CAPILLARY VISCOMETER

Motivation•Advanced instrument based upon our own patent•How to measure rheological and electric properties of blood?•Using MATLAB and LABVIEW for instrumentation

Task prepared within the project FRVS 90/2010

EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER

EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER

Aim of project: Measurement of rheological properties (viscosity of liquids) using a capillary viscometer, that is still under development. Computer control and MATLAB software devolopment.

1–glass cylinder, 2-metallic piston, 3-pressure transducer Kulite, 4-tested liquid, 5-plastic holder of needle, 6-needle, 7-calibrated resistor (electric current needle-tank), 8-calibrated resistor (current flowing in tank), 9-AC source (3-30V), 10-SS source for pressure transducer (10V), 11-A/D converter, 12-procesor, 13-metallic head,

14-push bar, 15-scale of volume

EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER

EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER

Rheology of liquids / fundamentalsConstitutive equation of fluids is relationship between kinematic stimulus (flow, characterized by rate of deformation tensor) and dynamic response (stress tensor). The simplest linear relationship holds for the so called Newtonial fluids (for example water, air, oils, but not more complicated liquids like yoghurt, ketchup, polymer melts)

is shear stress (one component of stress tensor) and is shear rate (one component of tensor of rate of deformation). Coefficient of proportionality is dynamic viscosity (units Pa.s) – this value should be evaluated from experiment. The equation (1) holds in this simplified one-dimensional form only for the so called simple shear flows, e.g. flows of a layer of fluid between two parallel plates one of them being fixed and the second one moving with a constant velocity uw, (a similar velocity profile develops also in a narrow gap between a steady outer cylinder and an inner rotating cylinder – this arrangement is typically used in rotational rheometers)

x

yuw

HH

u

y

u wx

EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER

Simple shear flow in pipeSimple shear flow exists also in laminar flow in a straight circular pipe, where

3

4)(

R

Q

r

ruxw

x

pRw

2

(2,3)

Therefore by measuring flowrate and pressure drop at a steady laminar flow in a tube (capillary) it is possible to evaluate viscosity as a ratio

Actual flowrate should be linear function of pressure gradient as follows from Eqs.(1-3)

volumetric flowrate [m3/s]

pipe of inner radius R

axial gradient of pressure

ww /

x

pRRRQ w

w

844

433

and this equation is known as the Hagen Poiseuille law (mention the fact that the flowrate increases very rapidly with radius of pipe - 4th power).

In this experiment the liquid is expelled by a piston from a syringe through a thin needle manually (therefore it is not possible to arrange a constant flowrate during the whole experimental run). Nevertheless it is not necessary to measure the whole course of flowrate as a function of time. It will be sufficient to record and to integrate the time course of pressure p(t). It follows from the fact that

the volume is the time integral of flowrate

end

start

end

start

end

start

t

t

t

t

t

t

pdtL

Rdtx

pRdtQV

88

44

L is length of needle, R is radius of needle and tstart, tend times of begin and end of the piston

displacement.

EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER

Measurement procedure

Check electrical connection of pressure transducer, connect 9V battery to its feeding (be careful about polarity), switch on NI-USB-62781 and start the program “Strikacka”.

Record temperature of the tested liquid by a portable thermometer. Fill the syringe by tested liquid, select and attach a needle. Expel air bubbles from the syringe’s content. Record volume of the sucked in liquid (using a grade on the syringe), usually 20 ml. Record geometry of needle (radius R and length L).

Fill the dialog forms in the “Strikacka” screen. Sampling rate (1 kHz recommended), scale factor for U1 channel (pressure transducer - this value has no effect upon recorded data, this scale is important only for graphics). Specify file name of results. Fill the item (“Header row”) with information about the needle (geometry), initial volume and the type of tested liquid.

Switch on “Write” button and start to expel the liquid from syringe by pushing a piston. Observe recorded pressure on screen. As soon as all liquid is expelled switch the write button “Off”.

All data are stored in the specified text file. The file can be imported to MATLAB or Excel program. The first row is header following rows contain time, voltage (output of pressure transducer). That is all what you need to evaluate viscosity using the theory described above.

EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER

LABVIEWExperiment is controlled by National Instruments software and is implemented as VI program STRIKACKA

Under preparation

File name, where time and 3 corresponding voltages will be recorded, after switching button WRITE.

Scales of voltages (only for graph, data will be stored always in Volts, without any scaling).

EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER

MATLAB programmingSimplest processing suitable only for Newtonian liquids (electrical resistance is not recorded)

t=a(1:end,1);p=a(1:end,2);ndata=length(t);nconst=ndata/20+2;pm=mean(p(1:nconst))ps=std(p(1:nconst));plim=pm+5*ps;i=1;while p(i)<plim & i<ndata/2 i=i+1;endnstart=ipme=mean(p(ndata-nconst:ndata))pse=std(p(ndata-nconst:ndata));plim=pme+5*pse;i=ndata;while p(i)<plim & i>nstart+5 i=i-1;endnend=i% pbar subtracted atmospheric pressure and recalculated by calibration% constant of Kulitepbar=(p-(pme+pm)/2)/14.303e-8;% integral of pressuredtdata=(t(ndata)-t(1))/(ndata-1);pint=sum(pbar(nstart:nend))*dtdata;% mju=pi.d^4/(128L.V/pint)% Gamma = 4V/(pi.d^3.deltat).mju=3.141*dn^4/(128*ln*vstart/pint)gamma=4*vstart/(3.141*dn^3*(t(nend)-t(nstart)))

EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER

MATLAB programmingAdvanced processing of non-Newtonian liquids (electrical resistance is used for flowrate measurement)

% dn-diameter of needle, Ln-length of needle% dp-diameter of piston% rf-fixed resistance% vstart-initial volume% vend-final volume% kp= calibration constant of pressure transducer (=1/14.303e-3)t=a(1:end,1);p=a(1:end,2);u1=a(1:end,3);u2=a(1:end,4);ndata=length(t)nconst=ndata/20+2;pm=mean(p(1:nconst))ps=std(p(1:nconst));plim=pm+5*ps;i=1;while p(i)<plim & i<ndata/2 i=i+1;endnstart=ipme=mean(p(ndata-nconst:ndata))pse=std(p(ndata-nconst:ndata));plim=pme+5*pse;i=ndata;while p(i)<plim & i>nstart+5 i=i-1;endnend=i% pbar subtracted atmospheric pressure and recalculated by calivration% constant of Kulitepbar=(p-(pme+pm)/2)*kp;%BINING dtdata=(t(ndata)-t(1))/(ndata-1);nb=round(0.03/dtdata)dt=dtdata*nb;nbin=floor(ndata/nb)

i=1;for ibin=1:nbin tmean=0; pmean=0; u1max=0; u2max=0; for j=1:nb tmean=tmean+t(i); pmean=pmean+pbar(i); u1max=max(u1max,u1(i)); u2max=max(u2max,u2(i)); i=i+1; end tb(ibin)=tmean/nb; pb(ibin)=pmean/nb; u1b(ibin)=u1max; u2b(ibin)=u2max;end% nbstart=floor(nstart/nb);nbend=floor(nend/nb);u1start=mean(u1b(1:nbstart-1));u2start=mean(u2b(1:nbstart-1));u1end=mean(u1b(nbend+1:nbin));u2end=mean(u2b(nbend+1:nbin));% even now it is possible to cut off initial and ending parttr=tb(nbstart:nbend);pr=pb(nbstart:nbend);u1r=u1b(nbstart:nbend);u2r=u2b(nbstart:nbend);m=length(tr)%filtration of pressure and voltageprf=max(0,sgolayfilt(pr,2,19));u1rf=sgolayfilt(u1r,2,19);u2rf=sgolayfilt(u2r,2,19);% recalculate voltages to volumesk=vstart*u1start/u2start;vr=k*u2rf./u1rf;

% flowratefor i=2:m-1 dvdt(i)=max(0,-(vr(i+1)-vr(i-1))/(2*dt));enddvdt(1)=-(vr(2)-vr(1))/dt;dvdt(m)=-(vr(m)-vr(m-1))/dt;dvdtf=max(0,sgolayfilt(dvdt,2,19));%gamv=32*dvdtf/(3.141*dn^3);%recalculated to pascalstauw=dn*prf/(4*ln)*1e5;% mean viscositymjuv=tauw./gamv;mju=mean(mjuv)plot(gamv,tauw,'ro')

LABORATORY REPORT

1. Front page: Title, authors, date

2. Content, list of symbols

3. Introduction, aims of project, references

4. Description of experimental setup

5. Theory and software design (MATLAB program)

6. Geometry of needles (D,L), processed volumes, used liquids

7. Experiments: Recorded time courses of pressure (graph)

8. Results: Viscosities (table) or graph (viscosity-temperature/shear rate)

9. Conclusion (identify interesting results and problems encountered)

EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER

LABORATORY REPORT

EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER

Exp.No.

Liquid Temperature [C]

Viscosity from table

[Pa.s]

Viscosity from experiment

Needle D (nominal)

[mm]

Needle D (calibration) [mm]

Length pf needle L [mm]

Length measured [mm]

Volume [ml]

tstart/tend

Flowrate [ml/s]

Shear rate [1/s]

Shear stress [Pa]

File name

1 Water 26 0.00095 0.8 0.624

2 Milk 30 Not known 0.8

3

EXPERIMENTAL METHODS 2011 PROJECT CAPILLARY VISCOMETER

LABVIEW improvedExperiment is controlled by National Instruments software and is implemented as VI program PUTEMP

Under preparation

supply voltage to Kulite

Voltages: pressure, fixed resistor,

syringe

Volume of liquid is evaluated from voltages

T-thermocouple

EXPERIMENTAL METHODS 2011 PROJECT CAPILLARY VISCOMETER

LABVIEW improvedExperiment is controlled by National Instruments software and is implemented as VI program PUTEMP

root mean square of voltage at trimmer (fixed

resistor)

root mean square of voltage at syringe

(variable liquid column)

ratio of voltages Usyringe/Utrimmer is

proportional to volume

EXPERIMENTAL METHODS 2011 PROJECT CAPILLARY VISCOMETER

LABVIEW improvedExperiment is controlled by National Instruments software and is implemented as VI program PUTEMP

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 2 4 6 8 10 12 14 16 18

0.01

0.012

0.014

0.016

0.018

0.02

0.022

0.024

0.026

0.028recorded

volume (relative)

recorded pressure (voltage)

0

0.5

1

1.5

2

2.5

0 5 10 15 20 25

EXPERIMENTAL METHODS 2011 PROJECT CAPILLARY VISCOMETER

LABVIEW improvedCalibration (repeated experiment with water)

recorded volume (relative) by

Labview

Volume in ml (from scale on

syringe)