Aerosol Particles

(Data from Whitby et al, J. Colloid Interface Sci, 39, 177, 1972)

Suggested Solution

First, we give D and dN from the data in the Table.

However, we also need the limits for the D intervals in order to work out the requested plots. This is a somewhat messy step.

  
D=1.E-6*[0.11 0.14 0.18 0.25 0.35 0.44 0.55 0.66 0.77 0.88 1.05 1.27 ...
1.48 1.82 2.22 2.75 3.30 4.12 5.22];

dN = [1800 1400 1600 1500 360 180 54 22 9.4 5.3 5.2 2.5 1.4 1.4 0.67 ...
0.26 0.11 0.24 0.02] ;

S=pi*dN.*D.^2;        % Surface of particle with diameter D

V=pi*dN.*(D.^3)/6;    % Volume of particle with diameter D


%________________________________________

% Work out the limits for D

dl(1)=0.09E-6;    % Lower limit according to problem
for i=1 :length(D)
  dl(i+1)=2*D(i)-dl(i);
end
dl(i+1)        % Should be close to 5.8E-6 according to text - just for testing

logd=log(D);   % Logarithm used for the plots
dlogd=diff(log(dl));    % delta log(D) to be used for the requested plots
                        % (And in integrals on p77)

%__________________________________________
% Plots of results

subplot(2,2,1)
plot(D,dN./dlogd)
title ('Number of particles of different sizes')
xlabel('D ') 
ylabel('dN/dlog')

subplot(2,2,2)
plot(logd,dN./dlogd)
xlabel('log(D) ') 
ylabel('dN/dlog')


subplot(2,2,3)
plot(logd,S./dlogd)
title ('Surface area')
xlabel('log (D) ') 
ylabel('dS/dlogD')

subplot(2,2,4)
plot(logd,V./dlogd)
title ('Volume')
xlabel('log (D) ') 
ylabel('dV/dlogD')

Ntot=sum(N)
Stot=sum(S)
Vtot=sum(V)         
rho = 1.7E6;              % g/m^3 
masscon=Vtot*rho*1.E12    %to get microgram/m^3