# Is there a relationship between density and viscosity of a fluid?

I'd like to know if there is a connection between the two physical quantities of density and viscosity.

e.g. How can you explain low density liquids such as mineral oils have a lower density than water but far greater viscosity?
e.g.2 Instead, for honey (18% of water and 82% of sugar...) a density of about 1.4 kg/litre but a greater viscosity?

• As you see there's no simple relationship, as you can see. Aug 20 '16 at 18:10
• I imagined it! Anyhow, I don't need a quantitative answer, I don't need a formula or an equation, it's enough a qualitative answer... for example, I think it's a molecular issue: density and viscosity depend on how much condensed are molecules, hence on the strength of chemical bonds... this is my thought, at least tell me if it is not the wrong way Aug 20 '16 at 18:57
• I don't understand the meaning of " how much condensed are molecules"- it doesn't sound right; but the strength of the bonds is important. Viscosity is kind of a measure of resistance to acceleration. The viscosity of solid steel is crazy high. The viscosity of air is really low, water, alcohol, silica and clay powder, and polymers like oil and gum have have viscosities in between. Temperature (kind of a measure of molecular velocity), density (heavy resists acceleration), and concentrations of mixtures of the fluid(s) and solutes affect the resistance to acceleration (viscosity). Aug 20 '16 at 19:42
• with condensed molecules I mean the intramolecular forces which make molecules more or less attractive or repulsive. In light of this consideration (my thought), I expect substances with high intramolecular forces have to show high density AND high viscosity. Hence, are oils an exception? Aug 21 '16 at 8:30

They are not directly related as such. Density is defined as mass/volume units $\ce{kg/m^3}$. Water has a value 1000, (liquid) iron 7000, (liquid) lithium 516 , ethanol 789 and carbon tetrachloride 1632 all in units of $\ce{kg/m^3}$.

Viscosity is the rate of transfer of momentum exerted on a plane of fluid when a second plane of fluid a parallel distance $x$ away is moved with viscosity $v$. The force exerted is $F=\eta \frac{v}{x}$, where $\eta$ is the viscosity.

The fundamental process that takes place when a liquid changes shape is that one layer of it has to slide past another. If we suppose that the liquid could be divided up into cells, then one cell has to 'hop' past another so that the liquid can move. The more difficult that this is the greater the viscosity. Thus to 'hop' a cell has to have an activation energy, that is it has to accumulate in itself enough energy to overcome resistance from other cells that prevent it from moving. Now defining just what a cell is is somewhat vague, but it is larger than a single molecule. But leaving that aside, the activation energy does reflect the inter-molecular interaction and shapes of individual molecules. Spheres with little inter-molecular interaction, e.g. small van-der-Waals forces, no hydrogen bonds, will have a lower viscosity than an awkward shaped molecule such as glycerol with the ability to form lots of hydrogen bonds.

Viscosity has units $\ce{Pa~s = N~m^{-2}S^{-1} = kg~m^{-1}~s^{-1}}$ but more commonly centipoise where $\ce{1~cP = 10^{-3} Pa~S}$. Some values (in CP at 25 $\ce{^oC}$) are water 1, $\ce{CCl4}$ 0.97, iodoethane 0.56, ethanol 1.07, cyclohexane 0.89, cyclohexanol 57.5, 1-propanol 1.945, ethylene glycol 16, glycerol 934.

• OK, so you agree with me on the importance of intramolecular forces, and this is a first result! Then let's make a further step deep into my issue: are intramolecular forces responsible (maybe, likely not the only) of substances density? Aug 21 '16 at 8:38
• I agree that intermolecular forces do hold liquids together and that they cause viscosity. Colloquially put, density measures how much stuff can you get into a given volume, viscosity about how easily this stuff can move about. Suppose that once molecules are packed together in a liquid intermolecular forces are quadrupled (say). This will have almost no effect on density (because electronic repulsion cuts in rapidly with separation), i.e. liquids are 'incompressible' but the increase in intermolecular force will increase viscosity. Aug 21 '16 at 12:58