Tip:
Highlight text to annotate it
X
We are going to have our first look at specific phenomena, which is gaining importance in
everyday research that is electro wetting;and how this has led tonew branch of physics,
which is known as digital micro fluidics.Now,the concept is electro wetting was known to us
for more than hundred years, but the use of electro wetting in order to specifically move
a drop of liquid from one point to another in a precisely controlled path has led to
the new branch of engineering, which manipulates fluid motion,and that is digital micro fluidics.
So, we are going to have our first look on the basics of electro wetting,its potential
uses the equations that govern the electro wetting process, the physics behind it, and
how this electro wetting can be applied in a variety of fields to move liquid from one
point to another. Now, whenever there isa need for precisemovement precise movement
of very small quantities of liquids, and those liquids could be discrete drops as well. The
question comes is what would be the method?How do we move a liquid droplet from one point
to another?Theusual methods and machines that we knowwill obviously beof no use to move
such a small quantity of let us say discrete drops.
So, one has to think of alternative ways by which the drop can be made to move.One way
ofhandling situations likethis could be to alter the surface of the solid surface on
which the drop is resting. Whenever the nature of the solid substrate is altered, it is going
to give rise toa different surface energy of the system, and this difference in surface
energy of the solid substrate in contact with the liquid can give rise to forces, which
are commonly known as surface tension forces. Normally,what we see that the surface tension
forces,they are not relevant mostly in micro scalesystems, but as the system dimensions
grows smaller and smaller, the effect of body and other forces would progressively diminish,
and the surface forces wouldtake over, and they could be the major force available, major
force applicable when the system dimension becomesmillimeter level,and even more prominent
when it becomes at the micron level. So, the basic problem boils down to how do
we change the surface energy of a surface, and if you can change the surface energy of
the surface would that lead to a motion in the droplet. So, we need to apply certain
external forces may be or certain operations need to be done on the solid surface to change
its surface energy. Soinitially, in the first part of this lecture on electro wetting, we
would constituteon the ways to change the surface energy and there by the surface tension
of the system.
So, as I mentioned that,the driving forces become different when we go into the micro
scale system, and compare to macro scale, the surface tension becomes starts to dominate
as the surface to volumeratio increases and in the micro scale.So, can we use surface
tension for the precise manipulation of droplet in the micrometer scale? So, thisis the fundamental
question or the fundamental process, which then has led to four distinctly different
fluidic operations. Can we use surface tension as a force to create a droplet or to transport
a droplet from one point to another? Can we cut a droplet into a number of smaller droplets,
and can be merge two droplets together to form a relatively bigger droplet? Because
these are going to be fundamental operations tofundamental operation which would be necessary,
which would convert the droplet based fluidic systems to digitize them in such a way and
this has given rise to a new micro fluidicsparadigm;that is commonlyknown as digital microfluidics.Soin
this class,we willgive we willsee what digital micro fluidics is all about and the forces,
the science and the engineering applications of digital micro fluidics.
So, this has gone given a rise to the firstthe first thing is, can we can we change the surface
energy?Now towards the middle of this lecture, Iwill give you some examples of changing the
surface energy of a surface by external means, whicharemay not be reversible,which are difficult
to maintain.So, the need to have something which is quote unquote switchable is extremely
important. Can we think of a system, in which the nature of the surface changes very quickly
to something drastically different; for example, from hydrophobic can we make the surface hydrophilic,
and then when that external effect is taken out of the system, it immediately goes back
to its previous stepstage state which is hydrophobic. So, electric field has been shown to alter
the surface energy in such a way that, this hydrophobic hydrophilic interaction or interchange
is easy to accomplish.The first example of this electric double, the first example of
electric field enhanced wettingpresent that can be encountered in a droplet was given
by the scientist Lippmann around 1875. This example that I am showing here, the figure
that I am showing here is;let ussay this is a liquid which forms a finite contact angle
a large contact angle with the solid which is a conductor.
So, this is a conductor and we have an electrolyte in contact in contact with the conductorand
as finite large contact angle is formed in between the solid-liquid interface. And then,
a potential difference is applied in between the electrode and the electrolyte and when
that happens, the electric double layer is formed in which, the charges opposite charges
are going to accumulate at the solid side of this solid-liquid interface and on the
liquid side.
So, if weif we can think the electric double layer can be thought of;let us say this is
a solid; this iswhich is the way and we would like to see, how the electric double layer
is going to be formed, and this is in contact with a battery and here I have one electrolyte.
So, when the circuit is on what weare going to see is that,positive charges are going
to accumulate on the solid side of the interface and the negative charges from the electrolyte
will form a layer in the electrolyte. So, this formation of oppositely charges near
the solid-liquid interface on application of an electric field is the thickness of this;
this is known as the double layer. So, wewould say, there is double layer has formed inside
the electroweight electrolyte on very close to the solid liquid interface, and when that
happens this accumulation of charges, since it is it is a spontaneous process.It is going
to lower the energy of this surface. As the surface energy is lowered, the solid-liquid
surface energy is lowered; this will give rise tospreading of the electrolyte on the
solid. So, this phenomena or this concept has been
utilized for electro wetting. So, if Ihave a droplet which is sitting on a solid and
then, I have an electric field being applied between the between the liquid of the droplet
and this being the conductor sowhat would happen is that, the charges are going to form
near the interface inside the droplet, and positive charges are going to accumulate on
the solid side of the interface. As a result, the surface energy will change and the droplet
will spread. So, this spreading of the dropletliquid present
in the droplet on application of an electro electric field is known as electro wetting,which
was first observed by the scientistLippmannsomewhere around 1800,1870s or so.So, can we can wenow
this is this was known for quite some time, but can we use this for some practicalapplications;
that is something which we would like to see. But,if you if you see thisentire process we
would see that there is a limitation because, if the potential difference between the solid
the electrode and the electrolyte is slightly large. Whenif it is only, if it is very small
then, this electro wettingphenomena can be observed, but if you would like to increase
the voltage then, this process will breakdown since a current would flow in between from
the electrodefrom the electrode to the electrolyte. So, only few tens ofvoltscan be applied in
between the electrolyte and the electrode without passing a current in between them.
So, howdo we…So, this limit severely limits the applicability of electro wetting in terms
ofin terms of changes in contact angle in terms of appreciable changes in contact angle.
So, we can only change the contact angle by a small amount because, any increase in voltage
would lead to a current flowing in between the solid and the electrolyte there by rendering
the entire electro wettingelectro wettingprocess inoperable.
So, in order to circumvent this specific problem, the concept has come later on is,if we could
introduce a dielectric layer in between the electrode and the droplet then, the question
of having a current passing through in between the solid and the electrolyteat slightly higher
voltages can be eliminated. So, that is the concept which has been shown hereand which
is commonly known as the electro wetting on dielectric. Soin electro wettingon dielectric,
a dielectric layer is placed in between is placed in between the electrodeandthe liquid.
So, the liquid would be here which is not in contact with the electrode any more, but
a dielectric will be layer will be introduced in between the two. So now, I can have appreciably
sufficiently higher voltages that can be applied in between the electrode and the liquid. So,
electric field is large and as the electric field is large, significant changes in contact
angle would be possible, and this is what is shownin this figure,which is taken from
publicationby Lee in 2002, which has appeared in sense in the journal sensors and actuators.
Here now, I have the solid covered with a dielectric coating. In… it is in contactin
contact with an aqueous liquid. So, when this circuit is closed that is not going to be
found any electric double layer, but the change in energychange in energy takes place in the
hydrophobic dielectric layer. So, the nature of this dielectric layer has to be hydrophobic
and since it is an ananan… since it is hydrophobic,the liquid is going to form a convex meniscus
over here.Now,when you apply sufficiently high electric field in between this and the
liquid then, the dielectric layer acts as an insulator, but sothere is goingnot going
to be formation of any electric double layer, but the change in energy surface energy of
the dielectric will cause a change in contact angle.
So, we can see that almost from an almost completely non wetting system, it has become
partially wetting system with distinct change in the curvature. So, the thethe iflet us
say, this is mercury and mercury then, we could see that the convex meniscus has been
depressed and it has become a concave meniscus. So, this depression and change in shape of
the liquid mercury meniscus can be monitored as a function of applied voltage and you would
see that it is going to follow a certain law, certain role which we will see subsequently.
But here, you can see that a hydrophobic surface giving rise to a retracting meniscus can be
changed to an hydrophilic substance giving rise to an advancing meniscus by simple application
of an externally applied electric field, which has anumber of advantages that I will list
subsequently.
Now,a digitalmicro fluidics system can be can be of two different can be a fundamentally
two different technologies. One is an open system and the other is in confined system.
So, when we are dealing with just a drop on a surfaceand this is an example of an open
system whereas, if I have a plug of liquid in another medium,and these this is the electrode
and this being the dielectric then,it is an example of a closed system. So, in digital
micro fluidicsor in the electro wetting, we would see applications of both an open system
or an closed system and with fundamental advantages.So, let us try to see, what are the advantages
of digital micro fluidics? Now,you…Let us say,youhave a reaction which is taking place
insidea droplet. Since the size of the droplet is extremely small, the resistances to mass
transfer that diffusion length, the diffusional resistances to mass transfer would be minimized
to a large extent inside a droplet. So, if you have a reactant droplet;reactant
one droplet and reactant two droplet, we could bring them close together; you could merge
them and you can form a larger droplet. Inside the larger droplet still it is very small
in size if it is of micro literdimensions, the resistance to mass transfer would be sosmall
that the kinetics of the reaction can be madecan be made faster.So, any reaction which is mass
transfer limited would be ideally suited for operation inside a micro droplet,and you couldyou
could you could design your system in such a way, that you start with a large droplet.That
large droplet could be split into a number of smaller droplets using a specific micro
fluidics operation. Then, each of these smaller droplets can be made to move in a path separate
from each other. Now, on the path sits something which is going
to react with the droplet which is coming in that path, and when that reaction take
takes place suppose, you can monitor the reaction from outside then, a specific let us say chemical
present in the micro droplet can be can be monitored or its concentration can be measured.
So, in this way depending on how many droplets you are you are dealing with, how many droplets
you have broken the initial droplet,you could have several chemicals which can be characterizedwith
by reacting them with different chemicals, different reagents.
So, this hasvery important application in many diagnostic devices or lab on a chip diagnostic
devices, where one drop of blood could be could be could be split into a large a would
be into a significant number of micro droplets, and any specificchemical of interest can be
measured into that micro droplet by making it react with some known reagent. So, one
droplet could be used for blood sugarmonitoring; the other could be for blood urea monitoring
and soon. Sothe compartmentalization of reactions in small droplets giving rise to larger rate
is one big advantage of this entire process.
So, what you can see thatthis in term would wouldwouldwouldreduce the amount of reagent
necessary for such an operation in the this kind of a; this kind of process can also enhance
and accelerate chemical and biochemical screening processes, crystallization of certainproteins,
the kinetics of enzymes andso on. So, this definitely has significant application.
And when we think of applying these concept of electro wetting to specific applications
for example, lab-on-a-chip,we need to take care of or we need to address certain issues;
like, what are the fundamental and applied aspects of electro wetting? What kind of basic
equation governing equationcan be used, can be developed for electro wetting?So, what
are the origin of electrostatic process that can change that can that canchange contact
angle or that can induce bothcontact angle and motion for the entire droplet.
Is thereany limitation of this electro wetting equation? Soin other words, we would like
to address, we would like to identify the failure of the electro wettingequation which
is known as saturation of the contact angle at high voltages. Apparently, it seems that
as voltage increases as the applied field is increasing, the contact angle will become
smaller and smaller, but is there any limit to it? We would see that beyond a certain
voltage, the contact angle becomes independent of the applied voltage.
Sono matter even if you increase the voltage beyond that point beyond that value,the contact
angle will not decrease anymore. So, your ability to induce a change in contact angle
would not follow the basic governing equation or ouror our idea that, by increasing the
valueof the contact, value of the applied voltage, we could reduce the contact angleto
any value that we desire. In other words, it is it isshown experimentally that you can
never make a partially wetting system or a non wetting system convert to a completely
wetting system. So, you would never be able to achieve zero
contact angle. So, this saturation of contact angle correspondingwith respect to the applied
voltage is one limitation that we have to keep in mind. And then, we have to also think
about,what is the dynamics of electro wetting?How do we make a droplet move from one point to
another? What are the factors that are going to govern the process? The speed of the process,
the response of the electro wetting phenomena as the droplet size is changed, thevelocity
with which the droplet would move. So, what are thedesign parameters that we
can change to make the droplet move with a constant velocity with some velocity that
we would like to have. And then finally, I would give an overview of the many exciting
commercial applications, upcoming commercial applications of the electro wetting concept.
So, I would I wouldconcentrate mostly on electro wetting on dielectrics which is which in the
short form is commonly known as EWOD.So, we will see…We willwe willgo into the depth
of the EWOD in this class and in the next class as well.
We all know that the important consequence of miniaturization is the increase rapid increase
in the ratio of surface to volume ratio. Now, one of the major focus of researchfor a very
long time is, how do wecontrol surface energy and the surface forces. When a system size
becomes smaller we know that the capillary forces would dominate so,which is the function
of this surface tension. So, how do we change the surface tension? So, before the concept
of electro wetting was utilized to change the surface energy.
So, there are there are several items to change the surface tension. So, ways to influence
the interfaces, one can use a temperature gradient to make a change in the surface energy.
What has beenwhat we know is that surface tension is astrong function of temperature.So,
if we can have a difference in temperature in between two points on the surface then,
the surface tension values at these two points would be different. Now, we are therefore,
creating a surface tension gradient on the surface. Sojust like pressure gradient that
is imposed from outside here through a temperature gradient, we are imposing a surface tension
gradient that can be used to make liquid flow to make a fluid flow from one point to another.
So, this temperature dependent motion of liquid which is which isdue to surface tension gradient
is known as Maranongoni flow. Now, this Maranongoni flow can be affected by surface tension gradient
by the imposition of a temperature gradient or by the imposition of concentration gradient
as well. So, if we can have a solution containing a solute and if the solute concentration at
two points are different, then what would happen is,this would create a surface tension
gradient and then this would give rise to flow.
So, we can have Marangoniflow a surface tension gradient driven flow caused by either a temperaturegradient
ora concentration gradient. So, this has been shown to become important when the system
size becomes smaller as the surface forces start to start to predominate over all other
forces. Now, the this this thishas been there has been some effort in order toin order to
use this for movement of fluid, but there are certain problems associated with it.In
order for a droplet to move on account of induced temperature gradient, the value of
induced temperature gradient has to be very large.
So,which is impractical in most of the cases to be used for practical applications;you
need several tens of or may be hundreds of degree centigrade per millimeter in order
to cause a liquid droplet to move on account of surface tension gradient. Similarly, how
do youhow do youpractically create a concentration gradient over such a over a very small distance.
So, this has given rise to secondary flows which people have encountered, but these cannot
be the primary ways to move liquid. Now, there has also been efforts to make atopographical
structuring of the surface or chemical model chemical modification of this surface which
would give rise to local wet ability gradient. So, there has been report in which,you can
have alterative, you can have a you can have a gradient of wet abilitywhich is which is
thrust upon the surface. You could create a wet ability gradient on a surface by chemical
means by the deposition of certain chemicals on a silicon wafer for example, there is a
specific chemical which when depositedby a vapor deposition process on the silicon wafersilicon
substrate, it would give rise to wet ability gradient, and he could show, it has been shown
that a droplet will movein the direction of enhanced hydrophilicityeven against gravity.
In other words, if you have an inclined surface and if you put a drop of liquid on the higher
hydrophobic side of this substrate then, that droplet will move against gravity along the
substrate. So, which is which is very obviousbecause,
the gravity effect of gravity becomes unimportant as the system size becomes smaller. So, the
gravity is no longer important. So, even if the substrate is at an angle inclined the
droplet due to the hydrophobicity gradient, it will move from the hydrophobic to the hydrophilic
side which is which is which is extremelyinterestingto see.It defies the logic and you would see
a droplet moving along the inclined moving up the inclined.
Now, that there are certain disadvantages of these chemical and topographical patterns
is that they are static in nature. Once you modify the chemical surface chemical nature
of the surface,it is going to remain that way. See, there is no way by which you can
switch it on and off. So, they are static in nature and therefore, it cannot effectively
control or effectively use the same surface we for a different application.Once you make
the surface, the surface will remain the way throughout the operation and there are obviously,
fabrication of such surfaces will be more complex and mostly this would give rise to
secondary flows and not primary flows. So, people are… We are stilllooking for
a switchable method of changing the nature of this surface which is reproducible, which
is easy to make and which would give rise to sufficient force for the effective movement
of droplets, and this has given a rise to the concept of or to the application of electric
field to change the nature of the surface.
Now sotherefore, electro wetting has a proven to be extremely successful. You can change
contact angles by tens of degrees 20, 30, 50 degree. Change in contact angle is also
possible and switching speeds are areare much more than compared to the other cases. Mostly
the switching speed is going to be governed or controlled or limited by the hydrodynamics
of the droplet. How would the droplet respond to the application of electric field? How
fast would be the response?And the response would depend onmostly on the viscous forces;may
not be on the inertia, but it is a viscous force which is going to dominate what would
be the frequency with which what would be the response frequency of a droplet with change
in potential difference across the across the surface, but still the switching speed
is much more than that of the other processes we have described so far. And this is extremely
important for commercial application, the stability of the surface without any noticeable
degradation. So, as long as we have a very stable surface
which is reproducible and when you do not see much degradation over repeated use that,
we with a with a with a reasonable switching speed. So, this essentially tells us that,electro
wetting will definitely be the method of choice for such operations.And,we see nowadays that
droplets are moved freely along the programmable path. So, you are going to have a large number
of electrodes in inin a probably in an arraylike this, where on the surface you have several
electrodes and depending on,
how you switch these off and on?A droplet sitting over here can be made to move either
in direction or it can take any path it wants. I mean, you can program the switching on and
off these electrodes and thereby, make the droplet move on any prescribed path.Therefore
thereby, creating enough flexibility in the entire design of the process such that it
can be split and one droplet will move in this direction, and the other droplet will
move in another direction. So, you can have reagents part on one of the
electrodes over here, and another electrode over hereand you can monitor the some property.
It could be fluorescence;some property of the droplet when droplet when it reacts with
the reagent present in this electrode, and present in the other electrode. Thereby, you
could monitor may be the concentration of two species present in this droplet. So, the
programmability the easy programmability of the entire matrix, electrode matrix, two dimensional
electromatrix is enough flexibility of the system which has which has lot of potential
for their subsequentcommercial use.
Now, this is classicalsetup figure of a setup wherein 1875Lippmann hasshown that there is
sufficient or considerable depression of mercury whenit in contact with an electrolyte solution,and
you can you can vary that depression of mercury meniscus by applying a voltage between the
mercury and the electrolyte. But,as I said it is limited by the application of a very
small amount of very small quantity of voltages. Soin the early 1990s,Bergehas introduced the
idea that a thin insulating layer can be placed in between the conductive liquid and the metallic
electrode to eliminate the thethe requirement of a very low voltage to eliminate the possibility
of a electrolysis, and this is given rise to electro wetting, the new concept electro
wetting on dielectric or in simply EWOD.
So, if you look at the basic aspects of electro wetting,one is we are dealing with droplets
the sizes are about a millimeter or it would be less, and they are going to be of partially
wetting liquids onsolid substrates. The solid substrates substrate could be a silicon wafer,
and the entire process is going to be governed by the bond number which is defined as g,
the acceleration due to gravity, the change in density,the difference in density,the radius
of the theradius of the droplet and sigma lv is a surface tension.
So, the bond number essentially gives us the relative strength of gravity with respect
to surface tension. So, since the effectfor these electro wetting,the effect of surface
tension because of the size of the system over shadows the effect of gravity, and the
bond numberbond number is smaller than unity. Sosince, the bond number… If the bond number
is less than unity then, the effect of gravity can be neglected, and the behavior of the
droplet is determined by surface tension alone. So now, we would like to take a look at the
different forces which arepresent in a droplet and what would be the governing equation for
free energy for energy of a droplet, when it is at equilibrium.
So, the free energy of the droplet is a function is a function of the different interfacial
energies of the solid-liquid interface of the solid-vapor interface and the liquid-vapor
interface. So, if this is the contact angle, then we know that at atatsteady state, the
sum of the free energy of a droplet is going to be the sum of the areas of the interfaces
wetted by the respective interfacial energies for example, sigma sv solid-vaporsolid-vapor,
solid-liquid and the liquidvapor; soat state thatthe equation that governs the free energy
is this, where lambda is equal to the pressure drop across the liquid-vapor interface.
So, if you minimize this equation, this would lead to two very well known equations, well
known conditions that the equilibrium morphology of the droplet must fulfill. One is the very
famous Laplace equation, which tells us the pressure jump at the across the liquid-vapor
interface. So, delta P lv is going to be equal to sigma lv that is the surface tension, liquid-vapor
surface tension and K, where K is the curvature of the drop.So, the curvature of the drop
is nothing but inverse of these radii of curvatures.And the second equation is young equation which
gives us the value of the equilibrium contact angle as a function of the solid-vapor surface
tension, the solid-liquid and the liquid-vapor surface tension. Now, one mustemphasize at
this point is that both of these equationsor approximations and they are valid only when,
the sizes are in macroscopic scale. When the systems size becomes smaller and smaller,this
type of equations may not be valid.
For example, if we if we think of when a liquid meets a solid as the thickness becomes smaller
and smaller.Let us say, when the size is less than 0.1 micron or more specifically, when
it is of the order of 500 angstrom near the point where the liquid is in close proximity
with the solid, additional forces apart from this apart from this sigma K that is delta
P is equal to sigma K. This is a surface tension liquid-vapor surface tension and K is the
curvature. But beyond this, when the size of the film really becomes very small, additional
forcessuch as intermolecular forces of attraction starts to become important in this range.
So, if I can… If I magnify this area, we would see for a partially wetting system,it
is going to be like this. So, there would be an adsorbed flat film ahead
of the meniscus and a transition region. Soin this region, the intermolecular force would
be important. In this region, both intermolecular and surface forces would be important and
in this row range is going to be controlled totally by surface forces denoted by sigma
K. So, the equations thetwo equations that we have seen sofarwe have seen, the Young’s
equation and Laplace equation are valid for the macroscopic scale. We must understand
we must understand, we must underline the fact is that these two equations will require
presence of additional terms when we aredealing a really thin microscopic label, microscopic
contact angles or the contact line in these cases.
So, wewe with withthis limitation in mind, now we move tonow our next part which is,how
do we how do we express the or what is the electro wetting theory for homogeneous substrates,
and we are…we have two different approaches; one is this homodynamic approach and the other
is electrochemical approach. And, it is basically between a metal electrolyte interface and
when we apply any voltage as we have, as I have mentioned double layer is going to build
up spontaneously at these solid-liquid interface. And, it consists of let us say positive charges
on the solid side, and negative charges on the liquid side.
Sothis presence of double layer, the formation of double layer is a spontaneous process.
Since,it is a spontaneous process;this spontaneous process must give rise to a change, a decrease
in the Gibbs free energy of the system. So, the change inchange in free energy is going
to manifest itself by a change in the effective interfacial tension which is connected with
the surface charge density and U is the applied voltage. So, the change in surface tension,
interfacial tension is going to be a function of the applied voltage, and it is also going
to depend on this surface charge density of the counter ions.
Sowith these now, we can move to the next part, next assumption which is like how would
the how would the charges are distributed in the liquid.
Obviously, the concentration of the charge is very near to the solid surface is going
to be more, and as we move away from the surface, the concentration of thecounter ions will
reduce progressively. In fact, it would reduce drastically. So, what kind of distribution
of counter ions should one take, when one goes from a solid-liquid interface and into
the liquid. Now, this is difficult to handlein a compact form.
So, the concept or the proposal of Helmholtz, the model ofthe model proposed by Helmholtz
is used which assures that, all the counter ions are going to be situated in a very thin
layer of the order of few nano meters, andthisHelmholtz model for the electric double layer has given
rise to the concept of a double layer with a fix capacitance per unit area. Sohere, epsilon
1 is a dielectric constant of a liquid and d H is the thickness of thethickness ofthe
thickness of the layer as proposed by the Helmholtz model; that is it is a all the charges,
all the counter ions are going to be located at a fixed distancefrom the surface.
So, when you youyou use this and integrate this if the previous equation, this is given
rise to the change in surface energy as a function of on application of some voltage
U; as a function of the surface energy when you do not have any electric field and these
are propertiesthese are properties of the solid liquid interface; this is the applied
voltage; this is the thickness as predicted by Helmholtz layer and U pzcis the potential
difference of zero charge, and this the introduction of U pzc is important because,mercuryand many
other surfaces acquire a spontaneous charge when they are immersed into an electric solution
even at zero voltage. So, in order to overcome that potential something, someexcess external
potential has to be applied in order to make the surface truly zero charged. So, pzc is
that charge which has to be applied in order to in order tomake this compensate for thiscompensate
for this accumulated potential difference or the generated potential difference even
at zero charge.
So, this equation now can be inserted into Young’s equation where the cos theta; theta
being the contact angle at any given voltage can be related to a equilibrium contact angle,
and in terms of system parameters such as the property epsilon 1 d H; sigma lv is the
surfacetension at the liquid vapor interface; U is the applied voltage; and pzc as I mentioned
is a potential at zero s. Sofor typical, if we take typical values of
d H, epsilon and sigma lv let us say for a water; this ratio of the right hand side of
the equation; this entire ratio isof the order of 1 volt to the power minus 2. Now, you can
see thatwith application of voltage,this increases rapidly. So, the contact angle would increase
rapidly upon application of a small voltage. So, the… But the limitation is you really
have to operate it below the onset of electrolytic electro electrolytic process. So therefore,
it can only be operated up to the few up to a fraction of mille volts. So, if yourif your
potential difference is beyond that fraction of mill voltthen,your electrolysis process
would start and the entire process will be unusable; entire process will break down.
So, even though it is a very interesting phenomena to look at a very lowthere the thethethe fact
that it can only be used at a very low value of the applied potential; limits is used for
any practical applications. So, simple electro wetting will be difficult
to implementfor any practical applications. So, one has to then go to thego to the application
or go to the introduction of an dielectric in between the electrolyte and the electrode
which would makethe electrolysis impossible at elevated voltages as well.
So that is what, we are going tolook at next. So, the thin dielectric film insulates the
droplet from the electrode. In the electric double layer builds up at theinsulated droplet
interface thereby, causing a change in the surface energy of the dielectric and the capacitance.
Since the insulator thickness d ismuch,much larger of the order of microns compared to
d H which is of the order of the nano meters then, the capacitors of this system is decreased,reducedto
a large extent and this is the capacitance of the insulator where this is thethis is
thethis is the…epsilon d stands for the dielectric and one has to see that, this d
isthickness of the dielectric and since the capacitance is sodifferent then, the entire
capacitance of the system can be approximated as if,it is the capacitance of the dielectric.
So, in the previous expression thereforeis modified by introducing only sigma d in here;
d being the thickness of the dielectric,andthe value of U pzc is sosmall that for EWOD cases,
where the applied voltages would be in the order of maybe 50, 100,200 and 300 volts;
the value of pzc would beunimportant and that is why, it has been dropped from the equation.So,
the compact equation for EWOD is the change in the effective surface energy of the system
on application of an a potential is going to be equal to whatever be the potential,
whatever be the surface energy at zero voltage minus this factor. Andthis…in this equation,
the entire dielectric layer is therefore, considered part of one effective solid-liquid
interface and withthickness of the order of 1 micron compared to the electric double layer
which is of the thickness offew nano meters.
Now, when you plug that into Young’sequation,this has given rise to the famous equation over
here forEWOD. Contact angle equilibriumcontact angle is equal to the equilibrium contact
angle plus this term multiplied by U square. This eta is known as the dimensionless electro
wetting number which measures the strength of the electrostatic energy compared to the
surface tension. So, thisis this is basically something on which you can control, which
you can design by changing the thickness of the dielectric layer or by changing the material,
and by changing the potential applied potential. You can have a different rate or different
value for the new contact angle on application of voltage. Sothis essentially, depends on
the properties of the insulating layer and on theon the on the thickness of the insulating
layer. So, this number for EWOD issmaller much smaller
than the number corresponding to electro wetting because of this d H over here and d over here.
Sothis means that, the voltage required to achieve the substantial contact angle decreasescontact
angle decrease in EWODis much higher. That means, if you would like to change the contact
angle by let us say 5 degree, the amount of potential difference that you have to apply
would be of the order of one-tenth of a mille volt let us say; one tenth of a mille volt
in simple electro wetting, but in order to obtain the same 10 degree change inelectro
wetting on dielectric, the applied potential would probably be about say 50 degree or may
be even more. So, you require higher voltages to actuate contact angle changes in electro
wettingon dielectric. However, the major advantage is that, now
you can you are not restricted to few hundred fewmille volts, you can go to 500mille volts.
You are only limited by the fact that acts very high elevated voltage. There could be
current passing through the dielectrode, which would result in a phenomena known as dielectric
breakdown. So, when that dielectric breakdown takes place, the entire surface becomes unusable
andthis is some sort of a limitation of the EWOD. But,it still gives us tremendous flexibility
in terms of effecting aaa major change in the contact angle which would besubsequently
very important for the dynamics of the droplet on a surface.
So, EWOD is a preferred methodover EW, and this is then example ofthe contact angle saturation,
where you could seethatthe parabolic nature of cos theta variation with the potential
is more or less valid up to let us say about 300 volt. But,beyond 200 volt, v will with
increase in in in the potential; this is this becomes more or less relatively in relatively,
it is free ofI mean, it is not going to it isit isit is not going to be a function of
U anymore. So, this contact angle saturation at somewhere around this value is another
limitation of EWOD. So, if…This is known as the contact angle
saturation. Andyou obviously, cannot walk beyond the value and… But even then, this
would probably be a change in contact angle by about 30 degree,50 degree that is possible.
But,you cannot make a non wetting system completely wetting by simply keepingon keep on increasing
the potential difference. So, you are either going to be limited by the dielectric breakdown
which is essentially passing of a current through the dielectric at a higher voltages,
rendering the process, rendering the surface unusable for subsequent use or you are going
to hate the contact angle saturation phenomena, and you would not be able to go beyond that.
So, that is what I have already said that,this you areyou get someexpression, but a saturation
value between 30 to 80 depending on the surface,depending on the system you are going to…Now, the
phenomenon of contact angle saturation isstill not well understood.
Nowin the next class, we are going to talk about more about the complex surface surfaces
and droplet morphologies. How we can change,how we canhow we can make a transition from a
hydrophobic surface to a hydrophilic surface by imparting certain structures on the surface;
and if you have substructures on the surface microscopic level structures on the surface,
how would that change the wetting nature, and how they can be integrated with EWOD to
have smoother motion of the droplets for example, over a surface. Andwe would also concentrate
on thedynamics of the electro wetting process;the factors on which that on which this electro
wetting process would depend, and how or what are the interesting and important applications
of EWOD for our everyday use. So, that is all for today thank you.