Purdue Engineering Faculty Colloquium: Dr. Michael Harris

Purdue Engineering Faculty Colloquium: Dr. Michael Harris

August 15, 2019 0 By Stanley Isaacs


OK. We’d like to welcome
everybody here this afternoon for our
latest celebration. If you’d like to take
your seats right now– the food will be
there afterwards. And then we can get started. We are focused this afternoon
on Professor Michael Harris. This program– The Celebration
of Faculty Careers– was actually started by the
college a couple of years ago. And it gives the opportunity
for individual faculty to sort of reflect
back over their careers and sort of see the
directions that they may be headed into the future,
or what might be intriguing for them to start anew. So this afternoon,
Dr. Harris is going to be looking over
his research career. But I’d first like to say a
few words to introduce him, for anyone who doesn’t
have all of his background. So Mike Harris, now, is the
Associate Dean for Engagement and Undergraduate Education,
as well as the Reilly Professor of Chemical Engineering
and Professor of Environmental and Ecological
Engineering in the college on the West Lafayette campus. He was actually a Purdue
University faculty scholar from 2002 to 2007 and
served as Programming Chair and Chair of the ASCE Minority
Division from 2011 to 2014. He was named a fellow
of AIChE in 2009. And he won the AIChE
Grimes Award for Excellence in Chemical Engineering in 2005
and the AIChE Minority Affairs Distinguished Service
Award in 2009. So he’s been a busy guy. He’s the author of 97
peer-reviewed publications and 11 patents. He actually– going
back– he received his BS in chemical engineering
from Mississippi State. And both his MS and PhD
degrees in chemical engineering from the University
of Cincinnati. Dr. Harris’s research is in the
area of nanomaterials, coloids and interfacial phenomena–
transport phenomena, particle science and technology,
microwave sensing of pharmaceutical
powders, solidification of drug excipient matrices,
environmental control technology, and
electrodispersion precipitation processes. So today, he’s going
to take us back a bit to a particular aspect
of his research activities of which he’s particularly fond. Dr. Harris. [APPLAUSE] Thank you. I hope you can hear me. They put a mic on
me, and I think my voice is loud enough to be
heard outside of a building without a mic. So let’s see how this goes. So today, I’ll talk about
metal coated biotemplates and particle deposition
during droplet evaporation. And first, I’ll start
off by giving you a brief overview of some
of my research projects that I’ve had in the
past that have actually led to me getting
to the point where I’m looking at
these biotemplates and looking at drop evaporation. Before I get
started, I would like to show you this
quote from– I think it was the 100th centennial
celebration for the department. And this was the
description that a man of great wisdom, Phil Wankat,
put in there about me. First he said that I
was– first of all, shown with another professor
from engineering education. The next thing he
says is that he’s “interested in everything.” And if you heard the description
of my research areas, that kind of summed it up. I do have kind of a wide
interest in many things. And the last thing he said is
that I’m “unable to say no.” And therefore, I ended up
being the Associate Dean for Undergraduate Education. I also was not able
to say no and ended up giving this presentation today. So yeah. So here’s a brief outline
of the presentation. I’ll give you a brief
historical overview of some of the
research activities that have occurred in my group. Then I’ll give you two more
in-depth presentations. One on metal coated biotemplates
and the other on particle deposition during
drop evaporation. These are some projects that
we’re currently working on and have worked on
for a little while. And then the last thing
that I’ll talk to you about is my future fun, or
future research projects. As a matter of fact, given the
title of this presentation, I almost decided to call
it Having Great Fun, because that’s the way I
view my research career. So the first thing that
I want to talk about is the dynamics of nanophase
formation and growth. And this is a creation
of the [INAUDIBLE]. In particular, I’m looking
at the formation of silica nanoparticles from
tetraethyl orthosilicate and carrying out that reaction
under basic conditions in an alcohol. The researchers that work
with me to contribute on this was David Green, one of my
former graduate students. And Hacene Boukari,
a postdoc who had math skills that
were out of this world. My math skills are
still in this world. But we worked on this from
about 1996 until 2003. And one of the
questions that was asked is how do these nanoparticles–
these very monodispersed nano silica particles form and grow? And there was a debate. One where one group said
the very small particles– one to two nanometer
particles– formed. And then they would
aggregate to form these very nice looking particles. And they are beauties. They really are. Every time I see these
particles, I get emotional. Now– oh, I’m supposed
to behave myself. I’m sorry. And another group
used cryo-TEM to show that the first particles
were about 20 nanometers in diameter. And so that debate kind
of went on for a while. And then I came on the scene. And decided, well, let’s look
at the hydrolysis of the TEOS and condensation of the TEOS
and see what species we can detect using silicon 29 NMR. And what we found is–
sure enough, what you see is the unhydrolized
TEOS silica [INAUDIBLE]. Particles. We looked at– the kinetic
data for that showed and we observed
the disappearance of the TEOS and
formation disappearance of the first [INAUDIBLE]. This is the TEOS curve here. And ethynol is a solvent. And then, another [INAUDIBLE]
using the ethynol as a solvent, the [INAUDIBLE]
disappearance of the TEOS. You can also see the first
hydrolized monitoring increase. In both cases, increases
and then kind of decreased somewhat. And then we [INAUDIBLE]
this is the place where we see the curve
side of particle formation. So using small-angle
electric scattering to look at the particle
growth, as well as looking at the slow-angle
growth tells you something about whether or not the particle is
kind of a fluffy type of object that’s doesn’t have a
particularly high density, to where it goes all
the way up to four, in the case of methanol. And at that
particular point, you have a spherical particle
that has a smooth surface and where it’s a solid–
pretty much a solid sphere. So these were some
of the things we’re able to get from the
small-angle electric scattering. So the cryo-TEM
[INAUDIBLE] particle was kind of a low
density particle. And sure enough,
X-ray scattering also showed that, indeed, the
particle– particularly, the low density particle
that intensified over time. And then, from these plots,
you can look at the [INAUDIBLE] and say something about the size
of the particles [INAUDIBLE]. And these are some data
showing the first particle that appears in ethanol,
the first particle that appears in methanol, where
the particle in ethanol gets bigger. It gets almost twice the size
of the first particle that we see coming out as methanol. And using the other data
on dynamic scattering, the results that measure
the hyrdrodynamic rate is. And if you look at the
data, the wide scattering and the small-angle
X-ray scattering results are consistent. So we answered that question of
looking at the first particles. Those very small nanometric
particle– one, two nanometer particle– one that
[INAUDIBLE] a 10 nanometer type particle, we
were able to answer that question, who’s right? The first person that talked
about the very small particles or the cryo-TEM? And the cryo-TEM
work was correct. And so we were able [INAUDIBLE]. Also used SAXS to look at the
particle size and [INAUDIBLE] scattering. So, as you can see, this work
was done quite some years ago. Almost 20 years ago. And the next thing I looked
at was these metal alkoxides, that are very fast reactions. And what I decided to do was
use rapid mixing techniques and continuous
flow-through experiments to measure the kinetics
of the hydraulics and the connotations
of these reactions. So once again, you have
the hydrolysis reaction and you also have
condensation reactions, where you release water or
you release the alcohol. So in a lot of the
papers I read [INAUDIBLE] look at the hydrolysis
and condensation kinetics, they used gel time
measurements to say something about the hydrolysis and
condensation reaction. Well, that’s a pretty old
technique for doing this. And I wanted to get
a better picture of the removal of the alkoxy
group with hydrolysis reaction. And also, get a
better understanding of the mechanics
of the formation of the nanostructures. So, once again, I used
spectroscopy and small-angle X-ray scattering. So this is a simple
technique that I use where we have a solution
of alkoxide and solvent. And hydrosolvent. And water and solvent. Also, sometimes we put an
acid in this system over here and mix these two in
a mixing T and then allow it to flow into
[INAUDIBLE] and then measure either through the FTR toward
with the small-angle X-ray scattering measurements, some
distance away from the mixing T. And with that, you can
get phonetic information. So these are the data
that we’re able to get. So we’re able to take
our first measurement in about 80 milliseconds. And we’re looking at
the water remaining in the reaction divided by the
initial concentration of water, and that quickly dropped about
0.8 in about 8 milliseconds. And then the alkoxy group–
about 60% of the alkoxy groups were removed with that
first [INAUDIBLE] as well. And so what I show over
here is, basically, what happens if you do the
first hydrolysis of water– what the water ratio
should be– 0.91. And if two water molecules are
reacting with the alkoxide, how much water should
remain, and so forth. All the way down–
if all four water molecules– if all four of the
alkoxy groups are hydrolyzed. One of the issues
is– typically, the first couple
of hydroxyl groups can come off very
quickly, but the other’s a little bit stubborn. So they don’t come off as fast. But what this shows is
for zirconium alkoxide– in this case, it was
zirconium butoxide– you see a very fast hydrolysis. And you see where, probably,
90% plus of the alkoxy groups are removed. If you look at
the water, you can see that the water basically
stays about the same. Which means that, initially,
you get a very fast hydrolysis of the first two alkoxy
groups, but then, later on, you have the condensation. The alcoho-produced
condensation reaction occurring. We also looked at
titanium ethoxide. And looked at how that
concentration varied both the water, shown here,
and the titanium epoxy liga. And as you can see, it does
not decrease as quickly as the zirconium alkoxide. And you can also see that
the water continuously decreases, showing
that you still have some hydrolysis occurring,
as well as condensation occurring in this
particular system. And this file shows
what happens if you look at the FTIR data
for the alkoxy groups and how they decrease over time. And then you look at the
rates of gyration from it from small-angle
X-ray scattering. And what you see is
these particles start growing very quickly. And so using this
particular technique, you should be able
to get a better picture of the hydrolysis
and condensation [INAUDIBLE] for these particular systems. So the conclusion with this
work is that yes, we can. We were able to look at the
zirconium and titanium alkoxide reactions, although they were
fast, using this rapid fixing flow-through technique. And also, if you look at
the hydrolysis of zirconium relative to titanium,
zirconium hydrolyzed much faster and more completly
than titanium alkoxide. And so– I forgot to
say– very quickly, but the individuals who
helped me with this project were two postdocs,
Singhal and Look. And the final individual
was an undergrad researcher that worked with me. And this work was actually
done when I was at Oak Ridge Advanced Laboratory. The next topic I would like
to talk about very briefly on some additional
research activities that we did in my
research group. One was part of the
Engineering Research Center that [INAUDIBLE] over. One research area was the
microwave development– microwave sensors for moisture
content and bulk density measurements of
pharmaceutical powders. For both static powders, as
well as floating powders. And several publications
came out of that. As you can see, that work was
done between 2006 and 2015. And then we did drop
printing of pharmaceutical– from solutions of
powders and solvents, as well as resolving the
pharmaceutical in metals and then looking at
the crystallization and the dissolution
of the drugs. This work was done between
the years 2006 and 2015. And the final thing that
I worked on from this list is the electrodispersion
precipitation process, where we were interested in
making hydrous metal oxides. And also calcium
alginate microspheres, where these calcium alginate
microspheres were increased to encapsulate protein. And this work was done
between 1995 and 2009. Now, the two major items
I want to talk about to wrap up this
presentation– and that means we’re all going to be
here for another 50 to 60 hours, so get comfortable. Metal coated biotemplates. This research was done by
several of my former graduate students– Samuel Lee,
Liz Royston, Lim, Freer. And is currently being
done by Mayo Adigun. There are two
undergraduate students who are working on
the project– who have or are working on the project. Gloria Novikova and
Erin Retzlaff-Roberts. This work has been going
on since about 1999, while I was still at the
University of Maryland. That’s when this
project first started. And Samuel Lee actually
started on this project with [INAUDIBLE] who transferred
here when I came to Purdue. And I guess his famous quote
on this project was I hate TMV. But he actually did
some very nice work. Early on, he encountered
a number of obstacles. But he did manage to
overcome them and publish some nice papers. So what is tobacco mosaic virus? Well, tobacco mosaic
virus is what I would say is a biotemplate–
from my research– that’s about 300
nanometers in length, 18 nanometers in diameter–
on the outside diameter– and it has an inner core
that’s about four nanometers in diameter. And researchers
have coated the TMV with metals on the
exterior surface, as well as in the
interior surface. TMV– the reason why it’s
such an excellent template is that it was first
discovered in 1880. So if it was discovered
that length of time ago, you would think we would
know a lot about it. It’s easy to grow. I mean, you can
harvest one kilogram to, perhaps, two kilograms of
purified TMV per acre of land. The particle is
very monodispersed. And they form nanotubes,
as you can see. The virus is also stable. Because you can see the attack
in the pH range from two to 10. And temperatures
below– up to, I should say– 90 degrees Celsius. So that means that
you can carry out a number of different
chemistries using TMV. And with genetic
engineering, you can make TMV– have it be stable
even in some organic matrices. We primarily use it in
water and, in some cases, alcohol water systems. But primarily in
[INAUDIBLE] solutions. So, with genetic
engineering, you’re basically adding more cysteine
groups on the surface. In our case, we
had cysteine groups on the surface of
the TMV so that you can have greater ability
towards certain metals. [INAUDIBLE] One application that– I
asked one of the grad students Liz Royston if she could
anchor the TMV on a substrate. And so she was able
to anchor the TMV on [INAUDIBLE] substrate. And what happens is the TMV
takes a stick straight up. And only one end on the TMV will
be anchored to the substrate. And then we can coat the
TMV with the palladium. And then after you coat
it with palladium metal, then you can coat
it with– you can reduce metals such as
[INAUDIBLE] and cobalt on palladium. And one of the applications for
that was in [INAUDIBLE] surface area electrodes technically
used as batteries. And push minds that the battery
has greater charging capacity with this porous surface
for the electrodes. We also have just used it
for detecting the hydrogen– the second hydrogen here. I gave a presentation
at the AIChE meeting and this reduction here–
that somehow hold that. [INAUDIBLE] these
palladium-coated TMV and he put it on an
acoustic wave device and was able to
detect hydrogen where, because the palladium
would absorb the hydrogen produced palladium hydride. And in the presence of
hydrogen and in the absence of hydrogen, when you release
the hydrogen from the palladium hydride. And so you have the swelling and
contraction of the palladium. Which was very good because
a lot of palladium sensors were filled with palladium
on the substrate. And if the hydrogen
absorbs the palladium, the palladium would swell. And if you removed the
hydrogen from the environment, the palladium would desorb and
the palladium would shrink. And what happens is eventually
the palladium would crack and the sensor would fail. But [INAUDIBLE] the
small nanoparticles, the palladium for
the [INAUDIBLE] and swell and shrink. Swell, shrink, you can
certainly– the hydrogen environment millions of times
without throwing of the device. So those are two
applications with TMV and there are probably
millions of others that we hadn’t thought about
and that people are currently building. But in addition to
palladium, there were other metals
that we’ve coated, in the sense of
palladium-coated TMV. And this would be
platinum-coated TMV and this is gold-coated TMV. Now, all this looks great. And early on, what
we were doing– we were using an external
reducing agent. An external reducing agent–
if you flip that end, you have palladium metal
that is not absorbed onto the surface of the TMV. The reducing agent would reduce
the palladium in solution. It was also reduce
the palladium that absorbed onto the surface
of the biotemplate. And what I noticed is that we
would have some material that was coated with palladium,
some material that was not coated with palladium. And that was a very inefficient
use of the palladium. So we decided that we would
look at the palladium in greater detail. And as I said earlier,
there are two methods. One where you use a
reducing agent in some of the reducing agents, like
sodium chlorohydride, sodium hydrophosphite, and
dimethylamine borane. So we can use any of these
to reduce the metals. And as I said, the coatings
weren’t always uniform when we did that. So you end up with
coatings that look somewhat like this on some
of the viruses, but not necessarily
all of the viruses. So one of our former
students, Lim, noticed that the
palladium would reduce on the surface of
silica particles when the particles were
heated at 50 degrees. Silica. These were silica
particles that were functionalized with either
amine, bio, or epoxy groups. And so he decided
to try the technique with just TMV and palladium. And just heating the
solution to a higher temperature– in this case, 50
degrees– to see what happens. And what he discovered is that
every single TMV was uniformly covered by the palladium. And so the camp virus behaved as
a– some type of reducing agent for the palladium ions. Well, we said,
well, what happens if we do multiple coatings? Can we make different coatings? And sure enough, we
went from one coat to six coats of the palladium. And down here, Alex Freer
showed that as you increase the coating, the
diameter thickness of the palladium on
the surface of the TMV increased, as shown here. And this was confirmed
by both small-ange X-ray scattering and transmission
electronic microscopy. But we still don’t understand
this whole weighted reduction. And we collaborated
with Jeff Miller. Because he was doing X-ray
absorption spectroscopy. So we could actually
look at the reduction kinetics of the palladium ion. And we also used
UV-Vis experiments. Because UV-Vis
experiments– we have some of UV-Vis instruments
here and it’s not that expensive to use. But this is the
reactor that we used, which also is one of
Jeff Miller’s reactors, where we could put our
solution in the [INAUDIBLE], as well as control
the temperature. And it only holds
three milliliters, but that’s not enough
for us to fix their data. And this just shows
you the procedure. I won’t go through that here. And here are the results. And using UV-Vis,
[INAUDIBLE] we had initial solution of 0.75
millimolar palladium and 0.022 milliliter or grams
per milliliter of TMV. The initial solution
was here, below the two. And this axis here
is all 100 times the palladium ion
concentration at time T divided by the initial
palladium concentration. And you see this big drop in
the first couple of minutes during the reaction. So afterwards, there was this
first order reaction kinetics exhibited by the rejection
of the palladium. And these are the rate constants
that we got from 2.2 hours, in the minus [INAUDIBLE]
hours per milligram of virus. Because we tried to normalize
by the amount of virus we had in here because
the rate constant tended to increase
as a later function of the mass of the virus. And so we showed a
wild-type TMV, a 1-cys TMV, and a 2-cys TMV–
1-cys and 2-cys. As you can see, going
from wild-type to 1-cys, the rate constant
was 3.2 However, the 2-cys remained at 3.2. And so these are the last two
of the genetically engineered wild-type TMV. And looking at the
activation energy, we’ve got an activation energy
of about 23 millijoules, which is consistent with
the literature for DMAV type of reduction. And what exactly does that mean? Right now, we
aren’t really sure. So that was for UV-Vis. So how do the kinetic constants
from here with X-ray absorption spectroscopy? And here is the cell that
was used for carrying out those measurements. Once again, this is where I
played around with Jeff Miller. And as you can see, for
X-ray absorption spectroscopy experiments, we get the same
type of first order connect. And I can tell you
that, for the UV-Vis, we were looking at the
disappearance of the palladium ion, not knowing if it was
converted to palladium metal or not. So the only way we would know
if it was converted to palladium metal was either by
looking at the particles and looking at a form
of high-resolution TDM or some type of XRD. Or, by using this X-ray
absorption spectroscopy method. And this method shows that,
yes, the material ends being converted to palladium. We’ve already demonstrated
the palladium ion to palladium metal. Now, we did have to go to higher
concentration of palladium and TMV for the X-ray absorption
spectroscopy experiments. But if you look at
the rate constant, for wild-type, it was
2.7, for 1-cys, 3.2, and for– in this
case, VSMV would have been another
virus, which had about the same rate
constant as the 1-cys TMV. So once again, we observed
first order rapid genetics and the rate constants–
Well, I think I must have removed one of my panels. But the rate constants
that were observed for using UV-Vis were very
consistent with the rate constants that we got using
X-ray absorption spectroscopy. However, one of the
things that we noticed was this– as we said–
this very quick drop in the palladium concentration
within about two minimus. That probably indicated
that some type of absorption–
palladium was absorbing, into the surface of the TMV. Because in the
UV-Vis surface, we have to filter
out the palladium. I mean, you have to
filter out the TMV. And if we’re
filtering out the TMV, then any palladium
absorbed from the TMV will be filtered out, as well. Even before it starts to reduce. So we looked at the
absorption of palladium on TMV and this is the loading of the
material on TMV– 127.3 moles of palladium per
milligram of TMV. And primarily, you get Langmuir
isotherm type of behavior. But in some cases, you get
Freundlich’s isotherm effect. And when we look at
the absorption capacity of palladium on the TMV– that
[INAUDIBLE] some palladium ions absorped on the
TMV– we can look at that and it does indicate that
the first data point should probably be somewhere
about 1.8 to about 1.7– that first data point. If you look at the
amount of palladium that’s absorbed on the TMV. So that was encouraging. But it also shows that there
is some reaction that’s probably occurring that’s
causing that drop, as well. It’s not just due to absorption. Now, we also wanted to look at
the particles that are growing on the surface of the TMV. And so we used small-angle
X-ray scattering. As you can see, I’m going back
to small-angle X-ray scattering over and over again. I started– for the
first set of experiments I did before coming to Purdue–
even when I was at Oak Ridge Medical Laboratory. And also, using some type
of spectroscopic technique in order to monitor the reaction
of the material through action kinetics. So here we used small-angle
X-ray scattering, where we have courts tube. And then, incident radiation
goes through the tube– sample in the tube. And you get scattering. And you get scattering happening
that looks something like this. And you see it varies
as a function of time. Especially if you
look down here, where you have a nice VK region. So that you can get the
size of the particle. And the model that–
and this is Mayo’s work that he used to model the data. There’s a second
level VK region. Exactly what those particles
are, I couldn’t tell you. But the small
particles are probably the very small particles that we
see on the surface of the TMV. There’s also some
questionable– could these also be the core spaces
between particles? But I think it’s probably
the very small particles that are on the surface of the TMV. But this second-level
world of [INAUDIBLE], we haven’t figured out
exactly what that is. So in terms of TMV, if we
go from the wild-type TMV to the 2-cys– TMV
2-cys, I should say– you end up with a
thicker coating of material when you have the 2-cys TMV. So by changing or modifying
the surface of the TMV, you can affect the coating
of materials on the surface. Mayo had an interest in
looking at other viruses. And the two viruses
that he looked at was Alfafa Mosaic Virus and
also the Barley Stripes Mosaic Virus. And when we used the
hypothermal synthesis technique to coat the palladium on
these viruses, what we found is the AMV didn’t
look as pretty. So we didn’t have
a pretty picture. But the BSMV is a real jewel. And as you can see, the
part of the uniformly coated just like the TMV. So now we need to
understand better what’s going on with BSMV. But like TMV, it looks like
the first and second coating, perhaps, we didn’t complete
the coat of the BSMV with a layer of particles
with the first coat. And so when we went up to
third and higher coatings, you see the sides of the
coating actually increases the number of coating cycles. And also, as I said
before, the rate constant– the first order
reduction rate constant actually increases as a function
of the concentration of BSMV. That’s why we’ve
actually divided the rate constant’s body
mass of the biotemplate. So the conclusions
from this work, using in situ X-ray absorption
spectroscopy and UV-Vis experiments, we were able to
decide the proper reduction of palladium. At least, a
competitive reduction of the palladium on metal. I mean, on the [INAUDIBLE]. And also, using in
situ SAXS, we could measure the size of these
palladium network particles and, basically, how they evolve
over time during the reaction. We are also investigating
the coating of BSMV and it behaves a lot like TMV. And so, we’ve used the
UV-Vis and USAXS to compare the– well, we’ve
been using it– they’re analyzing the
data now to compare the BSMV and the TMV, in
terms of plating reduction on these two biotemplates. So now for the last part of
my talk, which is particle deposition during
drop evaporation. This work was
started back in 1996, when I was a young man at
the University of Maryland. And the student who worked
with that was N. Liu. And later on, when I moved
here, PP Widjaja, [INAUDIBLE] Song, and most recently, Nicole
Devlin, worked on this problem. And Ms. Wang is now
working on the problem and I look forward to her
excellent work and future presentations. And of course, the most
important thing, publications. Now, in terms of
nanochromatography, which is something that Nicole
Devlin was very interested in. Up until Nicole,
most of the work was done on a single
particle size. And under hypothermal– where
the droplet was calculations and everything was done
under hypothermal conditions. But she ran into this paper
where some researchers looked at the evaporation
of a system of two particle sizes– one-micron
six-micron particles. And what they’ve noticed
is the smaller particles tended to go closer
to the contact angle than the larger particles. And so if you know the distance
between these two particles and– of course, you know the
diameter of the particle– teach something about
the contact angle right at the contact line. Now, if you could get
such nice separation just from drying a droplet,
that would be interesting. So, they did some modeling
but the only model the blue they didn’t
actually look at the particle deposition or anything. So we were very interested
in looking at that. Another group looked at three
different particle sizes. Four nanometers to
two micron in size. And once again, the
smaller particles were closer to the contact
line than the larger particles. So we said, well,
let’s do some uptakes from the modeling of this. First, using
hypothermal conditions, where you have a drop
here, and then you have a gas phase
located up here. And the drop is axisymmetric. And you have your
transport equations that all our grad students
and undergrad students have fallen so in love with. Because they’re so cool. I could take this and keep
going around like this and we’d get such
a cool equation. So this intervention
was formed so we’d have a couple of
dimensions– Reynolds number, the capillary number. And we also have the
stress tensor, shown here. And also– this is
the Cauchy equation, where the– I guess your
Cauchy equation down here. And then down here, we
have a continuity equation. And solving those, you can solve
for your velocity and the unit B direction– or the
radial direction, and the axial direction. And also P, which
is the pressure. So we have three equations. Three unknowns. And they could have a series
of boundary conditions, shown here. And we won’t go through
those because you’re well aware of those. And then, for vapor
compositions and vapor phase, out here, from the droplet. We assume that when you look at
the [INAUDIBLE] concentration and set it equal to zero. And so we have a quasi-static
governing equation. The convection-diffusion
equation– when we’ll bring
in the particles in that equation with particle
one and particle size two. And so you end up with these
two equations– Peclet numbers. And Peclet number is
given by this expression of characteristic lens
film, which is basically the radius of the droplet. And we’ve got radius
of the droplet that enables on the cross-section
of the base on the substrate. And the velocity– some
characteristic velocity scales. Depending upon the evaporation
rate of the droplet from the surface. And then your
subterfuge co-efficient, which is computed by the
Stokes-Einstein equation for the small particles. So we can put in boundary
conditions for the particles. We won’t go through
those, either. But there’s not a condition
for the symmetry boundary condition. The boundary condition
along the liquid area phase. And then the boundary
condition for the deposition of the particle
of the substrate. So here are the results. If you divide the
number of simulation, you get flow fields
that look something like this, where the liquid
is flowing in this direction. Then it flows to
the contact line, which in our calculations,
the contact line’s 10. So if we replenished the
fluid at the contact line, we have to bring the fluid
to that contact line. And here are the particles. And what you see is
that the large particles accumulate at the edge more
than the small particles. This is the large
particles here. And you see the has indication
that it’s around 20 right at the contact line, where
it says smaller particles has a mass of about six. Mass concentration’s about six. And if you look at the
outside of the droplet, you see the small particles
are more only near the contact line. And the inside of the
droplet is in this direction. And you see large
particles are not as close to the contact
line as the small particles. So though the simulations–
or [INAUDIBLE] using the few models that we
have, there are some problems. And another problem is if
you look at the deposition grade of the particle from
the substrate, at time 2.2– if this is time 2.28–
you see variable particle release near the contact line. At 4.04, there are probably a
few more particles, but most of the particles deposit right
towards the end of the drop dries. So the model, like
the [INAUDIBLE] model, has problems, in
terms of calculating the rate at which the particles
reach the contact line. So we’ve put in the
energy balance equation for non-hydrothermal systems. And in this case, we have
a thermal Peclet number. And then the value should be
shown here for, let’s say, the heat. The heat bugs that’s
due to the evaporation at the surface of the liquid. So we also have to take into
account that the surface tension, now, will change. Because it’s a function
of temperature. And we use this equation
to describe surface tension temperature. And also, the traction
boundary condition– no longer do we just have this surface. We have to add the gradient
of the surface tension because the surface tension is
changing along the interface. So when we do that, we
get this Marangoni flow that’s shown here. So rather than having a liquid
going to the contact line, as the drop evaporates,
we have a circulating flow within the drop. And when we do that, the
three micron particles don’t accumulate as fast in the
contact line area over here. And so this shows that the
particles aren’t depositing as quickly because
of the Marangoni flow, which is
consistent with what we see with the experiments. So with thermal variation, you
don’t get very rapid deposition of the big particles or the
particles at the contact line. Whereas, when you have
isothermal conditions, where the flow can go
directly to the contact line, you can have a very high
concentration of particles at the contact line early on. So you have to include
the thermal variation at the bottom. This whole thing
about the particles not being able to
reach the contact line is usually the fact that
the liquid height constrains large particles from
accumulating closer to the contact line. So the small particles can get
closer to the contact line. And what I want to show
here– well, maybe not. OK. Oh, there it is. If you can look
at the particles, the big particles stop
and the small particles keep going closer
to the contact line. So as long as the
number of big particles aren’t high enough in the layer
where the big particles stop, small particles can go
around the big particles or go between the big particles
to get to the contact line. Although the big
particles have actually arrived at the
contact line, but they start off in the same proximity
as the small particles within the droplet. The big particles will actually
migrate to the contact line path. That’s just another
static example. So you can have a
situation where, if your concentration
is slightly high, you can get a layer
of small particles. Because as big particles
form, the smaller particle can go around it. The big particles who reach
close to the contact line. The big particles are stuck,
again, some distance away from the contact line. And then, later on, once the
concentrated big particles get large enough, so
the small particles can’t filter through the
fore spaces, [INAUDIBLE] another layer of
very small particles. So we did this in thought
of the next question. So what happens if we
have a sessile drop versus a pendant drop? Well, when we did it
with the sessile drop, we’re going to get
some nice accumulation of the small particles
near to the contact line. But then you get
some big particles, small particles around here. And this is your contact line. If you look at the
pendant drop, and we want the contact line–
on a macro scale, it looks like it’s fixed. So, in the microscope,
you get this. Pendant drop, you get big
particles in the center. Sessile drop, you get big and
small particles in the center. And so, when you
model this, you have to include the
gravitational Peclet number. And finally, you get–
when you do the simulation, it shows that you
can get big particles in the center and virtually no
small particles in the center. And I will basically
not give it away. I didn’t see any. I’m sorry. OK. As I told you, I
could keep going. So, my future fun– I can
even have fun doing research. I guess I should put up
the acknowledgements. My collaborators. And I miss Brian
[? McDorse. ?] He comes to work with the
palladium coated TMV. Sorry about that, Brian. Don’t ask the tough questions. And a number of
undergrad students have worked on these
projects and funding sources are people that allow
research to move forward. So with that, any questions? [APPLAUSE] Any questions? Yes. What was the [INAUDIBLE] in
the droplets in the [INAUDIBLE] So, a lot of cases, it’s
either water or ethanol. Thank you very much. You’re welcome.