| 443 |
|
\begin{figure} |
| 444 |
|
\includegraphics[width=\linewidth]{bComicStrip} |
| 445 |
|
\caption{\label{fig:bComic} The basal interface with a shear rate of |
| 446 |
< |
XXXX. Lower panel: the local tetrahedral order parameter, $q(z)$, |
| 446 |
> |
1.3 ms\textsuperscript{-1}. Lower panel: the local tetrahedral order parameter, $q(z)$, |
| 447 |
|
(black circles) and the hyperbolic tangent fit (red line). Middle |
| 448 |
|
panel: the imposed thermal gradient required to maintain a fixed |
| 449 |
|
interfacial temperature. Upper panel: the transverse velocity |
| 455 |
|
\begin{figure} |
| 456 |
|
\includegraphics[width=\linewidth]{pComicStrip} |
| 457 |
|
\caption{\label{fig:pComic} The prismatic interface with a shear rate |
| 458 |
< |
of XXXX. Panel |
| 458 |
> |
of 2.0 ms\textsuperscript{-1}. Panel |
| 459 |
|
descriptions match those in figure \ref{fig:bComic}} |
| 460 |
|
\end{figure} |
| 461 |
|
|
| 596 |
|
$\tau_{middle}$, and $\tau_{long}$ at large displacements from the |
| 597 |
|
interface. Second, there appears to be a single distance, $d_{basal}$ |
| 598 |
|
or $d_{prismatic}$, from the interface at which all three decay times |
| 599 |
< |
begin to deviate from their bulk liquid values. We find these |
| 600 |
< |
distances to be approximately 15~\AA\ and 8~\AA\, respectively, |
| 601 |
< |
although significantly finer binning of the $C_2(t)$ data would be |
| 602 |
< |
necessary to provide better estimates of a ``dynamic'' interfacial |
| 603 |
< |
thickness. |
| 599 |
> |
begin to deviate from their bulk liquid values. To quantify this |
| 600 |
> |
distance, each of the decay constant $z$-profiles were fit to |
| 601 |
> |
\begin{equation}\label{tauFit} |
| 602 |
> |
\tau(z)\approx\tau_{liquid}+(\tau_{solid}-\tau_{liquid})e^{-(z-z_{wall})/d} |
| 603 |
> |
\end{equation} |
| 604 |
> |
where $\tau_{liquid}$ and $\tau_{solid}$ are the liquid and projected |
| 605 |
> |
solid values of the decay constants, $z_{wall}$ is the location of the |
| 606 |
> |
interface, and $d$ is the displacement the deviations occur at (see |
| 607 |
> |
Figures \ref{fig:basal_Tau_comic_strip} and |
| 608 |
> |
\ref{fig:prismatic_Tau_comic_strip}). The displacements $d_{basal}$ |
| 609 |
> |
and $d_{prismatic}$ were determined for each of the three decay |
| 610 |
> |
constants, and then averaged for better statistics. |
| 611 |
> |
For the basal system, we found $d_{basal}$ for the control set to be |
| 612 |
> |
2.9 \AA\, and 2.8 \AA\ for a simulation with a shear rate of 1.3 |
| 613 |
> |
ms\textsuperscript{-1}. We found $d_{prismatic}$ to be slightly |
| 614 |
> |
larger than $d_{basal}$ for both the control and an applied shear, |
| 615 |
> |
with displacements of 3.6 \AA\ for the control system and 3.5 \AA\ for |
| 616 |
> |
a simulation with a 2 ms\textsuperscript{-1} shear rate. From this we |
| 617 |
> |
can conclude there is no apparent dependence on the shear rate for the dynamic interface |
| 618 |
> |
width. |
| 619 |
|
|
| 620 |
+ |
%%%%%%%%Should we keep this paragraph???%%%%%%%%%%%%%%% |
| 621 |
|
Beaglehole and Wilson have measured the ice/water interface using |
| 622 |
|
ellipsometry and find a thickness of approximately 10~\AA\ for both |
| 623 |
|
the basal and prismatic faces.\cite{Beaglehole93} Structurally, we |
| 624 |
|
have found the basal and prismatic interfacial width to be |
| 625 |
< |
3.2~$\pm$~0.4~\AA\ and 3.6~$\pm$~0.2~\AA. However, decomposition of |
| 626 |
< |
the spatial dependence of the decay times of $C_2(t)$ indicates that a |
| 627 |
< |
somewhat thicker interfacial region exists in which the orientational |
| 628 |
< |
dynamics of the water molecules begin to resemble the trapped |
| 629 |
< |
interfacial water more than the surrounding liquid. |
| 625 |
> |
3.2~$\pm$~0.4~\AA\ and 3.6~$\pm$~0.2~\AA. Decomposition of |
| 626 |
> |
the spatial dependence of the decay times of $C_2(t)$ shows good |
| 627 |
> |
agreement with the structural interfacial width determined by the |
| 628 |
> |
local tetrahedrality. |
| 629 |
> |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 630 |
|
|
| 615 |
– |
Our results indicate that the dynamics of the water molecules within |
| 616 |
– |
$d_{basal}$ and $d_{prismatic}$ are being significantly perturbed by |
| 617 |
– |
the interface, even though the structural width of the interface via |
| 618 |
– |
analysis of the tetrahedrality profile indicates that bulk liquid |
| 619 |
– |
structure of water is recovered after about 4 \AA\ from the edge of |
| 620 |
– |
the ice. |
| 631 |
|
|
| 632 |
|
\subsection{Coefficient of Friction of the Interface} |
| 633 |
|
As liquid water flows over an ice interface, there is a distance from |
| 710 |
|
liquid (dashed red line) intersects the solid phase velocity (solid |
| 711 |
|
black line). The dotted line indicates the location of the ice as |
| 712 |
|
determined by the tetrahedrality profile. This example is taken |
| 713 |
< |
from the basal-face simulation with an applied shear rate of XXXX.} |
| 713 |
> |
from the basal-face simulation with an applied shear rate of 3.0 ms\textsuperscript{-1}.} |
| 714 |
|
\end{figure} |
| 715 |
|
|
| 716 |
|
|
| 745 |
|
proximity to the interface. There is also an apparent dynamic |
| 746 |
|
interface width, $d_{basal}$ and $d_{prismatic}$, at which these |
| 747 |
|
deviations from bulk liquid values begin. We found $d_{basal}$ and |
| 748 |
< |
$d_{prismatic}$ to be approximately 15~\AA\ and 8~\AA\ . This implies |
| 749 |
< |
that the dynamics of water molecules which have similar structural |
| 750 |
< |
environments to liquid phase molecules are dynamically perturbed by |
| 751 |
< |
the presence of the ice interface. |
| 748 |
> |
$d_{prismatic}$ to be approximately 2.8~\AA\ and 3.5~\AA\ . This |
| 749 |
> |
interfacial width is in good agreement with values determined by the |
| 750 |
> |
structural analysis of the interface, by the hyperbolic tangent fit of |
| 751 |
> |
the local tetrahedral order parameter. |
| 752 |
|
|
| 753 |
|
The coefficient of liquid-solid friction for each of the facets was |
| 754 |
|
also determined. They were found to be |
