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ʿ�ջ��������� $n_{i}^{\phi}$ �Ȥ�, ����������� $\delta m_{i}^{\phi}$ Υ�줿
�� $m_{i}^{\phi}$ �Τޤ��� 2 ���Υơ��顼Ÿ����Ԥ�. 
($m_{i}^{\phi}$ �ˤ����Ƥ������¸����­���Ƥ���Ȳ��ꤹ��.)


���١����ϰ���, ������֤Ǥ�ʪ���Υ��� $m_{i}$, 
���۵��Τ��ꤷ�����, ʿ�վ��֤Ǥ�ʪ���Υ����ϰʲ��μ�����������. 

\begin{eqnarray}
n_{i}^{\phi} = 
- \Gamma_{i}^{\phi}
+ \left( \frac{n^{\phi}}{m^{\phi}}\right) m_{i}^{\phi}
+ \sum_{e} \chi_{e} a_{ie}^{\phi} m_{i}^{\phi}. \nonumber
\end{eqnarray}

â��, �弰�˴ޤޤ���ѿ� $\chi_{e}, n^{\phi}$ ��
�ʲ��� 2 ����ϢΩ�����뤳�Ȥ�������. 


\begin{eqnarray}
&&\sum_{e} a_{ie}^{\phi} m_{i}^{\phi} \chi_{e} 
= \sum_{i} \Gamma_{i}^{\phi}
\nonumber \\
&&
\sum_{e} 
  \left\{ 
    \sum_{i} \sum_{\phi} a_{ie}^{\phi} a_{if}^{\phi} m_{i}^{\phi}
  \right\} 
  \chi_{e}
+ \sum_{\phi} \sum_{i} a_{if}^{\phi} m_{i}^{\phi}
  \left( 
     \frac{n^{\phi}}{m^{\phi}}
  \right) 
= \sum_{i}\sum_{\phi} a_{if}^{\phi} \Gamma_{i}^{\phi} + B_f
\nonumber 
\end{eqnarray}

��, ��� $\Gamma_{i}^{\phi}$ �ϰʲ�����������. 

\begin{eqnarray}
\Gamma_{i}^{\phi}
= m_{i}^{\phi}
  \left[
    \frac{{\mu_{i}^{\circ}}^{\phi}}{RT} 
    + \ln{\frac{m_{i}^{\phi}}{m^{\phi}}} 
    + \alpha \ln{p} 
  \right]. \nonumber
\end{eqnarray}

\begin{eqnarray}
m_{i}^{\phi} 
\left( \ln{\frac{m_{i}^{\phi}}{m^{\phi}}}  \right)
\rightarrow
\frac{m_{i}^{\phi}}{m^{\phi}} 
\left( \ln{\frac{m_{i}^{\phi}}{m^{\phi}}}  \right)
\nonumber
\end{eqnarray}

\end{document}


