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% Function Diffusion
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% Change file name to Diffusion.m for the function to work.
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% Calculate diffusion driven dilution of processing liquid in inner HFC
% For running, call e.g. Diffusion(1,1,1,5,4.5*1E2,20)
% Parameters (with example values):
%    Qi1 = 1;         Inner HFC: Injection flow rate [µl/min]
%    Qa1 = 1;         Inner HFC: Aspiration flow rate [µl/min]   
%    Qi2 = 1;         Outer HFC: Injection flow rate [µl/min]
%    Qa2 = 5;         Outer HFC: Aspiration flow rate [µl/min]
%    d = 20;          Apex-to-surface distance [µm]
%    D = 4.5*1E2;     Diffusion coefficient of analyte [µm^2*s^-1] 
%                     (Rhodamine B)
% For running, type e.g. Dilution = Diffusion(1,1,1,5,4.5*1E2,20)
% Diffusion will rate of dilution of analyte due to diffusive transport
% from inner HFC to outer HFC. Diffusion also displays data at various
% steps of the calculation routine for highlighting the key steps
% within the model.
% Diffusion calls the funciotn HFC for calculation of the flow field
% between the apex of the MFP head and the surface under treatment
% Diffusion returns the percentual dilution of analyte in the processing
% liquid aspirated through the inner aspiration aperture.
function Dilution = Diffusion(Qi1,Qa1,Qi2,Qa2,D,d)

% clc
close all

FlowField = HFC(Qi1,Qi2,Qa1,Qa2,d);  % Call HFC function to calculate maps
                                    % of vector components of velocity
X1 = FlowField{1};          % X component
Y1 = FlowField{2};          % Y component
V = FlowField{3};           % Amplitude


%% Grab Streamline X and Y data
figure(5)
Inner = streamline(X1);      % Plot streamlines for inner 
set(gcf, 'Visible', 'off')
L=findobj(Inner,'type','line'); % find the handles of the stream-
                                         % lines
xlines = zeros(size(get(L(1),'Xdata')));
ylines = zeros(size(get(L(1),'Ydata')));
for i=1:length(L)                       % Get rid of nan's
    x = get(L(i),'Xdata');
    x(isnan(x))=[];
    xlines(i,1:length(x))=x;
    y = get(L(i),'Ydata');
    y(isnan(y))=[];
    ylines(i,1:length(y))=y;
end
%% Find longest streamline in inner HFC, calculate mean V along
% this line, find its length and finally calculate the equivalent
% residence time
len = 0;
for n=1:length(xlines(:,1)) % Lines which are expected to be longest
    A = [xlines(n,:); ylines(n,:)];
    Line1X = A(1,:);
    Line1X(isnan(Line1X))=[];
    Line1X(find(Line1X==0)) = [];
    Line1Y = A(2,:);
    Line1Y(isnan(Line1Y))= [];
    Line1Y(find(Line1Y==0)) = [];
    if Line1X(end)<75          % Really going to inner aspiration?
        len1=sum(sqrt(diff(Line1X).^2+diff(Line1Y).^2));
        if len1 >= len
            len = len1;
            rem = n;
        end
    end
end

A = [xlines(rem,:);ylines(rem,:)];  % Longest streamline going from 
                                    % Qi1 to Qa1
Line1X = A(1,:);
Line1X(isnan(Line1X)) = [];
Line1X(find(Line1X==0)) = [];
Line1Y = A(2,:);
Line1Y(isnan(Line1Y)) = [];
Line1Y(find(Line1Y==0)) = []; 

% Now take the matrix of velocity amplitudes and interpolate for finding
% approximation of velocities along streamline A
[X,Y]=meshgrid(1:length(V(1,:)),1:length(V(:,1)));
SV = interp2(X,Y,V,Line1X,Line1Y);
SV = SV(1,isfinite(SV(1,:)))';   % Amplitude of flow velocity along the
                                % interface
dist = zeros(size(Line1X)-1);       % Aquire non-uniform distances
for n = 2:numel(Line1X)         % of points composing the interface
     dist(n-1) = 10*sqrt((Line1X(n)-Line1X(n-1))^2+...
         (Line1Y(n)-Line1Y(n-1))^2);
end

pos = zeros(size(dist));
for n = 1:numel(dist)
    pos(n+1) = pos(n)+dist(n);      % Create vector containing 1D position
                                    % of points composing the interface
end
pos = pos(1:numel(SV))';
len = pos(end);             % Total interface length
step = len/1000;
posLin = (0:step:len)';     % Create vector of 1D position along interface% 
                             % with liner spacing between points

VLin = interp1(pos,SV,posLin);    % Find velocity at positions defined
                                    % in posLin

TDif = zeros(size(VLin));       % Delta t between one position and another
for n = 1:numel(VLin)
        TDif(n) = step/VLin(n);
end
TLin = zeros(size(TDif));
for n=2:numel(TDif)
    TLin(n) = TLin(n-1)+TDif(n);    % Time spent up to corresponding
                                    % position in posLin
end



%% Diffusion
u = @(D,t) sqrt(D/(4*pi*t));       
             
u1 = @(D,X,t) (0.5+0.5*erf(X/sqrt(D*4*t)));     
X = -100:100;                                   

J = zeros(size(TLin));
Profile = zeros(numel(TLin), numel(X(1,:)));
for n = 2:numel(TLin)
    J(n) = u(D, TLin(n));
    Profile(n-1,:) = u1(D,X,TLin(n));
end
Profile = Profile(2:20:numel(TLin), :);
Jloss = trapz(posLin,J)*2*d;      % sum up, weight with gap distance
                                    % and account for symmetry
                                  % see Equation (3) in main paper

Qin = (Qi1/(6))*1E8;              %  Flow of species through 
                                    % injection aperture
Dilution = 100*Jloss/Qin;              % ratio of dilution in %

%% Visualize
Monitor = get(0, 'MonitorPositions');
for n = 1:numel(Monitor(:,1))
    if Monitor(n,1) == 1
        Monitor = Monitor(n,:);
    end
end

p1 = [90 (Monitor(4)-200)/2+110 (Monitor(3)-200)/2,...
    (Monitor(4)-200)/2];
p2 = [(Monitor(3)-200)/2+110 (Monitor(4)-200)/2+110 (Monitor(3)-200)/2,...
    (Monitor(4)-200)/2];
p3 = [90 90 (Monitor(3)-200)/2,...
    (Monitor(4)-200)/2];
p4 = [(Monitor(3)-200)/2+110 90 (Monitor(3)-200)/2,...
    (Monitor(4)-200)/2];

figure(3)
plot(posLin,TLin)
set(gcf, 'Position', p3)
xlim([0 posLin(end)])
title('Time spent up to a point along the interface')
xlabel('Position along interface [10^{-6}m]','Fontsize',11)
ylabel('Time [s]','Fontsize',11)

figure(4)
plot(X,Profile)
set(gcf, 'Position', p4)
title('Evolution of concentration profile perpendicular to interface')
xlabel('Position perpendicular to interface [10^{-6}m]','Fontsize',11)
ylabel('Normalized concentration [10^{-5}m]','Fontsize',11)

figure(1)
hold all
set(gcf, 'Position', p1)
title('HFC Streamlines, Interface highlighted')
fill([53.5;48.5;48.5;53.5],[53.5;53.5;48.5;48.5],[0.7 1 0.7]); % Apertures
fill([63.5;58.5;58.5;63.5],[53.5;53.5;48.5;48.5],[0.7 1 0.7]);
fill([73.5;68.5;68.5;73.5],[53.5;53.5;48.5;48.5],[1 0.7 0.7]);
fill([83.5;78.5;78.5;83.5],[53.5;53.5;48.5;48.5],[1 0.7 0.7]);
streamline(X1);      % Plot streamlines for inner 
Outer = streamline(Y1);             % and outer HFC
xlabel('X position [10^{-5}m]','Fontsize',11)
ylabel('Y position [10^{-5}m]','Fontsize',11)
Outerlines = findobj(Outer,'-property','LineStyle');
        for n=1:length(Outerlines)
            set(Outerlines(n),'LineStyle', ':');
            set(Outerlines(n), 'Color', [0 0 0]);
        end
xlim([20 100])
ylim([20 80])
plot(Line1X,Line1Y,'m','LineWidth', 1) % mark interaface streamline


figure(2)
plot(posLin, VLin)
set(gcf, 'Position', p2)
xlim([0 posLin(end)])
title('Amplitude of velocity along interface')
xlabel('Position along interface [10^{-6}m]','Fontsize',11)
ylabel('Velocity [µm*s^{-1}]','Fontsize',11)

end

%%
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% Function HFC
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% Parameters (with example values):
%    Qi1 = 1;         Inner HFC: Injection flow rate [µl/min]
%    Qa1 = 1;         Inner HFC: Aspiration flow rate [µl/min]   
%    Qi2 = 1;         Outer HFC: Injection flow rate [µl/min]
%    Qa2 = 5;         Outer HFC: Aspiration flow rate [µl/min]
%    d = 20;          Apex-to-surface distance [µm]
% HFC calculates the 2D velocity field between the apex of the MFP head and
% the surface undwer treatment by superimposing single radial flow fields
% generated by a set of apertures
% HFC returnes the cell Res containing the streamline data for the inner
% HFC XY!, the streamline data for the outer HFC XY" and the flied of
% velocity amplitude V
function Res = HFC(QI1, QI2, QA1, QA2, d)

QI1 = (1/6)*1E8*QI1;
QI2 = (1/6)*1E8*QI2;
QA1 = (1/6)*1E8*QA1;
QA2 = (1/6)*1E8*QA2;

% Define function for calculation of radial flow field
 U = @(r, Q) (3*Q/(pi*d^3*r))*(1/6)*d^2;    % Mean V of parabolic profile

[X1,Y1] = meshgrid(1:101,1:101);            % construct meshes
[X111,Y111] = meshgrid(-60:-51,1:101);
[X11,Y11] = meshgrid(51:70,1:101);
X1 = X1-51*ones(101,101);
Y1 = cat(2,Y111,Y1,Y11);
X1 = cat(2,X111,X1,X11);
Y1 = Y1-51*ones(101,131);

[X2,Y2] = meshgrid(1:101,1:101);            
[X22,Y22] = meshgrid(51:80,1:101);
X2 = X2-51*ones(101,101);
X2 = cat(2,X2,X22);
Y2 = cat(2,Y2,Y22);
Y2 = Y2-51*ones(101,131);

[X3,Y3] = meshgrid(1:101,1:101);
[X333,Y333] = meshgrid(-70:-51,1:101);
[X33,Y33] = meshgrid(51:60,1:101);
X3 = X3-51*ones(101,101);
Y3 = cat(2,Y333,Y3,Y33);
X3 = cat(2,X333,X3,X33);
Y3 = Y3-51*ones(101,131);

[X4,Y4] = meshgrid(1:101,1:101);
[X444,Y444] = meshgrid(-80:-51,1:101);
X4 = X4-51*ones(101,101);
X4 = cat(2,X444,X4);
Y4 = cat(2,Y444,Y4);
Y4 = Y4-51*ones(101,131);

for n=1:length(X1(:,1))
    for m=1:length(X1(1,:))
            R1(n,m) = 10*sqrt(X1(n,m)^2+Y1(n,m)^2);
            R2(n,m) = 10*sqrt(X2(n,m)^2+Y2(n,m)^2);
            R3(n,m) = 10*sqrt(X3(n,m)^2+Y3(n,m)^2);
            R4(n,m) = 10*sqrt(X4(n,m)^2+Y4(n,m)^2);
            
            V1 = U(R1(n,m), -QI1);                % Calculate flow field
            V2 = U(R2(n,m), -QI2);              % for each single aperture
            V3 = U(R3(n,m), QA1);
            V4 = U(R4(n,m), QA2);
            
            norm1 = 1/sqrt(X1(n,m)^2+Y1(n,m)^2);
            norm2 = 1/sqrt(X2(n,m)^2+Y2(n,m)^2);
            norm3 = 1/sqrt(X3(n,m)^2+Y3(n,m)^2);
            norm4 = 1/sqrt(X4(n,m)^2+Y4(n,m)^2);
                                            % get the signs right
            V1X(n,m)=-X1(n,m)*norm1*V1;      % and split amplitude of
            V2X(n,m)=-X2(n,m)*norm2*V2;      % velocity in x and y...
            V3X(n,m)=-X3(n,m)*norm3*V3;
            V4X(n,m)=-X4(n,m)*norm4*V4;

            V1Y(n,m)=-Y1(n,m)*norm1*V1;
            V2Y(n,m)=-Y2(n,m)*norm2*V2;
            V3Y(n,m)=-Y3(n,m)*norm3*V3;
            V4Y(n,m)=-Y4(n,m)*norm4*V4;
    end
end

VX = V1X+V2X+V3X+V4X;                     % Overlap velocity matrices
VY = V1Y+V2Y+V3Y+V4Y;

[x1,y1] = meshgrid(59.9:0.25:62.25,49.5:0.25:52.5);     % Seeding points
[x2,y2] = meshgrid(49.9:0.25:52.25,49.5:0.25:52.5); % for streamlines


XY1 = stream2(VX,VY,x1,y1);                 % Generate streamline data
XY2 = stream2(VX,VY,x2,y2);
V = sqrt(VX.^2+VY.^2);
Res = {XY1 XY2 V};
end