tested tutorial 4

Author: simongravelle

figures/NANOSHEAR-minimization.png

@@ -8,8 +8,8 @@ units real
 atom_style full
 bond_style harmonic
 angle_style harmonic
-pair_style lj/cut/tip4p/long O H O−H H−O−H 0.1546 12.0
-kspace_style pppm/tip4p 1.0e−5
+pair_style lj/cut/tip4p/long O H O-H H-O-H 0.1546 12.0
+kspace_style pppm/tip4p 1.0e-5
 kspace_modify slab 3.0
 
 read_data create.data
@@ -19,7 +19,7 @@ include groups.inc
 
 fix mynve fluid nve/limit 0.1
 fix myber fluid temp/berendsen 1 1 100
-fix myshk H2O shake 1.0e−5 200 0 b O−H a H−O−H
+fix myshk H2O shake 1.0e-5 200 0 b O-H a H-O-H
 timestep 0.5
 
 dump mydmp all image 200 myimage-*.ppm type type &
@@ -28,7 +28,7 @@ dump_modify mydmp backcolor white &
   acolor O red adiam O 2 &
   acolor H white adiam H 1 &
   acolor Na+ blue adiam Na+ 2.5 &
-  acolor Cl− cyan adiam Cl− 3 &
+  acolor Cl- cyan adiam Cl- 3 &
   acolor WALL gray adiam WALL 3
 
 compute Tfluid fluid temp

figures/NANOSHEAR-profiles.png

@@ -8,8 +8,8 @@ units real
 atom_style full
 bond_style harmonic
 angle_style harmonic
-pair_style lj/cut/tip4p/long O H O−H H−O−H 0.1546 12.0
-kspace_style pppm/tip4p 1.0e−5
+pair_style lj/cut/tip4p/long O H O-H H-O-H 0.1546 12.0
+kspace_style pppm/tip4p 1.0e-5
 kspace_modify slab 3.0
 
 read_data equilibrate.data
@@ -25,22 +25,22 @@ compute Twall wall temp/partial 0 1 1
 fix mynvt2 wall nvt temp 300 300 100
 fix_modify mynvt2 temp Twall
 
-fix myshk H2O shake 1.0e−5 200 0 b O−H a H−O−H
+fix myshk H2O shake 1.0e-5 200 0 b O-H a H-O-H
 fix myrct all recenter NULL NULL 0
 timestep 1.0
 
 fix mysf1 walltop setforce 0 NULL NULL
 fix mysf2 wallbot setforce 0 NULL NULL
-velocity wallbot set −2e−4 NULL NULL
-velocity walltop set 2e−4 NULL NULL
+velocity wallbot set -2e-4 NULL NULL
+velocity walltop set 2e-4 NULL NULL
 
 dump mydmp all image 250 myimage-*.ppm type type &
   shiny 0.1 box no 0.01 view 90 0 zoom 1.8
 dump_modify mydmp backcolor white &
   acolor O red adiam O 2 &
   acolor H white adiam H 1 &
   acolor Na+ blue adiam Na+ 2.5 &
-  acolor Cl− cyan adiam Cl− 3 &
+  acolor Cl- cyan adiam Cl- 3 &
   acolor WALL gray adiam WALL 3
 
 thermo 250
@@ -58,4 +58,4 @@ fix myac2 wall ave/chunk 10 15000 200000 &
 fix myac3 ions ave/chunk 10 15000 200000 &
   cc3 density/mass vx file shearing-ions.dat
 
-!run 200000
+run 200000

files/tutorial4/solution/minimize.ipynb

@@ -2347,7 +2347,7 @@ \subsubsection{System preparation}
 Therefore, to make the walls less hydrophilic, the value of $\epsilon_\text{O-WALL}$
 was reduced.
 
-The \flecmd{parameters.inc} file also contains the following two lines:
+Finally, the \flecmd{parameters.inc} file contains the following two lines:
 \begin{lstlisting}
 bond_coeff O-H 0 0.9572
 angle_coeff H-O-H 0 104.52
@@ -2732,38 +2732,48 @@ \subsubsection{Imposed shearing}
 the water, the walls, and the ions, respectively.  With values of \lmpcmd{10 15000 200000},
 the velocity \lmpcmd{vx} will be evaluated every 10 steps during the final 150,000
 steps of the simulations.  The result will be averaged and printed only once at the 200,000\,th step.
-Run the simulation using LAMMPS.  The averaged velocity and density
-profiles of the fluid are plotted in Fig.~\ref{fig:NANOSHEAR-profiles}.
-As expected for such Couette flow geometry, the fluid velocity increases linearly along $z$.
+Run the simulation using LAMMPS.  The averaged velocity
+profile for the fluid is plotted in Fig.~\ref{fig:NANOSHEAR-profiles}.
+As expected for such Couette flow geometry, the fluid velocity increases
+linearly along $z$, and is equal to the walls velocities at the fluid-solid
+interfaces (no-slip boundary conditions).
 
 \begin{figure}
 \centering
 \includegraphics[width=\linewidth]{NANOSHEAR-profiles}
-\caption{a) Water density $\rho$ along the $z$-axis as
-simulated in \hyperref[sheared-confined-label]{Tutorial 4}.
-b) Velocity profiles for water (blue) and walls
-(orange) along the $z$-axis.}
+\caption{Velocity profiles for water (blue) and walls (orange) along the $z$-axis as
+simulated in \hyperref[sheared-confined-label]{Tutorial 4}.}
 % The line is a linear fit assuming
 % that the pore size is $h = 1.8\,\text{nm}$.}
 \label{fig:NANOSHEAR-profiles}
 \end{figure}
 
 From the force applied by the fluid on the solid, one can extract the stress
 within the fluid, which enables the measurement of its viscosity $\eta$
-according to $\eta = \tau / \dot{\gamma}$ where $\tau$ is the stress applied by
+according to
+\begin{equation}
+\eta = \tau / \dot{\gamma}
+\label{eq:eta}
+\end{equation}
+where $\tau$ is the stress applied by
 the fluid on the shearing wall, and $\dot{\gamma}$ the shear rate
 \cite{gravelle2021violations}.  Here, the shear rate is
-approximately $\dot{\gamma} = 16 \cdot 10^9\,\text{s}^{-1}$, and using a
-surface area of $A = 6 \cdot 10^{-18}\,\text{m}^2$, one obtains an estimate for
-the shear viscosity for the confined fluid of $\eta = 6.6\,\text{mPa.s}$.  The
-viscosity calculated at such a high shear rate may differ from the expected
+approximately $\dot{\gamma} = 20 \cdot 10^9\,\text{s}^{-1}$ (Fig.~\ref{fig:NANOSHEAR-profiles}),
+the average force on each wall is given by \lmpcmd{f\_mysf1[1]} and \lmpcmd{f\_mysf2[1]}
+and is approximately $2.7\,\mathrm{kcal/mol/\AA}$ in magnitude.  Using a surface area
+for the walls of $A = 6 \cdot 10^{-18}\,\text{m}^2$, one obtains an estimate for
+the shear viscosity for the confined fluid of $\eta = 3.1\,\text{mPa.s}$ using Eq.~\eqref{eq:eta}. 
+
+\begin{note}
+The viscosity calculated at such a high shear rate may differ from the expected
 \emph{bulk} value.  In general, it is recommended to use a lower value for the
 shear rate.  Note that for lower shear rates, the ratio of noise-to-signal is
 larger, and longer simulations are needed.  Another important point to consider
 is that the viscosity of a fluid next to a solid surface is typically larger
 than in bulk due to interaction with the walls~\cite{wolde-kidanInterplayInterfacialViscosity2021}.
 Therefore, one expects the present simulation to yield a viscosity that is slightly
 higher than what would be measured in the absence of walls.
+\end{note}
 
 \subsection{Tutorial 5: Reactive silicon dioxide}
 \label{reactive-silicon-dioxide-label}