Efficient Handwashing

Like me, maybe you’ve heard that running water over your hands isn’t effective handwashing technique and promptly disregarded it.

We all know on a basic level that physically rubbing your hands together with soap is more effective, but just how much does this make a difference and can we quantify this?

Too begin, we are going to have to look at Reynolds numbers.

What are Reynolds numbers?

Reynolds numbers are taken from (surprise surprise) Osborne Reynolds (1842-1912).

In his 1883 paper, he examined turbulent flow in pipes. His showed that turbulence would occur in a pipe when the parameter defined by $\frac{V \rho x}{\mu}$ would exceed some critical value, where $x$ was the pipe diameter, $\rho$ was the fluid density, $V$ was the velocity and $\mu$ was the viscosity. This parameter would soon become known as the Reynolds number.

$Re = \frac{V\rho x}{\mu}$

$\begin{aligned}V & \textnormal{ \quad Velocity of fluid} \\\rho & \textnormal{ \quad Density of fluid} \\\mu & \textnormal{ \quad Viscosity of fluid} \\x & \textnormal{ \quad Some arbitary length} \end{aligned}$

Many phenomena are defined entirely by the Reynolds number. ¹ For example, in Reynold’s original experiment a value of more than 2300 for $Re$ caused turbulence in the pipe regardless of the indiviual values of $V$, $\rho$, $\mu$ and $x$.

To summarise, Reynolds numbers can be used as a tool to predict the conditions in which a given phenomenon will occur.

Back to washing hands

Using what we now know about Reynolds Numbers, lets generalise our problem into a two step process.

1. Find the critical Reynolds number at which a fluid carries away particles on a surface.

2. Apply this Reynolds number to find the conditions required for water to carry away bacteria or viruses

First note how broadly our phenomena is defined. Pebbles in a river; leaves and a leaf blower; sand on a dune – there are a lot of instances where this loosely defined event occurs.

Now this article is not a dissertation into the mechanics of handwashing. We could consider different examples for accurate values of this critical Reynolds number, but I find it amusing to apply a more tactile case.

Consider a dusty car:

Lets compare the speeds a car can drive at without shedding dust to the flow rate of water required to wash hands.

Now, both phenomena can be assumed to occur through the same mechanism that requires the same Reynolds number.

Wikipedia claims that the dynamic viscosity of air is fifty times smaller than the viscosity of water at the same temperature; we have:

$50\mu_a = \mu_w$

The density of water is about $1000\text{kgm}^{-3}$, and air has a density of around $1.25\text{kgm}^{-3}$, which cleanly divide so that:

$800 \rho_a = \rho_w$

With a little thought we can determine that $x$ is dependent on the diameter of the dust grains. ² Dust particles vary in size from $1$ to $100\mu\text{m}$, so lets pick $50 \mu\text{m}$. Likewise, current estimates put the diameter of COVID-19 to be around 50-200 nanometres wide, ³ lets pick $125 \text{nm}$ as a reasonable midway.

From this we can find the ratio of diameters between the dust $(x_a)$ and the virus $(x_w)$.

$x_a = 400x_w$

Deductions for $V_{car}$ are more arbitrary. Let’s pick $40 \text{mph}$ (about $20\text{ms}^{-2}$) as a reasonable speed for dust to blow off cars.

Putting this all together, we have:

$\begin{aligned} \frac{V_{car} \rho_a x_a}{\mu_a} &= \frac{V\rho_w x_w}{\mu_w} \\[12px] V_{car}\cdot\frac{\mu_w}{\mu_a}\cdot\frac{\rho_a}{\rho_w}\cdot\frac{x_a}{x_w} &= V \\[12px] 20 \cdot 50 \cdot \frac{1}{800} \cdot 400&= V \\[10px] V &= 100 \text{ms}^{-1} \\ \end{aligned}$

$100 \text{ms}^{-1}$ is equal to $223 \text{mph}$, clearly far greater than you can spray water at your hands and hence we have our contradiction:

The minimum speed required to remove viruses with water is greater than the speed of water used to wash hands, meaning that running water on your hands is virtually useless.

Why does handwashing work then?

There is one key difference: good handwashing technique involves rubbing your hands. In our extended analogy, rubbing your hands creates the microscopic equivalent of wiping dust from a surface. Running water over your hands achieves nothing. Rubbing your hands is what is required for good handwashing technique.

Of course, this ignores the effect of soap, which is pretty lethal to viruses. Supramolecular chemistry isn’t quite my speciality, so to conclude I’ll leave you with this viral twitter thread:

1/25 Part 1 - Why does soap work so well on the SARS-CoV-2, the coronavirus and indeed most viruses? Because it is a self-assembled nanoparticle in which the weakest link is the lipid (fatty) bilayer. A two part thread about soap, viruses and supramolecular chemistry #COVID19 pic.twitter.com/OCwqPjO5Ht

— Palli Thordarson (@PalliThordarson) March 8, 2020