MATLAB: How to fit a equation to a data set

curve fittingMATLABnonlinear

Hi I am trying to fit an equation to a set of data extracted from a paper as shown below.
The data set contains particle concentration, phi, across a gap of radius, R. The data for phi and R are given below.
I am trying to fit the equation 16 to the data set provided. I am at a complete loss as to how to fit an equation to a set of data where phi® is on the both side of the equation. I have fitted data to equation before. However it was always y = something….. . What do I do for these type of equation where the curve fitting tool can not be used?
Any help or guidance towards how I can learn move about these sort of fitting will be very much appreciated.
phi(Ri) = phi(1);
Ri = R(1);
n = 2;
phiM = 0.68
Kc / Ku = fitting parameters.
R = [4.47 4.59 4.69 4.81 4.92 5.02 5.13 5.24 5.35 5.46 5.57 5.68];
phi = [0.569 0.570 0.573 0.576 0.578 0.581 0.585 0.589 0.593 0.595 0.598 0.602];
Many thanks.

Best Answer

Hi, this is the final solution for this fit that I have implemented. Please do ask if you have any questions.
%% parameters known:
phi_Ri = xxx;
phiM = xxx;
Ri = xxx;
n = xxx;
% the model is implemented as follows:
F = @(x,y,kk) ((x/Ri).^2).*((1-phi_Ri/phiM)./(1-y/phiM)).^(n*(1-kk)) - (y/phi_Ri);% Min search based on norm, with initial guess KuKcMin = 1
%

KuKcMin = fminsearch(@(KuKc) norm(F(R,phi,KuKc)), 1);
%
Kc_Ku_fit = 1/ KuKcMin;
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