Selected Water Harvesting Mechanisms—Lessons from Living Nature

Abstract

Water moves continuously above and below the surface of the Earth. Bodies of water, clouds, evaporation and condensation all are part of the water cycle. Fog is composed of micron-sized water droplets that form when air becomes saturated with water vapor. Fog is a thick cloud that remains suspended in the atmosphere. Dew is the deposit of water droplets that are formed on cold surfaces, with temperature lower than the dew point, by condensation of water vapor in the air. In many plants and animals, living nature uses fog and condensation as a vital source of water, particularly in arid areas that receive little rainfall (Brown and Bhushan, 2016; Bhushan, 2018, 2019, 2020). Fog and dew always exist when the temperature decreases late at night and in the early morning. There is evidence that over 5000 years ago, hunter–gatherer groups were able to populate arid areas along the southern coast of Peru by utilizing fresh water from fog and condensation, though the collection method is unknown (Beresford-Jones et al. 2015).

Appendices

Appendix 3.A: Laplace Pressure Gradient on a Conical Surface

For a spherical droplet sitting on a surface, capillary pressure or Laplace pressure in the liquid $p_{\text{L}}$ is proportional to the surface tension of the liquid in air ($\gamma_{\text{LA}}$) divided by the local radius, R (Adamson and Gast 1997; Bhushan 2013a, b, 2018),

$$ p_{\text{L}} = \frac{{\gamma_{\text{LA}} }}{R} $$

(3.A.1)

The Laplace pressure can be attractive or repulsive depending on whether the surface is hydrophilic or hydrophobic, respectively. The $p_{\text{L}}$ remains constant on a flat surface.

Next, we consider a liquid droplet sitting on a conical object. We consider two adjacent locations A and B with the local radii of the cone, as R_A and R_B, respectively, Fig. 3.A.1 (Bhushan 2018). The surface curvature gradient results in the Laplace pressure difference between the two opposite ends of the droplet along the surface. The Laplace pressure difference is given as,

Fig. 3.A.1

Schematic of a liquid droplet on a conical object with a cone angle of 2α and local radii R_A and R_B at two locations of A and B, respectively. Shown is the Laplace force (F_L) which helps in driving the droplet towards a larger radius (adapted from Bhushan 2018)

$$ \Delta p_{\text{L}} = \gamma_{\text{LA}} \left( {\frac{1}{{R_{A}^{'} }} - \frac{1}{{R_{B}^{'} }}} \right) $$

(3.A.2)

where $R_{A}^{'}$ and $R_{B}^{'}$ are the radii of curvature at the front and rear contact lines of the droplet, respectively. The curvature gradient leading to Laplace pressure difference that acts on the contact area A, produces the Laplace force F_L,

$$ F_{\text{L}} = {\iint \limits_{A}} \Delta p_{\text{L}} {\text{d}}A $$

(3.A.3)

where the contact area is approximately equal to volume of the droplet, $V_{\text{droplet}}$ divided by the length L of the droplet,

$$ A \sim \frac{\sin \alpha }{{\left( {R_{B} - R_{A} } \right)}} V_{\text{droplet}} $$

(3.A.4)

where α is the half apex angle of the cone. Combining (3.A.2) to (3.A.5), we get,

$$ F_{\text{L}} \sim \gamma_{\text{LA}} \left( {\frac{1}{{R_{A}^{\prime} }} - \frac{1}{{R_{B}^{\prime} }}} \right)\frac{\sin \alpha }{{R_{B} - R_{A} }}V_{\text{droplet}} $$

(3.A.5)

The Laplace force acting on a conical object drives the droplet from regions of lower radius to larger radius as long as the Laplace force is larger than adhesion force. During this droplet movement, new droplets may be deposited in the path, which coalesce resulting in a large liquid volume and provide the additional movement.

Appendix 3.B: Definition of Various Wetting States

To define various wetting states of surfaces, we start with the definition of a few Greek words of interest for liquids: hydro- = water, oleo- = oil, amphi- = both (water and oil in this context), omni- = all or everything, and liquid- = an unspecified liquid. Within oils, edible oils have a surface tension larger than 30 mN/m and alkanes-based oils have a surface tension 20–30 mN/m. Greek suffixes of interest are: -philic = friendly or attracting, and -phobic = afraid of or repelling.

Figure 3.B.1 shows schematics of various wetting states (Bhushan 2016, 2018). If a liquid wet a surface, it is referred to as a wetting liquid and the value of the static contact angle is $0 \le \theta \le 90^\circ$. A surface that is wetted by a wetting liquid is referred to as hydrophilic if that wetting liquid is water, oleophilic if it is oil, amphiphilic if it can be wetted by water and oil, omniphilic if all liquids wet the surface, and liquiphilic if the liquid is unspecified. If the liquid does not wet the surface, it is referred to as a non-wetting liquid, and the value of the contact angle is 90° < θ ≤ 180°. A surface that repels a liquid is referred to as hydrophobic if it repels water, oleophobic for oil, amphiphobic if it repels both water and oil, omniphobic if it repels all liquids, and liquiphobic if the liquid is unspecified. Surfaces with a contact angle of less than 10° are called superliquiphilic, while surfaces with a contact angle between 150° and 180° are called superliquiphobic. The words superliquiphilic and superliquiphobic were coined by Bhushan (2016).

Fig. 3.B.1

Schematics of liquid droplets in contact with superliquiphobic, liquiphobic, liquiphilic, and superliquiphilic solid surfaces (Bhushan 2016)