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Quora Answer 1: https://www.quora.com/What-is-the-relationship-between-viscosity-and-density-Explain/answer/Rainald-Koch

Viscosity is related to energy dissipation (conversion of mechanical energy into thermal energy). How that? Multiplying the (dynamic) viscosity (unit Pa s) with the shear rate (unit 1/s) yields the shear stress (shear force per area = shear energy per volume, unit Pa). Since we are dealing with plastic instead of elastic deformation, the shear energy is ‘decaying’ by relaxation at the molecular level. The shear energy is replenished by continuing shear. Multiplying again with the shear rate yields the power per volume (unit Pa/s).

What is the mechanism of disspation? Let’s first talk about condensed matter (as opposed to gases). The relaxation takes place by conformational changes into less strained configurations. The change isn’t smooth but more or less uphill and downhill on the energy ‘landscape’ (potential energy over configuration space). Downhill movements are fast and this is exciting vibrations. More or less corrugation of the energy landscape leads to higher/lower viscosity.

For different substances, there is no correlation with density. Compare, for example, two almost-n-alkanes C30 and C60 (with the same small fraction of short side chains to reduce the melting point). At, say, 100 °C, the density is almost equal while the viscosity is much larger for the longer chains.

For gases, the shear stress develops by transport of momentum between adjacent layers. The Kinematic Theory of Gases predicts that the dynamic viscosity does not depend on density (at constant temperature). The argument is as follows: Particles from a higher layer and particles from a lower layer collide in a middle layer. The spacing between the layers is about the mean free path, so that the colliding particles do stem from the two outer layers. Before the collision, the relative speed of the two particles has a systematic component equal to the velocity difference between the outer layers. That component is directed. After the collision, the relative speed is the same, but the direction is (almost) random. The surplus of kinetic energy has been thermalized. Now, when the density is lowered two times, the rate of collisions per particle decreases by a factor of two, and per unit volume by a factor of four. But the mean free path between collisions increases by a factor of two, as is the velocity difference between the outer layers. The surplus in kinetic energy (proportional to the square of the velocity difference) increases by a factor of four, which cancels the decrease in collision rate. So the dissipation rate does not depend on density.

Now think of carbon dioxide above the critical temperature. You can control the density via the pressure from gas-like to liquid-like without a phase transition. At high enough pressure, energy barriers emerge hindering the movements. This is the point where viscosity becomes strongly dependent on density.

It should be mentioned that a given corrugation of the energy landscape can be made much shallower than the mean thermal energy by raising the temperature. Then the rate of lokal conformation changes is much higher than the shear rate, and the shear stress becomes low again. That is the reason for the liquid outer core of the earth has a rather low viscosity (close to that of water), while the density is 10 to 12 g/cm³, roughly 50 % higher than the same mixture at normal pressure (and manageable temperature).

Quora Answer 2: https://www.quora.com/Does-viscosity-depend-on-density/answer/Brian-Higgins-20?no_redirect=1

To address the posed question, it is helpful to first examine what we mean by viscosity based on intermolecular forces.

Three types of intermolecular forces exist between neutral molecules which are known as Van der Waals forces. They are:
Dipole-dipole ( between polar molecules)   
Hydrogen bonding(between molecules with H bound to small electronegative atoms such a O, N and F)   
London dispersion forces( between any two molecules)
The viscosity of a liquid is a measure of its resistance to flow. At a given temperature the flow resistance is determined by intermolecular forces between fluid molecules, as well as by the shape of those molecules. Thus it is not surprising that a fluid comprised of polymeric molecules is likely to be be more viscous than a fluid consisting of low molecular weight molecules. Liquids whose molecules are polar or can form hydrogen bonds are usually more viscous than similar non-polar fluids. Honey which consists of mostly glucose and fructose is a good example of a liquid which owes its viscosity to hydrogen bonding. As one might expect, if the fluid temperature increases then fluid molecules acquire more energy, and thus the average spacing between fluid molecules increases thereby reducing the intermolecular forces and hence the viscosity. Thus as a rule viscosity decreases with increasing temperature.

Now what about fluid density. Keep in mind at the molecular level the density is the mass per unit volume. Thus anything which increases the amount of mass in a particular volume will increase the density Anything that decreases the amount of mass in a particular volume will decrease the density. Intermolecular forces are the forces of attraction that hold bonded atoms together.

Thus although fluid density and fluid viscosity are determined by intermolecular forces, the physical description of each is quite different. Viscosity describes the resistance to flow while density describes the degree of packing of molecules. Although both depend on intermolecular forces they are independent properties of a fluid/liquid.

So in summary, there is no direct dependence of viscosity on density. For a liquid both physical properties decrease with increasing temperature.

Finally , there is a physical parameter called the kinematic viscosity which is the ratio of viscosity to density. Thus the kinematic viscosity does depend on density.

Quora Answer 3: https://www.quora.com/What-is-the-relationship-between-viscosity-and-density-Explain/answer/Barkha-Jha-22

The relationship between viscosity and density of petrol follows a general trend observed in most liquids, including petroleum-based products like petrol.

Inverse Relationship: In the case of petrol, there is an inverse relationship between viscosity and density. This means that as the density of petrol increases, its viscosity tends to decrease, and vice versa.

Higher Density, Lower Viscosity: Petrol with higher density typically has lower viscosity, meaning it flows more easily. This is because higher density in petrol indicates a higher concentration of hydrocarbon molecules, which results in more frequent molecular interactions. These interactions reduce the internal friction of the petrol and promote easier flow.

Lower Density, Higher Viscosity: Conversely, petrol with lower density generally has higher viscosity, meaning it flows more slowly. Lower density in petrol indicates a lower concentration of hydrocarbon molecules, leading to fewer molecular interactions and greater internal friction. This hinders the flow of petrol, making it less fluid.

However, it's essential to note that the viscosity of petrol can also be influenced by other factors, such as temperature and pressure. Higher temperatures typically reduce the viscosity of petrol, making it flow more easily, while lower temperatures can increase its viscosity, making it more resistant to flow. Similarly, pressure changes can have some impact on the viscosity of petrol, but this effect is generally smaller than the influence of temperature.

Quora Answer 4: https://www.quora.com/How-does-the-density-and-viscosity-of-a-fluid-alter-its-damping-effect/answer/Kim-Aaron

I have been thinking about your question for days. But I had not opened it up and read your comments and discussion with the other answerer until now. That is because of the way Quora handles notifications. As soon as I open a question, it disappears from my notifications area, so I sometimes leave the question unopened so it will stay there and keep reminding me to answer it. I do realize that the question will stay in my list of questions, but that is less effective as a notification method because I have to go open up the list of questions, and sometimes it is buried in a long list. So sorry for the delay.

I see that your interest was originally sparked by resonance of wine glasses with liquid in them. You also made mention of an equation that related reduction in resonant frequency to damping parameter. The equation you found indicated that the frequency goes down when the damping parameter is higher. I know the equation you mean and I’m concerned that you may have misunderstood it and that has led you to confusing conclusions.

This is the equation (or something similar to that) that I suspect you found:

In this, ω0
(typically spoken as “omega naught”) is the undamped resonant frequency (in radians per second). This can readily be converted to raw frequency using f0=ω02π. The damping parameter ζ (“zeta”) is related to dissipation of the energy of oscillation. The other omega, ω1

, is the new frequency when damping is turned on.

If I have understood what has happened, you have seen this equation and said, greater damping reduces the frequency. And that is correct, to a point. That ζ

is not directly equal to viscosity, by the way. It’s more of a system description of all the effects that contribute to damping of the oscillator. As I understand it, you have replaced wine by oil (a less dense but more viscous liquid) and seen a change in the resonant frequency of the wine glass. You’ve tried to understand how this equation works in that situation (IF I’ve correctly understood your comments).

You have some intuition that damping can be affected by density and by viscosity. But you are likely unsure about when one is important and when the other is important. In your example of a pendulum swinging through air, it’s the density that’s important. For that case, the viscosity of the air is not very important. Now suppose you did something silly with the pendulum. You change the air to a lighter gas, say helium. But you also made the pendulum longer. You would see a reduction in the frequency (because it’s longer) but you might incorrectly look at that equation and conclude that the frequency got lower because there was more damping. That would be an error. There would actually be less damping (because the helium is less dense than air). The main reason the frequency dropped is because of the increase in length. I’ve purposely made this example obvious. I hope it’s obvious. But I have a suspicion that you may have done something analogous with the wine glass. When you replaced the wine with oil, did you fill it up to the same level? That would be a very natural thing to do. The problem is that doing that is the same as shortening the pendulum. The oil is less dense, so that will make the frequency of the wine glass go up. You know that oil has more viscosity than wine, yet the frequency went up. You are confused because that equation made you expect the frequency to go down. Of course, I’m guessing a lot about what you might have done. But the point is, the density of the liquid is a bit like the mass on a spring. You make the mass lighter and it oscillates faster. The oil is the mass. It’s lighter than wine. So the frequency goes up. Not because of anything to do with damping. It’s just because the mass is smaller.

OK, I’ve rambled a bit based on speculation about your potential confusion. I can believe I’ve made you even more confused. If so, sorry. That’s not what I hoped to do. Please let me know what experiments you actually performed and what results you got. I’ll see if I can make it more clear what’s going on.

Quora Answer 5: https://www.quora.com/What-is-the-relationship-between-viscosity-and-density-Explain/answer/Jeff-H-Peterson

Short answer: they're unrelated. Look at the molecular weight for density and the intermolecular forces for viscosity.

The first question you should ask is what gives rise to density and what gives rise to viscosity.

Since density is just mass per unit volume, you can increase density in one of two ways: increase the atomic mass of the atoms that make up the liquid or somehow pack the liquid molecules closer together. There are many liquids with high atomic weights and mercury is probably the most obvious. Any other molten metal will also be quite dense.

In general though, liquids can only pack so tightly because they're all basically randomly packed. A liquid can be thought of as a random packing of spheres where the radius of each sphere is the atomic radius of an atom or the approximate length of a molecule. Some oddly shaped molecules won't pack that well while though so they'll have slightly lower densities. So liquid density is really just a function of atomic weight.

Now what leads to viscosity? Viscosity is the liquid's resistance to movement under a shear force. In other words, the speed at which a liquid flows under an applied force is going to be equal to the force divided by the viscosity. You can think of the flow as layers of liquid slipping past each other and so you can think of viscosity (dynamic viscosity specifically) as the resistance to this slippage. So viscosity is then related to how much each molecule is attached to its neighbors.

So viscosity is going to be high for compounds with strong bonding like water (hydrogen bonding) or ionic liquids. The classic example of a viscous liquid is honey and that's a complex mixture of mostly sugars but with enough water that technically the sugars are dissolved but to the point where they weigh more than the water itself. The large sugar molecules have lots of places for hydrogen bonding to occur and so they help make the water extremely viscous.

Edit -

I should mention that I've been specifically talking about dynamic viscosity and not kinematic viscosity. Kinematic viscosity is equal to the dynamic viscosity divided by the density. Why? Because kinematic viscosity describes how fast momentum diffuses in a liquid. In other words, if you put fluid between two plates and begin to move the top plate, the kinematic viscosity tells you how long it will take until the fluid in the center starts moving. This will depend on how strongly the fluid layers interact, the dynamic viscosity, and how quickly the lower layers start to move when they feel a force, the inertia or density.

To Read - on 'Are Viscosity and Density Related'