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SEDIMENTATION, CREAMING, CENTRIFUGATION AND DIFFUSION

Sedimentation volume ( $ V_$sed) or cream volume ( $ V_$cr) is the volume of sediment or cream formed in a suspension or emulsion. If the sediment is formed in a centrifugal field, the strength of this field should be explicitly indicated, otherwise normal gravity is understood.

Sedimentation equilibrium is the equilibrium between sedimentation and diffusion.

Rate of sedimentation is the velocity of sedimentation ( $ v_$sed or $ v$).

Sedimentation coefficient ($ s$) is the rate of sedimentation divided by acceleration, expressed in seconds () or in Svedbergs (Sv); Sv $ = 10^{-13}$.

Limiting sedimentation coefficient, $ [s]$, is the sedimentation coefficient extrapolated to zero concentration of the sedimenting component,

$\displaystyle [s]=\lim_{c\to0}s.$

Reduced sedimentation coefficient, $ s^0$ (20)25 is the sedimentation coefficient reduced to a standard temperature, usually 20 and to a standard solvent, usually water.

$\displaystyle s^0(20\celsius)=s(t)\frac{{\eta}(t)}{{\eta}^0(20\celsius)}{\cdot}
\frac{1-v_s(20\celsius){\rho}^0(20\celsius)}{1-v_s(t){\rho}(t)},$

where $ {\eta}(t) =$ coefficient of viscosity of the solution at temperature $ t$,
$ {\eta}^0(20\celsius)=$ coefficient of viscosity of standard solvent at 20,
$ v_s(t) =$ partial specific volume of sedimenting substance at temperature $ t$,
$ {\rho}(t) =$ density of solution at temperature $ t$,
$ {\rho}^0(20\celsius) =$ density of the standard solvent at 20.

Reduced limiting sedimentation coefficient, $ [s^0(20\celsius)]$, is the reduced sedimentation coefficient extrapolated to zero concentration of the sedimenting component:

$\displaystyle [s^0(20\celsius)] = \lim_{c\to0}s^0(20\celsius),$

Differential diffusion coefficient, $ D_i$, of species $ i$ is defined by

$\displaystyle D_i = -\bm{J}_i/$grad $\displaystyle c_i,$

where $ \bm{J}_i$ is the amount of species $ i$ flowing through unit area in unit time and grad $ c_i$ is the concentration gradient of species $ i$. Different diffusion coefficients may be defined depending on the choice of the frame of reference used for $ \bm{J}_i$ and grad $ c_i$. For systems with more than two components, the flow of any component and hence its diffusion coefficient depends on the concentration distribution of all components.

Limiting differential diffusion coefficient, $ [D_i]$, is the value of $ D_i$ extrapolated to zero concentration of the diffusing species:

$\displaystyle [D_i] = \lim_{c_i\to0} D_i.$

Self-diffusion coefficient, $ D^*_i$, of species $ i$ is the diffusion coefficient in the absence of a chemical potential gradient. It is related to the diffusion coefficient $ D_i$ by

$\displaystyle D^*_i=D_i\frac{{\partial}\ln c_i}{{\partial}\ln a_i},$

where $ a_i$ is the activity of $ i$ in the solution. If an isotopically labelled species ($ i^*$) is used to study diffusion, the tracer diffusion coefficient, $ D_{i^*}$ is practically identical to the self-diffusion coefficient provided that the isotope effect is sufficiently small.

Rotational diffusion coefficient, $ D_{\theta}$, is defined by the equation:

$\displaystyle D_{\theta}=\frac{t_{\theta}}{\left\{{\partial}f({\theta},{\varphi})/{\partial}{\theta}\right\}\sin{\theta}}$

where $ f({\theta},{\varphi})\sin{\theta}$d$ {\theta}$d$ {\varphi}$ is the traction of particles whose axes make an angle between $ {\theta}$ and $ {\theta}+$d$ {\theta}$ with the direction $ {\theta}= 0$, and have an azimuth between $ {\varphi}$ and $ {\varphi}+$   d$ {\varphi}$; $ t_{\theta}$d$ {\varphi}$ is the fraction of particles having an azimuth between $ {\varphi}$ and $ {\varphi}+$   d$ {\varphi}$, whose axis passes from values $ <{\theta}$ to values $ >{\theta}$ in unit time. The axis whose rotational diffusion is considered has to be clearly indicated.


next up previous contents
Next: ELECTROCHEMICAL TERMS IN COLLOID Up: DEFINITIONS AND TERMINOLOGY Previous: ATTRACTION AND REPULSION   Contents
2002-09-05