How to fit a equation to a data set?

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.

Answer 1

[Abhi Ove]

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;

Answer 2

[Torsten]

Use lsqnonlin.

Since it minimizes sum_i f(x_i,y_i,p)^2 instead of sum_i (y_i - f(x_i,p))^2, the fit model does not need to be explicit in the dependent variable y_i.

Best wishes

Torsten.