The following protocol calculated flow rate in the microfluidic channels using data obtained from PIV using the rectangular channel flow equations.
%Calculates flow rate from velocity according to the exact solution of %rectangular channel flow %Enter everything as u:m/s, W,H: micron, L: mm function[q]=profilecalc(W,H,L) %Definitions, converting to standard SI %Width w=W*10ˆ-6; %Height h=H*10ˆ-6; %Length l=L*10ˆ-3; %Viscosity mu=8.9*10ˆ-4; %Aspect ratio a=h/w; %Velocity u=zeros; sum=0; term=0; %Define time step (us) time step=55; %Read in the image vectors v=loadvec(’*.vc7’); %For each time step/file: %Access the x-component of velocity data, vx and find the maximum velocity %Average the velocity data along each column to represent a global average %for the divided pixel down the image window. Store in an array maximum velocity=zeros(1,numel(v)); for i = 1 : numel(v) %Average each column and store in a row each average velocity along y=mean(v(i).vx,1); %account for negatives (oscillatory flow) avg=mean(average velocity along y); if avg¿0 maximum velocity(i)=max(average velocity along y); else maximum velocity(i)=min(average velocity along y); end end %Before Mark’s oscillatory/pulsatile flow changes % for i = 1 : numel(v) %Average each column and store in a row each average velocity along y=mean(v(i).vx,1); %Maximum velocity maximum velocity(i)=max(average velocity along y); end % %Comes out currently in units of pixels %Multiply by pixel to micron scaling factor for 10x magnification lens. %Number of microns/pixels pixel to micron=550/839.75; %So now in units of microns maximum velocity=maximum velocity*pixel to micron; %Convert to m maximum velocity=maximum velocity*10ˆ-6; %Divide by time step to get velocity in m/s maximum velocity=maximum velocity/(time step*10ˆ-6); u=maximum velocity; %Calculate the bracketed term in the flow rate equation for m=1:2:19 t=((192*a)/(m*pi)ˆ5)*tanh((m*pi)/(2*a)); term=term+t; end Tterm=1-term; %Calculate the sum term in the velocity expression, assuming we are using %maximum velocities from PIV analysis at mid-channel, with z=h/2 and y=0. %We here assume that we correctly found the correct z-plane while scanning %with microscope, and the PIV analysis uses a maximum velocity value in %middle of channel but this is theoretically the case for k=1:2:19 s=(1/kˆ3)*(1-(1/(cosh(k*pi*w/(2*h)))))*sind(k*180/2); sum=sum+s; end Hterm=sum; %Now find the flow rate in mˆ3/s q=(u*piˆ3*Tterm*w*h)/(48*Hterm); %Convert to ml/min q=q*1000*1000*60; q=q’;
