dm2zp.m

% DM2ZP     Calculate electric mobility from a vector of mobility diameter.
% Author:   Timothy Sipkens, 2019-01-02
% 
% Inputs:
%   d           Particle mobility diameter
%   z           Integer charge state
%   T           System temperature  (Optional, see note 1 below)
%   P           System pressure     (Optional, see note 1 below)
%
% Outputs:
%   Zp          Electromobility
%   B           Mechanical mobility
%
% Notes:
% 1 Temperature (T) and pressure (p) must both be specified before 
%   they are used. Otherwise, they are ignored and the code from Buckley
%   et al. (2017) is used.
% 2 Some of the code is adapted from Buckley et al. (2017) and Olfert 
%   laboratory.
%=========================================================================%

function [B,Zp] = dm2zp(d,z,T,p)


%-- Parse inputs ---------------------------------------------------------%
if ~exist('z','var') % if integer charge state not specified use z = 1
    z = 1;
elseif isempty(z)
    z = 1;
end


%-- Perform calculation --------------------------------------------------%
e = 1.6022e-19; % define electron charge [C]

if nargin<=3 % if P and T are not specified, use Buckley/Davies
    mu = 1.82e-5; % gas viscosity [Pa*s]
    B = Cc(d)./(3*pi*mu.*d); % mechanical mobility
    
else % If P and T are Olfert laboratory / Kim et al.
    S = 110.4; % temperature [K]
    T_0 = 296.15; % reference temperature [K]
    vis_23 = 1.83245e-5; % reference viscosity [kg/(m*s)]
    mu = vis_23 * ((T / T_0) ^ 1.5) * ((T_0 + S)/(T + S)); % gas viscosity
        % Kim et al. (2005), ISO 15900, Eqn 3
    
    B = Cc(d,T,p) ./ (3*pi*mu.*d); % mechanical mobility
    
end
%-------------------------------------------------------------------------%


Zp = B .* e .* z; % electromobility

end


%== CC.m =================================================================%
%   Function to evaluate Cunningham slip correction factor.
%   Author:  Timothy Sipkens, 2019-01-02
function Cc = Cc(d,T,p)
%-------------------------------------------------------------------------%
% Inputs:
%   d           Particle mobility diameter
%   T           System temperature  
%                   (Optional, s)
%   P           System pressure     (Optional, same as above)
%
% Outputs:
%   Zp          Electromobility
%   B           Mechanical mobility
% 
% Note:
% 1 As with above, the temperature (T) and pressure (p) must both be 
%   specified before they are used. Otherwise, they are ignored and the 
%   code from Buckley et al. (2017) is used.
%-------------------------------------------------------------------------%

if nargin==1 % if P and T are not specified, use Buckley/Davies
    mfp = 66.5e-9; % mean free path
    
    % for air, from Davies (1945)
    A1 = 1.257;
    A2 = 0.4;
    A3 = 0.55;
    
else % from Olfert laboratory / Kim et al.
    S = 110.4; % temperature [K]
    mfp_0 = 6.730e-8; % mean free path of gas molecules in air [m]
    T_0 = 296.15; % reference temperature [K]
    p_0 = 101325; % reference pressure, [Pa] (760 mmHg to Pa)
    
    p = p*p_0;
    
    mfp = mfp_0*(T/T_0)^2*(p_0/p)*((T_0+S)/(T+S)); % mean free path
        % Kim et al. (2005) (doi:10.6028/jres.110.005), ISO 15900 Eqn 4
    
    A1 = 1.165;
    A2 = 0.483;
    A3 = 0.997/2;
    
end

Kn = (2*mfp)./d; % Knudsen number
Cc = 1 + Kn.*(A1 + A2.*exp(-(2*A3)./Kn)); % Cunningham slip correction factor

end