# Why does dust stick to rotating fan propeller?

Why does dust stick to rotating fan propeller?

Intuitively, most people (including I) think of the dust will not stick to rotating fan propellers.

EDIT 1:

Thank you for the great explanations. I am still waiting for the "better" one if any.

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You are looking for a "better" answer, but you have not commented on the several highly-rated answers already available. Maybe if you comment on those answers describing which parts are unclear, you'll get a response you find more useful. – Mark Eichenlaub Dec 7 '10 at 6:11
Possible related posting here math.stackexchange.com/q/13884/3301 – ja72 Dec 11 '10 at 15:34
@jalexiou, the link was made about 18 hours ago. – xport Dec 12 '10 at 1:48
We can actually learn a lot from this thread. The basic question you are answering is how to promote a topic on a platform like this, how to get answers and so, how to reach the community. One should not underestimate such things. – Robert Filter Dec 14 '10 at 9:01

## 11 Answers

Dust sticking to things is a complex process but can be broken down into several stages and analyzed. First though lets define our dust.

## Dust Size

The aerodynamics of dust are most easily approximated by pretending all of the particles are spheres with a density equal to water ($1000 \frac{kg}{m^3}$). Each particle is assigned an aerodynamic diameter that is the diameter of one of these hypothetical spheres that would fall at the same rate as the actual particle (gravity and air resistance balance at the same settling velocity for the sphere and real particle.) Whenever an unqualified particle size is mentioned, this post is referring to this aerodynamic diameter. Most (by mass) household dust particles have aerodynamic diameters between $20 - 400 \, \mu m$. This diameter range will determine the magnitudes of the forces that act on the dust.

Now that we've defined our dust the following steps are necessary for dust accumulation.

## Dust arrival

In order for dust to accumulate, it has to come from somewhere. I won't go into how dust gets into the air, but lets presume that well circulated air has a constant concentration of dust that is renewed through generation, mixing, and diffusion. Normally, dust that accumulates on surfaces approaches those surfaces by settling; gravity pulls the particles downward so that their average velocity is downward (this is why horizontal surfaces accumulate dust while vertical ones generally accumulate much less). In the horizontal surface case, the amount of dust approaching the surface would follow $\dot m= m_p\;C\;V_s$ Where $m_p$ is the mass of a particle, $C$ is the concentration (particles per volume), and $V_s$ is the settling velocity ($0.25 \frac{m}s$ for $100 \mu m$ particles.

For a ceiling fan, the rate at which dust approaches the surfaces is not dominated by gravity but rather by the speed that the blade moves through the air. The maximum velocity for blades less than $\frac18''$ is limited by the UL to $2400\frac{ft}{min}$ or about $12\frac{m}s$. If dust arrival were the only thing important for dust accumulation then fans would accumulate dust about 50 times faster than a horizontal surface.

## Dust Impaction

For particles to hit the blade they will have to move towards the blade, but the air must flow around the blade. This necessitates that the particles move relative to the air. In the case of dust settling this is accomplished through gravity, and diffusion. The dust that accumulates on walls is due to diffusion, while gravity pulls the dust onto horizontal surfaces. In the case of fan blades, there's another way that the particles can move relative to the air: inertia.

Take the example of a sand blaster. Both the sand and the air jet from the nozzle towards a surface. The sand continues at nearly this velocity until it hits the surface. The air however spreads out and slows down to the point were it has zero velocity at the wall (no slip condition). In this instance the path of the sand is hardly effected at all by the air flow because the sand particles have a lot of inertia compared to the air resistance and time scale.

Now think about what would happen if a fog machine was pointed at a surface. The fog would just spread out with the air and very little fog would actually impact the surface. Sure it would move along the surface, but it would only bump into the surface through diffusion.

If we reduced the size of the sand particles in a sand blaster, they would behave more and more like the fog as their inertia ($\propto d^3$) was reduced relative to their drag ($\propto d^2$ to $\propto d$ as the particles get even smaller)

The aerodynamics of this process, known as inertial impaction, is well understood for jets perpendicular to a surface, but can be applied to a fan blade moving through the air. As the fan blade moves, the air at the front of the blade must move to either side, creating a very pronounced acceleration in the air. Once the air is on one side or the other it does not have to accelerate much. This is similar to how the air in a jet only has to accelerate while turning from traveling towards the surface to traveling along the surface. I would estimate that the radius of curvature for a fan blade width of $w_f$ would be comparable to the radius of curvature for a jet of width $w_j$ if $w_f\approx 3w_j$

The equation for the cutoff size of particles impacting vs. going with the flow is given as $$d_{50} = \sqrt{\frac{9\,\eta\,w_j\,Stk_{50}}{\rho_p\,V}}$$

Where $\eta$ is the viscosity of the air, $Stk_{50}$ is an experimentally determined Stokes number ( 0.59 for rectangular jets), $\rho_p$ is the density of the particles, and $V$ is the average jet velocity.

Plugging in for the previous velocity of $12 \frac{m}s$, the density of water as particle density, and $\frac18''$ as the width of the fan blade yields $d_{50}\approx20\mu m$. This shows that particles above $20\mu m$ would impact the front of the fan blade. As this covers the majority of household dust, most household dust would impact the leading edge of this fan blade.

For the large surfaces of the fan blade, the air and dust with it moves along the surface so the only reason dust would impact the surface would be through diffusion, or if there is a small defect that the air must move around. We could model any of these small defects in a similar manner. In this case the velocity would be the velocity within the boundary layer at the height of the defect. The velocity in a boundary layer very close to the surface can be modeled as

$$V(x,y)=0.002V_0\sqrt{\frac{\rho\,V_0}{\eta\,x}}\,y$$

Were $x$ is distance along the flow, and $y$ is the height off the surface.

If we plug this into our cutoff diameter equation the height of the defects end up canceling out giving

$$d_{50} = 40\sqrt{\frac{\eta\,Stk_{50}}{\rho_p\,V_0\sqrt{\frac{\rho\,V_0}{\eta\,x}}}}$$

Plugging in for air and our velocity yields

$$d_{50} = (5\times10^{-13}m^3\,x)^{\frac14}$$

Lets assume that we can only catch particles that are as large as our defects. A typical value for surface roughness of sanded wood across the grain (as is typical of ceiling fans) is about $20\mu m$. If we say a defect is 5 times that size we could only catch particles that are $100\mu u$ or smaller. However, if we plug in $0.4mm$ for $x$ we get a cutoff diameter bigger than $100\mu m$ indicating that no particles we could catch would actually impact our defect. This means that only very large defects or defects very close to the leading edge of the fan will be impacted and have a chance to stick.

## Dust Adhesion

Now the question is "will it stick?" In order for particles to stick they must be held to the surface with the Van Der Waals force, static charge, or surface tension of ambient liquids. These forces scales with $d$ while the removal forces centripetal acceleration and drag scale with $d^3$ and $d^2$ respectively. This means that as the particles get smaller they will be more and more likely to stick, and as they get bigger they will be less likely to stick. So we can find the size particle that would be equally likely to stick and if our particles are smaller than that they will stick.

The initial adhesion force is most easily estimated with an experimentally derived formula.

$$F_{adh}= 0.063 \frac{kg}{s^2} d (1+0.009\,RH)$$ Where $RH$ is the relative humidity in percent. This model was created for glass spheres. The adhesion force for our dust would likely increase with time as the dust deformed to come closer to the surface.

The centripetal force (which appears as a real force rotating reference frames) would just be $$F_c=\rho_p\,d^3\,\frac{V^2}{r}$$ So for a fan with a radius of $70 cm$ the adhesion force would balance with the centripetal force at a diameter of $550\mu m$. This is larger than all of our particles so our particles would not be immediately thrown off, so they would have to to deform and further adhere to the surface.

The drag force can be modeled as $$F_d=\frac14\,\rho\,V^2\,\pi\,d^2$$ Where an overestimated value of 2 was chosen as a drag coefficient. For this force, the particles would need to be about $560\mu m$ to be blown off. This of course was using the full flow velocity of $12\frac{m}s$ but the boundary layer around the fan would ensure that the dust would never actually see velocities that high.

In reality there are other phenomena that play a role in particle removal, for example when a new particle impacts a particle that's already attached, there is a chance that both particles will be removed. It's difficult to model these interactions as they depend on many variables including particle stiffness and geometry. There are of course statistical models based on experiments to estimate these factors, but I believe the information already provided should be sufficient to explain why dust sticks to fan blades and why there is much more dust on the leading edge than anywhere else.

Most of the information in this post that was not elementary aerodynamics, my own analysis, or otherwise cited was from "Aerosol Technology" by William C. Hinds

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True, the boundary layer makes it so that the dust can't get blown by the fan itself. But it could not answer the question of why the dust is attracted to the blade in the first place. I think it's linked to the cavitation phenomenon. But instead causing boiling bubbles that can be ruptured by a rotating fan in liquid, it just attracts the dust particles. Maybe because air density is 1/1000's the density of water.

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since it seems like participating in bounty questions is something like our group sport, I could not resist to also think about the question.

I think the answers given according to the vanishing velocity on the propeller are unlikely to explain the phenomenon. Dust particles, even though they are very thin, have a three dimensional shape. So even if there is no velocity at zero distance (which is the mentioned boundary condition), there will be a relative movement along the dust particle (Remember that turbulence takes place on every scale for the Navier-Stokes equations) which to my opinion acts as a pulling force on the particle.

To my mind, the problem relates to an electrostatic one. The propeller is very likely to have some charge due to his movement through air and the ongoing friction. The (might even be very small) charge induces a dipole moment on the dust particles nearby which I guess might be treated as dielectric balls.

This dipole moment will then attract the dust particles which as a result touch the surface. If now everything would be metal, there would be immediate (full) charge balance and the attractive force would vanish. But under the assumption of a dielectric medium, some dipole moment stays, so does the attractive force and the dust on the propeller.

Greetings

Edit: I just saw that the electrostatic argument already came up. Nevertheless, I hope my explanations are still usefull.

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Dust sticks almost anywhere. Almost? Yes almost, because yet we don't have no super perfect nano-surfaces. The point is that every macroscopic surface is raspy and not perfectly smooth. Therefore very small dust can easily stick. This very small dust makes the surface even more raspy, making it easy for the heavier dust to arrive.

In the near future we might have fan propellors that have no easy visible dust sticking.

And of course it is the electro-magnetic force that lets the dust stick. Make yourself clear how very, very small pieces of dust look like and you understand how it can easily stick on a non-smooth surface by means of the Coulomb-Force. In the end: Most things you see are electrically charged, at least if you "zoom in" a lot. Looking from far away the charges are effectively neutralized. Of course a super perfect nano surface even looks very good is you "zoom in".

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What about this hypothesis:

Dust sticks everywhere, but since the propeller cuts through a lot of air, it meets more dust particles. Thus, more dust sticks to the propeller than elsewhere.

Evidence

I (Mark) took photos my the fan my room to support Damien's hypothesis. The first photo is of the leading edge of the fan blade, which impacts a lot of air, and the second photo is of the trailing edge of the same fan blade. I've never cleaned this fan. The leading edge is covered in a thick, 3-5mm layer of dust, while the trailing edge is almost clean.

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That's pretty must the simplest explanation to the question. Though @Vagelford's explanation regarding the boundary layer is also relevant since we're dealing with fluid motion. – user346 Nov 29 '10 at 4:15
@Mark: I could be an arse and answer that "you don't convince me". But I think you are actually correct :-) Dust sticks (as everyone that has a house to clean knows!), and the forefront tip of the blade meets more dust. +1 – Sklivvz Dec 9 '10 at 23:19
Well, my answer has to do with the why the dust sticks on the fan and doesn't go away when it is used. I didn't consider the why the fan has more dust than let's say a table. I think that it is obvious that the fans blades come in contact with more dust, since there is more air that passes from them. – Vagelford Dec 11 '10 at 9:25
"I've never cleaned this fan". Hmmm, don't invite me over for tea :) – Gordon Jan 27 '11 at 21:42

The short answer is that there's no wind near the blade. This is called no-slip condition in hydrodynamics of viscous fluids.

[Concession] It is actually more than that. There's minor van der waals sticking which contributes to this otherwise purely hydrodynamic phenomenon.

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Here are some of my observations:

• If a fan is not used, the sticking of dust is at the same rate as other objects.

• If a fan is used, even the rotation is slow, the dust can still stick much faster than un-used fan.

• The dust not only stick at the propeller, but also the cover bar behind and in front of it. It can give a thick layer of dust at both place.

• There is (plastic ?) coating around the fan, so not metal is direct expose there.

• Dust accumulation is a bit faster near the kitchen. The fan surface also has many oil.

Hence, I think that the most important reason of high sticking rate should be the high throughput of the air. Dust will not move toward the fan itself.

For the reason of sticking, I think the it should be due to the electrostatic charge on the dust. It is similar to the dust removal in power plant. Also, dust can adhere at most common surface such as table, wall and plastic, so whether the fan has charge should not be important factor.

Both electrostatic charge and oil should increase the sticking rate. After the initial sticking, the rough surface should allow easier sticking for later dust, so I guess the accumulation rate speed up.

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Wind doesn't actually touch the surface. You can see the same effect on a car: even if you move at speeds beyond 70mph, the dust doesn't get blown away.

If you look closely, there is a boundary layer between the matter of the fan and the air around the fan. When you get closer to the fan blades, the air starts to move with the fan (the blade pulls it along), so air very close to the blade doesn't move (much) relative to the blade itself.

Obviously, this is true when you add matter to the blade (like dust). In this case, the friction of the air is less than the adhesion of the dust to the blade, so the dust sticks to the surface.

On my fans, I find a lot of dust and short strands on the edge that cuts the air. Here, the air flow presses the strands to the blade (parts of it on either side of the edge). This way, the fan actively collects dust. Again, the force of the air pressing the strands against the blade (plus the friction between dust and blade) is much stronger than the centrifugal force which might pull them sideways. Since the strands cling to the surface, the blade isn't strong enough to cut them, so they stay where they are.

This relation is true for all fan speeds, so the dust always ever gets more.

A simple countermeasure is a coarse net on the side where the fan sucks the air in. Most dust strands will get caught in the net and you can easily wash them away every few weeks or collect them with a vacuum cleaner.

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The reason is that you have a boundary layer on the surface of the blade of the fan. On the frame of the blade (the blade moves with some velocity, but at the frame of the blade the air moves) the boundary layer starts from the surface of the blade where the fluids velocity is zero and as you move away from the blade, the velocity increases up to the value of the velocity of the blade (you can call that the undisturbed velocity of the flow).

So if you have some fine dust, it actually doesn't feel much wind and it can't be blown away. Static electricity could be an other factor, but you can see that on metallic propellers also.

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Why do you think that static is only an issue on metallic propellers? After all, most of the usual classroom static electricity demos use dielectric materials (glass, amber, plastic, latex) because any charge established on them will not migrate efficiently. – dmckee Nov 27 '10 at 18:49
No, I am saying that static could be an issue in the case of plastic propellers, but you can also see the dust on metallic propellers where you can't have static electricity. – Vagelford Nov 27 '10 at 19:30
@Vagelfold. Ah. Clear now. – dmckee Nov 27 '10 at 20:00
"static" can be a issue on metal as well. If only the dust particle has a sufficient surface resistance. The parts of the particle making contact with the metallic surface will discharge, the parts further away dont. A model for that is a electrophorus. – Georg Jan 26 '11 at 13:57
This doesn't address why the leading edge has so much more dust. – Rick Aug 27 '15 at 19:32

I'm guessing that a very thin layer of oil covers the blade, maybe because of proximity to the oiled bearings, making it a little sticky. The blade would pick up excess dust because it moves through more air than if it were stationary. According to this hypothesis, static electricity is not involved.

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I always wash the propeller using detergent many times when cleaning it. The dust still sticks to the propeller. The dust also sticks to the cell-like protecting cover. – xport Nov 28 '10 at 4:06
Fans can often be found in kitchens, which makes them even more likely to be sticky with oil. Maybe not your fan, but I'm sure this explanation accounts for at least half the dust found on fan blades! – ptomato Dec 7 '10 at 9:21

First taking only speed of the fan into the account. If the fan rotates slowly then the situation is obviously not very much different from if it weren't rotating at all. The centrifugal force on the dust particles is not big enough to throw them away off the fan.

Second, there's static electricity that has to be taken into the account. It's perfectly possible that some residual charge is generated on the fan (this depends very much on what is the fan made off) and as the dust particles are often charged the ones with correct polarity will get attracted to the fan. In this case they would stick even if fan were rotating very fast.

Now, you can test whether the second option is realized in your case by touching the fan to discharge it and it should "kick" you a little. Or if you don't like that you can bring some charged object close to the fan and see whether it is affected.

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## protected by Qmechanic♦Mar 31 '13 at 16:00

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