How to change values in previous made loop?

Hi everyone,

I am trying to model a centrifuge with higher concentrations. My problem is that the formed pellet in a centrifuge can only have a certain volumetric fraction (cmax). I made a loop where the volumetric fraction is calculated. At the end of the centrifuge it will give values higher than cmax. Now, I want to give the excess back to the previous cell when cmax is reached. For this, I made a small loop, which calculates backwards from the end of the centrifuge to the beginning:

for i = Nr:-1:2         % Force system to give back excess to previous cells
    c(i) = c(i)+excess;
    if c(i)>cmax
    excess = c(i)-cmax;
    c(i) = cmax;
    c(i-1) = c(i-1)+excess;
    else
        excess = 0;
    end
end

However, my code seems to ignore this loop. Without this loop, I get the same values as without it and I am puzzled why.

I also added the files I work with.

Thank you very much in advance!

Answer 1

[Shubh Dhyani]

Hi Jort,

I understand that you are having a problem with updating the values in your code through a loop.

It seems that the main logic for the centrifugation process is contained in two files: “odepaper.m”, which defines the ordinary differential equation (ODE) system, and “centrifugation.m”, which sets up the parameters and solves the ODE using ode45.

I noticed that the loop you are referring to in “odepaper.m” attempts to modify the concentration c(i) by giving back excess to the previous cells. However, this modification is done after the calculation of the derivatives “dcdt” and does not affect the output of the function. Consequently, the ode45 solver, which calls “odepaper”, does not see the changes made in the loop.

To address this, you may need to modify the function to take into account the excess concentration during the calculation of the derivatives dcdt.

The key change is to move the loop that handles excess concentrations before the calculation of the derivatives. This will ensure that the excess concentrations are properly redistributed among the cells before the derivatives are computed.

Here’s the modified “odepaper.m” file,

function [dcdt] = odepaper(t, c, Nr, dr, vgs, cmax, cini, n)

    dcdt = zeros(Nr,1);
    r = zeros(Nr,1);
    v = zeros(Nr,1);
    excess = 0;
    
    %% Mass replacement
    for i = Nr:-1:2 % Force system to give back excess to previous cells
        c(i) = c(i) + excess;
        if c(i) > cmax
            excess = c(i) - cmax;
            c(i) = cmax;
            c(i-1) = c(i-1) + excess;
        else
            excess = 0;
        end
    end
    
    %% Loop
    for i = 2:Nr
        r(i) = r(i-1) + dr;
        v(i) = (1 - c(i))^n * vgs;
        vin = (1 - cini)^n * vgs;
        rin = 0.5 * dr;
        if i == 1 % Initial conditions
            dcdt(1) = (1/dr) * ((rin * cini * vin) / r(i) - c(i) * v(i));
        elseif i == Nr % Wall conditions
            dcdt(Nr) = (1/dr) * ((r(i-1) * c(i-1) * v(i-1)) / r(i)) + excess;
        else % Everything in between
            dcdt(i) = (1/dr) * ((r(i-1) * c(i-1) * v(i-1)) / r(i) - c(i) * v(i)) + excess;
        end
    end
end

I moved the section handling excess concentrations to the beginning of the function, so that it modifies the concentrations "c" before the derivatives "dcdt" are computed.