Percent Solution, Viscosity, and Density
Date: November 2008
If I make a 10% solution of sucrose and a 40% solution of
sucrose, the density of the sucrose in solution increases. Does the
viscosity stay the same? It seems like the dense sucrose solution is
also more viscous. Yet density and viscosity are not related?
Your assumption that "density" and "viscosity" are unrelated is not correct in
general. Both depend upon the concentration of the solution components,
although the relation may not be simple. Keep in mind that while "density"
is a static property of the solution, "viscosity" is a dynamic property.
The viscosity of a solution may increase / decrease / remain constant,
depending upon the solution components and the shear rate as well as other
variables such as temperature. But the major error in your reasoning is the
assumption that density and viscosity are not related.
True, more solute is often both more viscous and more dense.
But let's see if I can explain a distinction.
One useable concept is that each solute has its own characteristic
"specific viscosity" in water, that is,
how much the water's viscosity increases per mole/liter of dissolved solute.
More solute (with high specific viscosity) usually makes the water more viscous,
It is just that density never was a good predictor for specific viscosity.
Knowing the density of a solute substance does not help you guess its specific viscosity.
Some dense solutes have little specific viscosity (i.e., salt, NaCl).
And some very viscous solutes could possibly be less dense than water.
Poly-vinyl-alcohol (sometimes abrev. "PVA")
has long stringy water-soluble molecules that make it notable
for making viscous water-solutions with modest concentrations,
i.e., less than 10wt%.
But its density is very near that of water. Maybe a little lighter, I am not sure.
So the solution's density will not change much
as the viscosity changes from very low to very high.
If one weighs very precisely, the ratio of (density_change)/(viscosity_change)
will probably be a steady number not quite equal to zero.
But that ratio could be positive or negative.
As you add more PVA, the solution might get 1% lighter as it gets 10x thicker.
Its concentration that matters.
Density and viscosity both usually follow concentration,
but each has a different proportionality constant for every solute-substance.
For a given substance,
the density-constant and viscosity-constant have almost nothing to do with each
other either could be big or little, independently.
Specific volume in water (d_vol_solution)/(d_moles_solute_added)
is yet another quirky thing to guess about.
Since a given substance has a fixed (mass/mole),
one could define a specific density
1/ [ (d_vol_solution)/(d_mass_solute_added) ] .
Specific density doesn't follow the pure dry crystallized density of the pure
substance very well.
In water there is some empty space between molecules,
and some substances fit themselves into it better than others.
If we go to the most basic ideas concerning density and viscosity, we might say
that the factors affecting density is how close together the molecules get
(which leads us to an analysis of intermolecular forces), whereas the factors
affecting viscosity is how easily molecules slip past each other or flow.
At first glance, it is correct to imagine that if molecules are close together
(dense) then they must not flow well past each other. And this would be a good
However, there are many more contributing factors to how easily molecules flow
past each other than just intermolecular attractive forces. For example, in long
molecules that entangle with each other (like strands of twine) even though the
molecules are held loosely (not dense), they can get in each other's way,
entangle, wrap around each other - so that the effect is that they do not flow
Plastics usually have a density of around 0.9g/mL but are very viscous.
Greg (Roberto Gregorius)
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Update: June 2012