# Error using odearguments?

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Matthew Charles on 12 Jul 2022
Edited: Torsten on 12 Jul 2022
Hi, I tried to run the code below but I was greeted with the below error message. Any assistance will be greatly appreciated
function f = emu(t, nd, alpha, mu, D0, Vol, g, L)
%% Oil/Water System at 30C (Paraffin)
% Concentration for this system is 200ppm
lambda = 1;
theta_0 = nd*pi*D0^3 /(6*Vol);
theta_m = nd*pi*(D0+L)^3 /(6*Vol);
ftheta_0 = (1 - theta_0)^5.3;
Delta_rho = 9.98*10^-9 - 7.97*10^-9;
Vst0 = Delta_rho*g*D0^2 /(18*mu); % Settling Velocity in mm/s
D = sqrt((abs((2/3)*alpha*Vst0*ftheta_0/((theta_m/theta_0)^(1/3)-1)*D0*t +D0^2)));
K1 = abs((2/3)*alpha*Vst0^2 *ftheta_0^2 /(D*((theta_m/theta_0)^(1/3)-1)));
dhs = lambda*(K1*t + Vst0*ftheta_0);
dD = lambda*alpha/3 *(Vst0*ftheta_0)/((theta_m/theta_0)^(1/3) - 1) *D0/D;
f = [dhs;dD];
end
USing the following to generate the figure:
clc, clear all, close all
%% Oil/Water System at 30C (Paraffin)
Vol = 900; % Volume for emulsion injected
g = 9810; % mm/s^2 - gravity
L = 0.5e-6; % distance between the surfaces of neighboring bubbles (guessed value)
nd = 1000; % guessed value for no. of bubbles
mu = 3.8; % Viscosity in mPa.s-1
alpha = 0.08;
D0 = 0.3; % converted 300umVst0 = Delta_rho*g*D0^2 /(18*mu);
tspan = [0 180];
hs0 = 225; % in millimeters - initial height
figure
[t,dhs] = ode45(@(t,dhs)emu(t, nd, alpha, mu, D0, Vol, g, L), tspan, hs0);
hs = x(:,1);
plot (t, dhs(:,1), '-o')
grid on
ylabel ('H(mm)')
xlabel ('Time (s)')
title ('Simulation of Sedimentation-Coalesence Experiment')
Unfortunately, I got the following error message:
Error using odearguments
@(T,DHS)EMU(T,ND,ALPHA,MU,D0,VOL,G,L) returns a vector of length 2, but the length of initial conditions vector is 1. The vector returned
by @(T,DHS)EMU(T,ND,ALPHA,MU,D0,VOL,G,L) and the initial conditions vector must have the same number of elements.
Error in ode45 (line 107)
odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);
Error in fig (line 22)
[t,dhs] = ode45(@(t,dhs)emu(t, nd, alpha, mu, D0, Vol, g, L), tspan, hs0);
##### 2 CommentsShowHide 1 older comment
Matthew Charles on 12 Jul 2022
Hi @Torsten it largely deends on the change in droplet diameter (D) with time (t). Should i still switch to "integral" instead of the ODE45 given this case? and if so, I am not sure how to go about that? Any assistance will be appreciated

Torsten on 12 Jul 2022
Edited: Torsten on 12 Jul 2022
syms t
Vol = 900; % Volume for emulsion injected
g = 9810; % mm/s^2 - gravity
L = 0.5e-6; % distance between the surfaces of neighboring bubbles (guessed value)
nd = 1000; % guessed value for no. of bubbles
mu = 3.8; % Viscosity in mPa.s-1
alpha = 0.08;
tspan = [0 18000];
dt = 0.1;
hs0 = 225; % in millimeters - initial height
D0 = 0.3; % converted 300umVst0 = Delta_rho*g*D0^2 /(18*mu);
lambda = 1;
theta_0 = nd*pi*D0^3 /(6*Vol);
theta_m = nd*pi*(D0+L)^3 /(6*Vol);
ftheta_0 = (1 - theta_0)^5.3;
Delta_rho = 9.98*10^-9 - 7.97*10^-9;
Vst0 = Delta_rho*g*D0^2 /(18*mu); % Settling Velocity in mm/s
D = sqrt((abs((2/3)*alpha*Vst0*ftheta_0/((theta_m/theta_0)^(1/3)-1)*D0*t +D0^2)));
K1 = abs((2/3)*alpha*Vst0^2 *ftheta_0^2 /(D*((theta_m/theta_0)^(1/3)-1)));
dhs = lambda*(K1*t + Vst0*ftheta_0);
dD = lambda*alpha/3 *(Vst0*ftheta_0)/((theta_m/theta_0)^(1/3) - 1) *D0/D;
% Integrate dhs
hs = int(dhs,t);
hs = hs0 + hs - subs(hs,t,0);
hs = matlabFunction(hs);
% Use D directly
D = matlabFunction(D);
% Integrate dD to get back D
DD = int(dD,t);
DD = D0 + DD - subs(DD,t,0);
DD = matlabFunction(DD);
% Plot quantities
t = tspan(1):dt:tspan(2)
t = 1×180001
0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 1.1000 1.2000 1.3000 1.4000 1.5000 1.6000 1.7000 1.8000 1.9000 2.0000 2.1000 2.2000 2.3000 2.4000 2.5000 2.6000 2.7000 2.8000 2.9000
figure(1)
plot(t,hs(t))
% Compare D and DD
figure(2)
plot(t,D(t))
hold on
plot(t,DD(t))

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