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### CAPILLARY VISCOMETER

EXPERIMENTAL METHODS 2010 PROJECT 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

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-plasticholder of needle, 6-needle, 7-calibrated resistor (electric currentneedle-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

y

uw

H

x

Rheology of liquids / fundamentals

Constitutive 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)

EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER

Simple shear flow in pipe

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

volumetric flowrate [m3/s]

axial gradient of pressure

pipe of inner radius R

(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)

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

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

EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER

LABVIEW

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

Under preparation

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

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

EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER

MATLAB programming

Simplest 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;

end

nstart=i

pme=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;

end

nend=i

% pbar subtracted atmospheric pressure and recalculated by calibration

% constant of Kulite

pbar=(p-(pme+pm)/2)/14.303e-8;

% integral of pressure

dtdata=(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 programming

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

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 part

tr=tb(nbstart:nbend);

pr=pb(nbstart:nbend);

u1r=u1b(nbstart:nbend);

u2r=u2b(nbstart:nbend);

m=length(tr)

%filtration of pressure and voltage

prf=max(0,sgolayfilt(pr,2,19));

u1rf=sgolayfilt(u1r,2,19);

u2rf=sgolayfilt(u2r,2,19);

% recalculate voltages to volumes

k=vstart*u1start/u2start;

vr=k*u2rf./u1rf;

% flowrate

for i=2:m-1

dvdt(i)=max(0,-(vr(i+1)-vr(i-1))/(2*dt));

end

dvdt(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 pascals

tauw=dn*prf/(4*ln)*1e5;

% mean viscosity

mjuv=tauw./gamv;

mju=mean(mjuv)

plot(gamv,tauw,\'ro\')

% 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;

end

nstart=i

pme=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;

end

nend=i

% pbar subtracted atmospheric pressure and recalculated by calivration

% constant of Kulite

pbar=(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)

EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER

LABORATORY REPORT- Front page: Title, authors, date
- Content, list of symbols
- Introduction, aims of project, references
- Description of experimental setup
- Theory and software design (MATLAB program)
- Geometry of needles (D,L), processed volumes, used liquids
- Experiments: Recorded time courses of pressure (graph)
- Results: Viscosities (table) or graph (viscosity-temperature/shear rate)
- Conclusion (identify interesting results and problems encountered)

EXPERIMENTAL METHODS 2011 PROJECT CAPILLARY VISCOMETER

LABVIEW improved

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

supply voltage to Kulite

Voltages: pressure, fixed resistor, syringe

Under preparation

T-thermocouple

Volume of liquid is evaluated from voltages

EXPERIMENTAL METHODS 2011 PROJECT CAPILLARY VISCOMETER

LABVIEW improved

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

root mean square of voltage at trimmer (fixed resistor)

ratio of voltages Usyringe/Utrimmer is proportional to volume

root mean square of voltage at syringe (variable liquid column)

EXPERIMENTAL METHODS 2011 PROJECT CAPILLARY VISCOMETER

LABVIEW improved

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

recorded volume (relative)

recorded pressure (voltage)

EXPERIMENTAL METHODS 2011 PROJECT CAPILLARY VISCOMETER

LABVIEW improved

Calibration (repeated experiment with water)

recorded volume (relative) by Labview

Volume in ml (from scale on syringe)

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