flow rate calculation in the microfluidic channels using data obtained from PIV using the Purday approximation.
%Program uses the maximum velocity obtained from PIV to calculate the flow %rate %Define time step (us) time step=90; %Channel width (um) w=1500; %Channel height (um) h=212.5; %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 %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); %Calculate channel area (in mˆ2) A=w*h*(10ˆ-6)ˆ2; %Calculate flow rate through Purday Approximation - Calculate n and m as %well alpha=h/w; %Calculate n if alpha ¿= (1/3); n=2+0.3*(alpha-(1/3)); else n=2; end %Calculate m m=1.7+0.5*alphaˆ-1.4; %Flow rate in mˆ3/s Q=(m/(m+1))*(n/(n+1))*A*maximum velocity; %Convert to ml/min Q=Q*60*10ˆ3*10ˆ3;
