Viscosity

Definition

Viscosity is a fluid property that describes a fluids internal resistance to flow or deformation, and is one of the most important fluid properties to consider when designing a mixer. There are two common measures of viscosity, dynamic viscosity (µ) and kinematic viscosity (ν). The relationship between dynamic viscosity and kinematic viscosity is shown below:

$\displaystyle \nu = \frac{\mu}{\rho}$

ν – Kinematic viscosity (cSt)
µ – Dynamic viscosity (cP)
ρ – Density (g/cm³)

Dynamic viscosity is the most relevant to mixing applications as this describes the fluid resistance to flow under shear stress, whereas kinematic viscosity describes the resistance to flow under the pull of gravity.

Newtonian Fluids

In Newtonian fluids the dynamic viscosity is described as the ratio of the shear stress to the velocity gradient in a fluid. The viscosity remains constant through varying shear stress and over time, and the relationship is shown in the equation below:

$\displaystyle \tau = \mu \frac{du}{dy}$

τ – Shear stress
µ – Dynamic viscosity
du/dy – Velocity gradient

The majority of fluids can be modelled as Newtonian fluids and this is the type of fluid that we come across in the majority of mixing applications.

Non-Newtonian Fluids

Other types of fluid can exhibit non-Newtonian behaviour where the viscosity is not a constant value, and changes in response to some other variable.
Some of these are listed below:

Pseudo-plastic or shear-thinning fluids are the most common type of non-Newtonian fluid that we encounter.
In these fluids the viscosity decreases with an increase in the shear stress applied.
Thixotropic fluids behave like pseudo-plastic fluids, except that the viscosity also decreases with time under shear stress.
Dilatant and Preoptic fluids are the equivalent of pseudo-plastic and thixotropic fluids respectively,
except that their viscosity increases with shear rate and time respectively.
Viscoelastic fluids exhibit a combination of viscous and elastic properties when stressed.
This means that they behave partially like an elastic solid and have a tendency to revert back to their original shape after deformation.
Bingham plastics have a minimum shear stress required before any flow of the material will take place.

Some common non-Newtonian fluids are water based paints, polymer solutions, and many food and personal care products such as toothpaste and tomato ketchup.

Measuring Viscosity

Viscosity is measured with an instrument known as a viscometer, or rheometer, and there are multiple different types, the most common of which are explained below:

Falling Sphere Viscometer

The falling sphere type viscometers consist of a small sphere and a stationary glass tube filled with the fluid to be tested. The sphere is allowed to fall through the fluid and the time taken to pass between two points is measured. Using Stokes’ law the dynamic viscosity can then be calculated using the density of the fluid and sphere.

Viscosity Cups

Viscosity cups are a type of viscosity measuring device consisting of a cup with a precisely sized aperture in the base. The cup is filled with the liquid to be measured and the time taken for the liquid to drain from the cup through the aperture is taken. From this time value, the kinematic viscosity can be calculated using conversion formulas or tables provided by the manufacturer.

Viscosity cups are commonly used in the paints and coatings industries.

Rotational Viscometer

A more sophisticated type of rheometer is the rotational spindle type viscometer. These instruments work based on the Searle principle, where the torque required to rotate a spindle in each fluid at a certain speed is proportional to the fluid viscosity.

The speed of the rotating spindle can usually be varied which has the effect of varying the shear stress experienced by the fluid. This allows rotational viscometers to be used to measure the viscosity profile of non-Newtonian fluids which exhibit different viscosities at different levels of shear stress.

Category	Liquid	Specific gravity @ 16°C	Absolute viscosity (cP)	Temperature (°C)	Viscosity Type
Industrial Products	Acetate Glue		1200 - 1400	20	T
Industrial Products	Alcohol, sopropyl		2	Room Temp
Industrial Products	Alkyd resins		500 - 3,000	Room Temp
Industrial Products	Anti - freeze		15	Room Temp
Food Products	Baby Food		1400	93	T
Food Products	Batter		29500	30	T
Food Products	Beer		18	Room Temp
Food Products	Beet Sauce		1950	76	T
Industrial Products	Benzine		5	Room Temp
Food Products	Biscuit Cream Premix		29200	18	T
Pharmaceuticals	Blood		10	Room Temp
Fish & Animal Oils	Bone Oil	0,92	48	54	N
Food Products	Brewers Yeast		368	18	T
Food Products	Broth Mix		430	18	T
Dairy Products	Butter Deodorised		45	50	N
Dairy Products	Butter Fat		20	65	N
Dairy Products	Butter		30,000	Room Temp
Dairy Products	Butter cream, sour		550	Room Temp
Food Products	Carob Bean Sauce		1500	30	T
Vegetable Oils	Castor Oil	0,96	580	27	N
Industrial Products	Caulking compound		5,000,000 - 10,000,000	Room Temp
Industrial Products	Caustic soda 50%		45	Room Temp
Dairy Products	Cheese, soft		30,000	Room Temp
Vegetable Oils	Chinawood Oil	0,94	300	21	N
Food Products	Chocolate		280	49	T
Food Products	Chocolate syrup		2,250	Room Temp
Food Products	Citrus Fruit Pulp	1,27	600	20	T
Industrial Products	Cleaning emulsions		1,500	Room Temp
Dairy Products	Cocoa Butter	0,92	50	60	N
Vegetable Oils	Coconut Oil	0,93	55	24	N
Fish & Animal Oils	Cod Oil	0,93	32	38	N
Food Products	Coffee Liquor 30-40		10 - 100	20	T
Dairy Products	Condensed Milk		40 - 80	40-50	N
Dairy Products	Condensed Milk 75 Solids	1,3	2160	20	T
Vegetable Oils	Corn Oil	0,92	28	57	N
Food Products	Corn syrup		15,000	Room Temp
Dairy Products	Cottage Cheese		30000	18	T
Vegetable Oils	Cotton Seed Oil	0,88	62	24	N
Dairy Products	Cream 30 Fat	1	14	16	N
Dairy Products	Cream 45 Fat	0,99	48	16	N
Dairy Products	Cream 50 Fat	0,98	112	16	N
Dairy Products	Cream 50 Fat		55	32	N
Dairy Products	Cream, cheese		100,000	Room Temp
Dairy Products	Cream, clotted		20,000	Room Temp
Dairy Products	Cream, double		120	Room Temp
Dairy Products	Cream, single		50	Room Temp
Dairy Products	Cream, sour		15,200	Room Temp
Industrial Products	Cresol Crystals		10	18	T
Food Products	Custard	1,6	1500	85-90	T
Pharmaceuticals	Detergents		1470	70	T
Industrial Products	Diesel		14	Room Temp
Glycol Products	Diethylene	1,12	32	21	N
Industrial Products	Dipropyleneglycol		107	Room Temp
Food Products	Edible Oil	0,9	65	20	N
Industrial Products	Epoxy resin		5,000 - 10,000	Room Temp
Glycol Products	Ethylene	1,12	18	21	N
Glycol Products	Ethylene glycol		16	Room Temp
Food Products	Fruit Juice	1,04	55-75	18	N
Fuel & Lubricating Oils	Fuel oil no 4		12	Room Temp
Food Products	Gelatine 37 Solids		1190	43	T
Food Products	Gelatine		1,200	Room Temp
Food Products	Glucose	1,3	4300 - 8600	25-30	T
Industrial Products	Glue, gun grade		5,000 - 50,000	Room Temp
Industrial Products	Glue, pourable		3,000 - 5000	Room Temp
Industrial Products	Glycerine 100	1.26 at 20°C	648	20	N
Pharmaceuticals	Glycerine		1,000 - 2,000	Room Temp
Glycol Products	Glycol		20	Room Temp
Food Products	Gravy Slurry	1	110	80	T
Pharmaceuticals	Hand cream		8,000	Room Temp
Pharmaceuticals	Hand lotion		5,000	Room Temp
Food Products	Honey		1,800 - 3,000	Room Temp
Fuel & Lubricating Oils	Hydraulic oil		30 - 120	Room Temp
Food Products	Icing		10,000	Room Temp
Industrial Products	Ink, printing, liquid		550 - 2,200	Room Temp
Industrial Products	Isopropyl Alcohol	1,11	1,9	85	N
Food Products	Jam Garnish		8440	16	T
Food Products	Jam		8,500	Room Temp
Industrial Products	Kerosene		10	Room Temp
Industrial Products	Lacquer 25 Solids		3000	18	T
Paints & Varnishes	Lacquer, water - based		900	Room Temp
Paints & Varnishes	Lacquers 25% pigments		3,000	Room Temp
Fish & Animal Oils	Lard	0,96	62	38	N
Fish & Animal Oils	Lard Oil	0.91-0.93	40 - 47	38	N
Pharmaceuticals	Latex Emulsion	1	200	24	T
Paints & Varnishes	Latex neoprene		5,000	Room Temp	T
Paints & Varnishes	Latex paint		750	Room Temp	T
Vegetable Oils	Linseed Oil Raw	0.93-0.94	29	38	N
Vegetable Oils	Linseed oil		30- 70	Room Temp
Pharmaceuticals	Liquid soap		85	Room Temp
Fuel & Lubricating Oils	Lubricating oil		60- 200	Room Temp
Fuel & Lubricating Oils	Machine oil, heavy		600	Room Temp
Fuel & Lubricating Oils	Machine oil, light		150	Room Temp
Food Products	Malt Extract	1,4	3000	60	T
Food Products	Malt Extract 80		9500	18	T
Food Products	Maple syrup		150 - 300	Room Temp
Food Products	Mayonnaise		5,000 - 20,000	Room Temp
Industrial Products	Methyl ethyl ketone		4	Room Temp
Dairy Products	Milk	1.02-1.05	2	18	N
Dairy Products	Milk Whey 48 Sugar		800 - 1500	40	T
Dairy Products	Milk condensed		6,000	Room Temp
Dairy Products	Milk evaporated		6,100	Room Temp
Food Products	Mincemeat		100000	30	T
Food Products	Molasses		5,000 - 10,000	Room Temp
Fuel & Lubricating Oils	Motor oil SAE 10		50	Room Temp
Fuel & Lubricating Oils	Motor oil SAE 20		125	Room Temp
Fuel & Lubricating Oils	Motor oil SAE 30		200	Room Temp
Fuel & Lubricating Oils	Motor oil SAE 40		320	Room Temp
Fuel & Lubricating Oils	Motor oil SAE 50		540	Room Temp
Fuel & Lubricating Oils	Motor oil SAE 60		1,000	Room Temp
Fuel & Lubricating Oils	Motor oil SAE 70		1,600	Room Temp
Food Products	Mousse Mix		1200	5	T
Industrial Products	NaOH 20	1,22	1	18	N
Industrial Products	NaOH 30	1,33	1	18	N
Industrial Products	NaOH 40	1,43	20	18	N
Vegetable Oils	Oleic acid		40	Room Temp
Vegetable Oils	Olive Oil	0,91	40	38	N
Food Products	Orange Juice Concentrate	30 Brix	630	20	N
Paints & Varnishes	Paint, water based		2,400	Room Temp
Vegetable Oils	Palm Oil	0,92	43	38	N
Food Products	Pancake batter		2,200	Room Temp
Pharmaceuticals	Paraffin Emulsion	1,2	3000	18	T
Industrial Products	Paraffin		10	Room Temp
Vegetable Oils	Peanut Oil	0,92	38	38	N
Food Products	Peanut butter		150,000 - 250,000	Room Temp
Vegetable Oils	Peanut oil		100	Room Temp
Food Products	Pectin		300	38	N
Industrial Products	Petrol, gasoline		8	Room Temp
Pharmaceuticals	Petroleum jelly		64,000	Room Temp
Industrial Products	Plastisol	2,5	28000	18	T
Industrial Products	Polyester	1.1 at 30	3000	30	T
Industrial Products	Polyester resin		3,000	Room Temp
Industrial Products	Polyglycerine caprinate		6,000 - 7,000	Room Temp
Industrial Products	Polyisobutylene	1.09 at 85°	12500	85	T
Industrial Products	Polymer solution		20,000	Room Temp	T
Industrial Products	Polyol, non - pigmented		500 - 5,000	Room Temp
Industrial Products	Polypropylene		240000	50	T
Industrial Products	Potassium hydroxide		67	Room Temp
Industrial Products	Printers Ink		550 -2200	38	T
Dairy Products	Process Cheese		30000	18	T
Glycol Products	Propylene	1,04	52	21	N
Industrial Products	Putty		100,000,000	Room Temp
Industrial Products	PVA resin		65,000	Room Temp
Industrial Products	Resin Solution		880	24	T
Industrial Products	Resin pourable		880 - 975	Room Temp
Industrial Products	Resin solution		7,100	Room Temp
Food Products	Rice Pudding		10000	100	T
Food Products	Salad Cream		1300 -2600	18	T
Food Products	Sauce - Apple	1,1	500	80	T
Vegetable Oils	Sesame oil		94	Room Temp
Pharmaceuticals	Shampoo		3,000 - 5,000	Room Temp
Pharmaceuticals	Soap Arylan	1.0 at 40°C	630	60	T
Pharmaceuticals	Soap Solution	1.03 at 60°C	82	60	T
Food Products	Sorbitol	1,29	200	20	N
Vegetable Oils	Soya Bean Oil	0,93	60	24	N
Food Products	Soya Bean Slurry		5000 -10,000	50-90	T
Food Products	Spaghetti sauce		1,000	Room Temp
Fish & Animal Oils	Sperm Oil	0,88	24	38	N
Food Products	Starch solution 25%		300	Room Temp
Food Products	Sugar syrup, sucrose		1,210	Room Temp
Industrial Products	Sulphonic Acid	1,04	125	30	T
Industrial Products	Titanium dioxide		5,000	Room Temp
Industrial Products	Toluol		6	Room Temp
Food Products	Tomato Ketchup		1000	30	T
Food Products	Tomato Paste 30		195	18	T
Food Products	Tomato juice		180	Room Temp
Food Products	Tomato ketchup		1,000	Room Temp
Food Products	Tomato puree		50,000	Room Temp
Food Products	Tomato sauce		2,600	Room Temp
Pharmaceuticals	Toothpaste		70,000 - 100,000	18	T
Industrial Products	Triacetate Dope		48,000 / 60,000	40	T
Glycol Products	Triethylene	1,12	40	21	N
Vegetable Oils	Turpentine	0,86	2	16	N
Paints & Varnishes	Varnish		320	Room Temp
Vegetable Oils	Vegetable oil		40	Room Temp
Food Products	Vinegar		12 - 15	20	N
Pharmaceuticals	Wax	0,9	500	93	T
Fish & Animal Oils	Whale Oil	0,93	25 - 39	38	N
Dairy Products	Whey		800 - 1,500	Room Temp
Dairy Products	Whole Egg		150	4,5	T
Food Products	Yeast Surry		20	18	T
Dairy Products	Yoghurt		3,000 - 8,000	Room Temp

DO NOT DELETE THIS SECTION

Kinematic Viscosity (cSt) Cup Type	1	2	3	4	7.5	10	15	20	25	30	40	50	60	70	80	90	100	125	150	175	200	225	250	275	300	325	350	375	400	500	600	700	800	900	1000	1250
‘Ultra Low’ Cup	53	68	84
Shell Cup #1	17	21.5	26	35	46	57
Shell Cup #2					18.3	22	30.4	39	47	56
Shell Cup #2.5							19	25	30	35.6	46.6	57
Shell Cup #3									18.6	22	28.6	35	42	48	55
Shell Cup #3.5										17.5	20	24.6	29.2	34	38.4	43	47.8	59.4
Shell Cup #4													18	21	24	27	30	37	45	52	60
Shell Cup #5																	16	20	24	28	32	36	40	44	48	52	56	60	64
Shell Cup #6																								17.5	19	20.5	22.5	24	25	31.5	37.5	44	50	56.5	63	78
Zahn Cup #1					30.5	32	35	38	42	45	52	60	68
Zahn Cup #2								18	19	20	22.5	25	28	30	34	38	43	53	63	72
Zahn Cup #3																	17	19.5	22	24.5	27	30	32	35.5	38	41	43	45	48.5	58	70
Zahn Cup #4																				17	18	19.5	21	22.5	24	26	28	30	32	38	45	51	54	65	70
Zahn Cup #5																									17	18.5	20	21	22.5	27	31	35	40	45	49	60
Ford Cup #3														32	37	40	43	53	63	73	83	93	103	113	120	130
Ford Cup #4														20	22	25	28	35	40	48	55	62	70	76	82	90	98	103
ISO Cup #4										26	33	39	46	53	60
DIN Cup #4												20	22	24	26	28	30	35	40	46	50	56	61	71
AFNOR Cup #4												20	22	24	26	28	30	35	40	46	50	56	61	71
Norcross Cup #1	31	36	40	53	70	87
Norcross Cup #2			19	23	28	34	45	55	67	76
Norcross Cup #3									17	20	25	30	35	40	45	50	55	68	79
Norcross Cup #4																	18	22	27	32	36	40	44	48	53	57	61	65	68	85
Norcross Cup #5																												20	22	26	31	36	41	45	50	62

Kinematic Viscosity (cSt) Cup Type	1	2	3	4	7.5	10	15	20	25	30	40	50	60	70	80	90	100	125	150	175	200	225	250	275	300	325	350	375	400	500	600	700	800	900	1000	1250
‘Ultra Low’ Cup	53	68	84
Shell Cup #1	17	21.5	26	35	46	57
Shell Cup #2					18.3	22	30.4	39	47	56
Shell Cup #2.5							19	25	30	35.6	46.6	57
Shell Cup #3									18.6	22	28.6	35	42	48	55
Shell Cup #3.5										17.5	20	24.6	29.2	34	38.4	43	47.8	59.4
Shell Cup #4													18	21	24	27	30	37	45	52	60
Shell Cup #5																	16	20	24	28	32	36	40	44	48	52	56	60	64
Shell Cup #6																								17.5	19	20.5	22.5	24	25	31.5	37.5	44	50	56.5	63	78
Zahn Cup #1					30.5	32	35	38	42	45	52	60	68
Zahn Cup #2								18	19	20	22.5	25	28	30	34	38	43	53	63	72
Zahn Cup #3																	17	19.5	22	24.5	27	30	32	35.5	38	41	43	45	48.5	58	70
Zahn Cup #4																				17	18	19.5	21	22.5	24	26	28	30	32	38	45	51	54	65	70
Zahn Cup #5																									17	18.5	20	21	22.5	27	31	35	40	45	49	60
Ford Cup #3														32	37	40	43	53	63	73	83	93	103	113	120	130
Ford Cup #4														20	22	25	28	35	40	48	55	62	70	76	82	90	98	103
ISO Cup #4										26	33	39	46	53	60
DIN Cup #4												20	22	24	26	28	30	35	40	46	50	56	61	71
AFNOR Cup #4												20	22	24	26	28	30	35	40	46	50	56	61	71
Norcross Cup #1	31	36	40	53	70	87
Norcross Cup #2			19	23	28	34	45	55	67	76
Norcross Cup #3									17	20	25	30	35	40	45	50	55	68	79
Norcross Cup #4																	18	22	27	32	36	40	44	48	53	57	61	65	68	85
Norcross Cup #5																												20	22	26	31	36	41	45	50	62

Effect on Mixing

A fluids viscosity is one of the most important considerations when designing a mixer for a given application.

The greater a fluids viscosity, the more energy input is required to mix the fluid, and this means larger impellers, and more powerful motors to turn them. For highly viscous materials it may be necessary to use a close clearance type impeller, such as a gate or spiral type impeller, to achieve adequate mixing across the full tank volume.

Laminar & Turbulent Mixing

Mixing at low viscosity almost always takes place under turbulent conditions.
This means that mixing is controlled by inertial forces rather than by molecular diffusion, and mixing is achieved by the many eddies and vortices created by the mixer impeller.

Impellers such as the hydrofoil and pitched blade turbine type impellers are used for low viscosity mixing as they provide large pumping capacities and create large amounts of turbulence in the mixing vessel.

On the other hand, mixing at high viscosities takes place mainly in the laminar flow regime where the viscous forces dominate, damping down any turbulence, and molecular diffusion is the main source of mixing. To aid the molecular diffusion the aim of mixing in the laminar regime is to “cut and fold” the fluid so that there is greater interfacial area between the different fluids for the diffusion to take place.

Here, gate or screw type impellers are used as the large surface area
presented to the fluid helps to increase the “cutting and folding” action
across the entire tank volume.

The below plot shows the suitable viscosity ranges for various types of standard impellers.

Plot of Impeller Types vs Their Suitable Operating Viscosities

Non-Newtonian Mixing

Achieving adequate mixing in non-Newtonian fluids can be challenging. If you have a non-Newtonian mixing application and you require assistance in selecting a suitable agitator, please get in touch and one of our application engineers will be happy to help.

Static Mixers

The effect of viscosity on mixing in an inline static mixer is like the effects on stirred tank mixers. For lower viscosity applications the mixing is dominated by turbulent eddies, whereas higher viscosity applications are still dominated by molecular diffusion and rely on the same “cut and fold” method of mixing as stirred tank mixers described above.

Different types of mixing element are used for low and high viscosity fluids and generally follow the same principles as stirred tank impellers. The higher the viscosity, the larger and more complex the mixer elements placed in the pipe to ensure mixing across the entire pipe diameter, and this increases the pressure drop across the mixer. This increases the power required from the pump so, as in stirred tank mixers, more power is required for mixing high viscosity fluids.

John Whittle MEng (Hons)