 = 3.0 nm for all surfaces considered. At these separations, the CT holds without including any line tension and the results are robust relative to the method employed to obtain the WCB profile from MD simulations. At approximately 2.0 nm ≤ h < h 0 , the contact angle of water θ varies with h, suggesting that at such wall separations the CT requires the inclusion of a line tension τ. However, we find that the specific behavior of θ(h) and the associated value of τ are inherently dependent on the method employed to calculate the WCB profile from MD simulations. Interestingly, the forces induced by the WCBs on the walls obey the prediction of the CT without the need to include a line tension for approximately h ≥ 2.5 nm for all surfaces considered. Our results are interpreted in terms of the rearrangement of water molecules within the WCBs and show that the CT breaks down at h < h 0 because its assumptions, that the WCB is a bulklike water volume confined by solid−liquid and liquid−vapor interfaces, do not hold.

Molecular simulations reveal that heterogeneous ice nucleation occurs at higher temperatures in water under capillary tension

“…Other research (Elliott, 2021) supports that capillary theory can extend to the nano-scale used in our simulations, which our results corroborate. Meanwhile, our results are also consistent with Almeida et al (2021), who indicate that the capillary theory breaks down with separations less than ≈ 20 Å.…”

Harvesting Energy from Changes in Relative Humidity Using Nanoscale Water Capillary Bridges

“…In these calculations, we set h min = 3.0 nm since this is approximately the smallest wall separations at which CT holds. 23,45 We also set RH max = 1 since this value of RH minimizes the force produced by the WCB on the walls along path 3 → 4, which in turn maximizes the E hvd . The value of 25 ≈21300 carbon nanotubes hybrid yarn 44 ≈1800 regenerated silk film 47 ≈1626 bioinspired polymer (PEE−PPy) 48 ≈114 graphene fiber 49 ≈520 As shown in Figure 5c, E hvd * (b) ∝ b.…”

“…Figure a shows the energy harvested by the WCB for selected values of hydrophilic patch width b at T = 400 K. E hvd is calculated for the thermodynamic closed path of Figure e as a function of the minimum RH of the cycle. In these calculations, we set h min = 3.0 nm since this is approximately the smallest wall separations at which CT holds. , We also set RH max = 1 since this value of RH minimizes the force produced by the WCB on the walls along path 3 → 4, which in turn maximizes the E hvd . The value of h max depends on RH min , and it is set to h max = prefix− 2 r ( RH min ) 0.0ex0.0ex0.25em normalf normalo normalr 0.0ex0.0ex0.25em b − 2 r ( RH min ) , and h max = − 4 r ( RH min ) b − b 2 for b = 2 r (RH min ), where r (RH min ) is the negative radius of curvature found from eq .…”

Factors Predicting Fertility Rate in Indonesia

“…On the other hand, Social Capillarity Theory is based on the analogy that the liquid will rise rapidly in a narrow capillary tube, which is identical to the number of children (Almeida et al, 2021). Social capillarity theory can develop well in democratic countries, where every individual has the freedom to achieve a position in society, including determining the number of children.…”