VISCOSITY OF BIODIESEL FUELS


 Lucas Allen
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1 VISCOSITY OF BIODIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use statistical mechanics to pedict a vaiety of behavios fo gases, including the distibution of velocities as a function of tempeatue and mass. The assumptions made fo an ideal gas begin to beak down when the molecules ae bought close togethe by inceasing pessue and deceasing the volume. As gas molecules ae bought close, they begin to expeience intemolecula foces that cause the gas to deviate fom Boyle s PV=nRT gas law. These intemolecula inteactions, howeve, ae still mino when one consides the amount of time that a gas molecule spends in fee space as compaed to time spent close to othe molecules. The motion of liquids can theoetically be calculated in a simila manne using statistical mechanics. In pactice, howeve, the much stonge intemolecula foces pesent in a liquid make the calculations impactical unless one esots to the powe of a supecompute. Even though we cannot calculate them fom fundamentals, paticle velocities and othe motion infomation is still impotant when it comes to poblems like chemical kinetics o the design of chemical pocessing equipment. As an altenative to a fundamental teatment of paticle motion, the common appoach with liquids is to use macoscopic desciptos like viscosity to descibe the motion of liquid paticles. Viscosity can be thought of as a esistance to flow. Altenatively, we can descibe the fluidity of a liquid, which is a measue of the ability of molecules to flow past one anothe. Fluidity and viscosity have a simple ecipocal elationship to one anothe. Both paametes ae equally valid, with one o the othe having advantages fo diffeent applications. Both ae affected by intemolecula attactive foces which educe fluidity and incease viscosity. F = fluidity η = viscosity F = 1/η Consideed macoscopically, viscosity is a fictional foce that aises fom the motion of molecules as they move past each othe in liquids. Fom a micoscopic viewpoint, viscosity eflects the enegetics of molecula association in the liquid state. In ode fo a liquid to flow, an applied foce (F app ) must be applied to ovecome the attactive foces between the molecules (F im ). Suface Aea, A F app z F im V x z y x Viscosity, η, is defined elative to the applied foce and the change in velocity. dfapp dvx (1) = η da dz Genty, 2013
2 The peceding figue shows a single pai of paticles inteacting with one anothe. In pactical applications thee ae a numbe of successive inteactions. Fo example, a fluid flowing though a capillay tube has a seies of inteactions beginning with foces between the outemost paticles and the stationay wall of the tube. The esult is that a velocity gadient is fomed, with the wall having zeo velocity and fluid paticles moving faste as they ae positioned futhe and futhe away fom the wall. velocity pofile A useful application of equation (1) is the case of mass tanspot though a cicula tube of small intenal diamete. Poiseuille (1844) showed that dv π 4 P (2) =, dt 8η L whee dv/dt is the volume flow ate though the tube, is the diamete and L is the length of the tube, and P is the is the pessue diffeential acoss the two ends of the tube. Viscosity is typically epoted in units of poise (P) o centapoise (cp). One poise = 1 g/(cm*sec) and 100 cp = 1P. Poise must be conveted to Pa*s if SI units ae needed (10P = 1 Pa*s) By way of compaison, the viscosity of an ideal gas is given by the expession: η = MRT 3 π σ (with σ =molecula diamete, N A = Avogado s numbe) 4 2 N A This pedicts gas viscosities on the ode of µp as compaed to liquid wate which has a viscosity of 1 cp. Tempeatue Dependence of Viscosity Given the need to ovecome intemolecula foces, it is not supising that the viscosity depends on tempeatue. In 1912, Ahenius developed the following equation. (3) 1 Eη / RT = Ae η A is the scaling facto fo a given liquid. E η is the viscous heat (in units of enegy/mol) and is elated to the enegy needed fo paticles to beak away fom thei neighbos. T is in units of Kelvin
3 Measuing Viscosity Technique 1: Low Viscosities Using an Ostwald Viscomete Low viscosities can be measued using an Ostwald viscomete. This appaatus has a naow capillay tube though which the sample can flow unde hydostatic pessue due to gavity. The time fo a given amount of fluid to flow fom one etched line to the othe will depend on the viscosity of the liquid. Integating eqn (2) gives: Etched Lines (4) 4 π Pt η = 8VL t = time to flow fom 1 st mak to 2 nd P = hydostatic pessue V = volume of liquid The hydostatic pessue pushing the liquid down the tube is due to gavity. It depends on the density (ρ) of the mateial, thus leading to a elationship whee P has a linea dependence on density. The unique shape of the viscomete helps contol othe hydostatic pessue factos that would change if the fluid level at the input o output end changed too much duing the couse of the measuement. In theoy, one could solve eqn. (4) exactly if one knew all the vaiables. In pactice, it is easie to calibate the equipment with a known efeence sample (in this case pue wate) and use the esult to detemine the viscosity of the sample. Assuming that the equipment doesn t change and hence collecting all of the constant tems togethe in one single constant, equation (4) fo the appaatus can be ewitten as: (5) η = ( Constant) ρ t ρ = density of fluid Fom eqn (5), one can compae the esults of a efeence liquid (ρ, t, η ) to find the viscosity of the sample in question. Of couse this equies looking up the density and viscosity fo the efeence fluid as well as knowing the density of the sample liquid. (6) η ρ t η = ρ t  3 
4 Pocedue: We will use cyclohexane as ou efeence fluid. You will need to look up the density fo cyclohexane. Viscosity of Cyclohexane 1 Tempeatue Viscosity 17 ºC 1.03 cps 22 ºC ºC ºC 0.75 Refeence Fluid 1) Immese the Ostwald viscomete in a oomtempeatue wate bath and ecod the tempeatue. 2) Pipet 10 ml of the efeence fluid into the viscomete. All subsequent measuements must use this same amount of fluid to insue the same hydaulic backpessues ae pesent in the system. 3) Use a pipet bulb to push the liquid level up above the uppe scibed mak on the viscomete. Allow the fluid to un back down, stating a time exactly as the meniscus moves past the uppe mak. Measue the time necessay fo the meniscus to each the lowe mak. 4) Repeat the measuement 4 moe times using the same fluid in the appaatus. 5) Clean the viscomete well befoe switching to each new fluid. Use acetone then inse twice with next sample. Use pipet bulb to foce ai though capillay to emove excess fluid. Sample Fluids 6) Detemine the density of the biodiesel and petodiesel samples if you have not aleady done so. 7) Repeat the above pocess fo measuing the oom tempeatue viscosity of both the biodiesel and the petodiesel samples. Calculate the viscosities fo the two samples using the cyclohexane data fom above as you efeence mateial fo Eqn. 6 8) Put the wate bath and viscomete on a hot plate. Continue measuing the viscosity of the biodiesel sample as a function of tempeatue, collecting 35 eplicate data fo each of 5 tempeatues acoss a ange of oom tempeatue to appoximately 60ºC. The viscomete has aleady been calibated so the cyclohexane measuements do not need to be epeated
5 DATA ANALYSIS: 1) Pepae a table compaing the oom tempeatue viscosities of the two diesel fuels (using the cyclohexane data fom above as you efeence mateial fo Eqn. 6). 2) Fom the data, calculate the viscosity of you biodiesel at diffeent tempeatues anging fom an ice bath to 60ºC. Tabulate you esults. 3) Plot you tempeatue data on both a η vs. T and a ln(1/η) vs. 1/T gaph and analyze the latte using the Ahenius equation (Eq 3). [Be caeful to conside what needs to be on the x axis and the y axis to get the appopiate slope.] Based on you gaphical analysis, detemine the activation enegy fo viscous flow in you fuel. Going to the intenet o to you feshman chemisty text, what is the typical bond enegy fo a caboncabon covalent bond. How does you viscousflow activation enegy compae to the enegy needed to beak a covalent bond? Compae and discuss the diffeence in magnitudes of the two numbes and whee those foces aise fom. 4) How might the tempeatue pofile affect the pefomance of diesel fuel in an engine? What about unning the engine in Minnesota in Decembe, o unning the engine in Tucson in August? 5) How did the oom tempeatue viscosities of the two diesel fuels compae. Discuss the suitability of switching fom petodiesel to you biodiesel. REFERENCES: 1) Lange s Handbook of Chemisty, 10 th ed,
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