Units

Notation

We use the following definitions:
Command double string
hunits \(l\) l_unit
temp \(T\) T_unit
mass \(m\) m_unit
viscosity \(\eta\) \(\mathbf{\eta}\)_unit

Properties with length scaling

If the units of the output is length to the \(x\) power, and \(r\) is the result prior to unit conversion, then the output is

\(r \cdot l^x\) l_unit\(^x\).

Intrinsic viscosity with mass units

If l_unit = L, then

\([\eta]_{m}=q_\eta \langle\alpha\rangle/m \cdot l^3\) l_unit\(^3\)/m_unit

else

\([\eta]_{m}=q_\eta \langle\alpha\rangle/m \cdot l^3 a_{l}^3 a_{m}\) cm\(^3\)/g.

Friction coefficient

If l_unit is different than L, then

\(f = 6\pi\eta R_H \cdot 10^{-2} l a_l a_\eta\) dyne\(\cdot\)s/cm.

Diffusion coefficient

If l_unit is different than L, then

\(D = k_{B}(T + a_T)/(6\pi\eta R_H) \cdot 10^{9} l^{-1} a_l^{-1} a_\eta^{-1}\) cm\(^2\)/s.

Sedimentation coefficient

If l_unit is different than L, then

\(s = mb/(6\pi\eta R_H) \cdot 10^{15} l^{-1} a_l^{-1} a_\eta^{-1} a_m^{-1}\) Sved.

Conversion tables

l_unit \(a_{l}\) uncertainty
m 100 0
cm 1 0
nm \(10^{-7}\) 0
A \(10^{-8}\) 0

T_unit \(a_{T}\) uncertainty
C 273.15 0
K 0 0

m_unit \(a_{m}\) uncertainty
Da \(6.02214 \cdot 10^{23}\) \(10^{18}\)
kDa \(6.02214 \cdot 10^{20}\) \(10^{15}\)
g \(1\) 0
kg \(10^{-3}\) 0

\(\eta\)_unit \(a_{\eta}\) uncertainty
cP 1 0
P 100 0

\(k_B\) uncertainty
\(1.38065 \cdot 10^{-23}\) \(10^{-28}\)