### Viscosity

Viscosity of Liquids Part I: Low Viscosities Mona Kanj Harakeh 1 Objectives • To measure and analyze the viscosities of ideal (Toluene/p-Xylene) and nonideal (Methanol/Water) binary solutions and their components. • To determine the Activation Energy to viscous flow. • The effect of temperature change on the viscosity will be studied. Method: The viscosities of liquids are determined by measuring the flow time for various liquids in an Ostwald viscometer. 2 Ostwald viscometer 3 Viscosity • The resistance of a liquid to flow is called its viscosity Viscosity is a property of liquids that is important in applications ranging from oil flow in engines to blood flow through arteries and veins. Measuring viscosity • How long a liquid takes to flow out of a pipette under the force of gravity. • How fast an object (steel ball) sinks through the liquid under gravitational force. 4 Molecular properties contributing to viscosity Viscosity arises from the directed motion of molecules past each other, it is a measure of the ease with which molecules move past one another. It is affected by many factors such as: • Molecular size. Molecular shape. • Intermolecular interactions (attractive force between the molecules). • Structure of the liquid itself. • Temperature(Viscosity decreases with increasing temperature the increasing kinetic energy overcomes the attractive forces and molecules can more easily move past each other). 5 Viscosity ? The IUPAC symbol of viscosity is the greek symbol eta “? ”. ? Viscosity “? ” of a fluid is its resistance to flow. ? When a Liquid flows, whether through a tube or as the result of pouring from a container. Layers of liquid slide over each other. The force (f) required is directly proportional to the Area (A) and velocity (v) of the layers and inversely proportional to the distance (d) between them. Av Equ. 1 f ?? fd gcms cm ? ? gcm ? 1 s ? 1 ? 1 piose ? 1P Av cm 2 cms ? 2 ?2 d unit of viscosity 6 Viscosity Units The unit of viscosity is the poise named after Poiseuille Jean Louis Marie. It is most commonly expressed in terms of centipoise “cP”. The centipoise is commonly used because water has a viscosity of 1. 0020 cP at 20oC; the closeness to one is a convenient coincidence. The SI unit of viscosity is Pascal-second (Pa·s) = N·s m–2 or Kg m-1 s-1. • In cgs unit 1 Poise “P” = 1 g. cm-1. s-1 (dyne . s) 10-2 Poise “P”= 1 centipoise “cP” 1 Pa. s = 103 cP 10 P = 1 Kg·m? 1·s? 1 = 1 Pa. s 1 cP = 0. 001 Pa. s = 1 mPa. s • The conversion between the units: 1 P = 0. 1 Pa. s For many liquids at room temperature the viscosity is very small 7 (0. 002-0. 04) therefore (10-2 P), centiP is often used. Ostwald Method • Time for fixed volume V of liquid to fall through a capillary into a reservoir Upper Fiducial mark – Depends on density. – Depends on viscosity. Reference liquid is used. • This type can be used for liquids of viscosity up to 100 poise. Lower Fiducial mark 8 Ostwald Method The rate of flow R (cm3/sec) of a liquid through a cylindrical tube of radius r and length l under a pressure head P is given by the Pousille equation. Equ. 2 Measurement of P, r, t, V, and l permits the calculation of the viscosity: Equ. 3 It is easier to measure the viscosity of a liquid by comparing it with another liquid of known viscosity. Since P = ? gh Equ. 4 The viscosity of a solution can be determined relative to a reference liquid (de-ionized H2O). 9

Oswald viscometer The Oswald viscometer is a simple device for comparing the flow times of two liquids of known density. If the viscosity of one liquid is known, the other can be calculated. Ostwald viscometer is used to measure the low viscosities’ liquid. After the reservoir is filled with a liquid, it is pulled by suction above the upper mark. The time required for the liquid to fall from mark 1 to mark 2 is recorded. Then the time required for the same volume of a liquid of known viscosity to flow under identical conditions is recorded, and the viscosity is calculated with Equation ? ? ? k? Equ. 5 ? ? ( r ) ? t ? r tr Where “r” refers to the viscosity, density and flow time for a reference liquid, usually water. Therefore it is important to do set of measurements of known liquid and at controlled temperature. 10 Fluidity Equ. 6 • The reciprocal of viscosity is fluidity, F ? ? • The concept of fluidity can be used to determine the viscosity of an ideal solution. • One particular advantage for fluidity is that the fluidities of mixed binary solutions of liquids a and b are approximately additive. So if each pure liquid has fluidities Fa and Fb, the fluidity of a mixture is given by: where ? a and ? b is the mole fraction of component a and b respectively, • Fluidity equation is only slightly simpler than the equivalent equation in terms of viscosity µ = ? : Equ. 8 • where ? a and ? b is the mole fraction of component a and b respectively, and ? a and ? b are the components of pure viscosities. • The viscosity of the mixture is not linear 11 Kendall proposed another approach for expressing the viscosity of a mixture: ln? ? ? A ln? A ? ? B ln? B Equ. 9 Where xA and xB are the mole fractions of component A and B respectively, and ? A and ?

B are the components as pure viscosities. The above equation is valid for the Ideal Solutions such as Toluene/p-Xylene in which the interaction energies between the components are the same as those between the pure components. The failure of component fluidities to be additive in the mixed state arises, then, either from the formation of association complexes between the components or from the destruction of such complexes that may be present in the pure components after the pure components are mixed. Under this circumstance the following equations would not be valid: and ln? ? ? A ln?

A ? ? B ln? B 12 Temperature Dependence of Viscosity • Over a reasonably wide temperature range, the viscosity of a pure liquid increases exponentially with inverse absolute temperature. • This relation was first expressed quantitatively by Arrhenius E? (1912). ? ? A exp( • Where A is a constant for a given liquid and E? is the activation energy of viscosity. • The transported molecules should overcome the activation energy in order to overcome intermolecular attractive forces. RT ) Equ. 10 • A plot of ln ? against 1/T (Arrhenius plot) should be linear and have a slope equal to E? R. E ln ? ? ln A ? ? Equ. 9 RT 13 Experimental • To measure the viscosity by Ostwald method, A liquid is allowed to flow through a thin-bore tube (< 1 mm) then the flow rate is determined and the physical dimensions for the tube should be known exactly. • Ostwald viscometer should be calibrated with a reference liquid therefore the radius and Length of the viscometer can be known precisely. • Operationally, the experiment is done by measuring the time required for a given volume of liquid to flow through the viscometer capillary. • The driving force is the gravity. Ostwald viscometer is designed to keep the height of the separation of the upper and lower levels of the flowing liquid as constant as possible. 14 Calibration of the Ostwald Viscometer • Ostwald viscometer is calibrated using 10 mL of purified water. The flow rate, density and known viscosity of purified water are used to calculate k. Measurement of viscosity of different solutions • The viscosity of two mixed solutions with different percentages of liquids will be measured using Ostwald method. Chemicals Molar Mass(g/mol) Molecular Formula Methanol 32. 04 CH O Toluene 92. 4 CH A- Toluene/p-xylene p-Xylene 106. 16 CH Water 18. 02 HO B- Methanol/Water • Measure the viscosity for each pure liquid then measure the viscosity 20%, 40%, 60% and 80% percentages by volume. 4 7 8 8 10 2 15 Procedure: Suspend the viscometer into a large beaker (2-L) of water that is placed on a hot plate, that is as close to 25° C as possible. Make sure the viscometer is fully immersed in the water. 1. Pipette 10 ml of de-ionized water of known density into the Ostwald viscometer and allow time for the liquid to equilibrate to the temperature of the bath.

Then use a pipette bulb to push or pull the liquid level up above the upper fiducial mark on the viscometer. Allow the water to run back down and start the timer exactly as the meniscus passes the upper mark. Stop the timer just as the meniscus passes the lower mark. Repeat at least twice. Your flow times should agree to within about 0. 4 seconds. 2. Clean and dry the viscometer by running a few milliliters of acetone through it. Drain the acetone and aspirate for about a minute to evaporate all the acetone. 3. Determine the flow times of each of your methanol/water 16 solutions at 25° C. Procedure: cont’d . Complete the series by measuring the flow time for pure Methanol. Repeat each at least twice. Your flow times should agree to within about 0. 4 seconds. 5. Clean and dry the viscometer as before. 6. Determine the flow times of each toluene/p-xylene solution as in step 3. End the determinations with the pure p-xylene. 7. For our temperature work heat the water bath in roughly 5 to 10 degree increments and determine the flow time of the pure pxylene as before at each temperature. Make sure that the temperature is constant. The exact temperature is not important as long as it is known to ± 0. °C, and that the viscometer has had time to equilibrate to a new temperature. Stop at about 60° C. 17 Table Data 1: The flow times of each of ( methanol/water) and (toluene/p-xylene) solutions at 25oC %by volume 100% water 20% methanol 40% methanol 60% methanol 80% methanol 100% methanol Flow time (1) (s) Flow time (2) (s) Flow time (3) (s) Average Flow time (s) 100% p-xylene 20% toluene 40% toluene 60% toluene 80% toluene 100% toluene 18 The flow times of methanol at different temperature: Table Data 2: The flow times of p-xylene at different temperature.

Temperature Flow time (1) (s) Flow time (2) (s) (°C) 25 30 35 40 45 50 55 60 65 Flow time (3) (s) Average Flow time (s) 19 Viscosity Table of Results 1: Methanol, volume % 0% Methanol Methanol , weight % The flow times of a series of Water/Methanol solutions that are 0,20,40,60, 80, and 100% by volume. Average Flow time, t (sec) viscosity, ? (cP) ? ? k? t Fluidity F ? Density, ? (g/mL) ? 1 100% Water 20 40 0 density of H2O 0. 99704 0. 971 0. 944 ? of H2O 0. 8904 16. 54 34. 57 60 80 100 54. 33 76. 02 100 0. 909 0. 859 0. 788 20 Density of Methanol/Water Mixtures at 25 0C

Viscosity Table of Results 1: Cont’d %by volume Densi Mole fraction ln? ? ? ln? ? ? ln? A A B B ty (g/ml ) 0. 997 0. 971 0. 944 0. 909 0. 859 0. 788 Xwater =1 Xwater= Xmethanol= Xwater= Xmethanol= Xwater= Xmethanol= Xwater= Xmethanol= Xmethanol=1 viscosity ? (cP) Fluidity F ? ? A FA ? ? B FB 100% water 20% methanol 40% methanol 60% methanol 80% methanol 100% methanol 21 Viscosity Table of Results 2: The flow times of a series of toluene/p-xylene solutions that are 0,20,40,60, 80, and 100% by volume. Density, ? (g/mL) Average Flow time, t (sec) Viscosity, ? (cP) ? k? t Toluene, volume % Fluidity F ? ? 1 0%Toluene (100% pxylene) 20% Toluene 40 60 80 100 0. 857 0. 858 0. 859 0. 859 0. 960 0. 861 Density of Toluene/p-Xylene Mixtures at 25°C 22 Viscosity Table of Results 2: Cont’d %by volume 100% pxylene 20% toluene 40% toluene 60% toluene 80% toluene 100% toluene Densit y (g/ml ) 0. 857 0. 858 0. 859 0. 859 0. 960 0. 861 Mole fraction ln? ? ? A ln? A ? ? B ln? B viscosity ? (cP) Fluidity F ? ? A FA ? ? B FB Xp-xylene =1 Xtoluene = Xp-xylene = Xtoluene = Xp-xylene = Xtoluene = Xp-xylene = Xtoluene = Xp-xylene = Xtoluene =1 3 Table of Results 3 : T(oC) 20 25 D (g mL-1) 0. 879 0. 857 ln ? vs. 1/T ln ? T(K) 1/T Average ? Flow time, ? ? k? t t (sec) 30 35 0. 852 0. 848 40 45 0. 943 0. 839 50 55 0. 834 0. 830 60 0. 825 24 1. Determine the viscosity coefficient for the methanol/water solutions and toluene/p-xylene solutions using equation ? ? k?. t Calculate Fluidity using equation ? 2. Calculate viscosity ? for the above solutions using equation ln? ? ? A ln? A ? ? B ln? B Calculate Fluidity using equation for all above solutions using equation F ? ? A FA ? ? B FB

Data Analysis F ? 1 3. Compare the viscosity of the methanol/water mixtures to the toluene/pxylene mixtures by graphing the value of the viscosity coefficient (? ) versus the volume percentage of each mixture. Comment on the shape of the graphs. Comment on the “ideality” of the two solutions. 4. Next look at the dependence of viscosity of p-Xylene on temperature. Plot ln ? vs. 1/T and determine the activation energy and the error in the activation energy. (Use Excel to get the error in the slope and use it in a simple propagated error analysis) 25