 So, today we shall discuss this mechanism of wetting and the broad area to be covered is surface coating by wetting. Now, what is mean by wetting? It is a process which aims at coating on one or more solid phase with materials which are in liquid state and which comes in contact with the solid surface. So, it basically means the spontaneity in spreading of the liquid over the solid surface once it is brought in contact with that solid. Now, the application of this wetting process which can lead to a surface coating immediately we can see that coating on metallic sheet and wear and it is commonly used for putting some resistance against corrosion this is a very common use of this wetting process. Then comes the manufacture of composite materials in this case what happens the hard materials that is the dispersion of hard material that is done in a metal matrix and this metal should be able to form a fine coating or one encapsulation over the composite material. Then manufacturing of the surmet it is basically a composite material where the ceramic particles are dispersed within a matrix of metal properly chosen metal and in this case also the metal holds the ceramic surface by putting a coating and this coating is done by the mechanism of wetting. Then very important use of this wetting process is metal ceramic joining where the ceramic surface need to be coated with a metal and this metal serves like a brazing or bonding alloy which can get attached to the metal base to be joined. So, this metal layer which adheres to the basic ceramic that is also done by this wetting process. Now comes wetting and spreading now when we have a solid surface for example like this and over which a small block is placed and which can be later on melted over the solid surface then we may arrive at four situations. Number one this is the solid surface and just after complete melting of this small block this molten liquid can assume the shape of a sphere or a ball that means it is total de wetting or non wetting situation this is one extremity. We can have another extremity also we have another extremity also where this metal block after melting this metal block after melting it can have spontaneous spreading over this solid surface that means this is the solid surface and this block of a metal which after melting can have instantaneous spreading over the surface and we can get a layer and this layer is actually a coating over the surface by this wetting mechanism. However, we can have a situation at least two situations in between these two extreme absolute non wetting instantaneous spreading there is a spontaneity of spreading of the liquid and we have another one situation this is the solid and after melting the liquid assumes this shape and here this is the wetting is somewhere in between these two extreme situation and now we have the fourth one where this liquid after being melted it takes this shape this shape. So this is absolute non wetting spontaneous spreading and wetting this is a favorable situation for wetting and this is unfavorable situation for wetting more towards this extreme situation and this one is very favorable approaching towards this end. So this way we can understand the wetting or spreading of a liquid over a solid surface. Now here more important is the term contact angle and by this contact angle we can assess the degree of wetting of a liquid over a solid surface. So this is the solid surface and here this liquid is in equilibrium with the solid surface and making such a shape which is a part of a sphere like thing. Now here what we can draw at this point if we draw one tangent then this angle is theta and that is called the contact angle on this side also it is theta. So that is the contact angle now this contact angle is a measure of wetting. So when we see that it is spontaneous spreading then theta is almost equal to 0 it is approaching 0 and when it is like a sphere that means like a ball resting on a solid surface it is approaching 180 degree and when it is favorable wetting then we can find that this theta is less than theta is less than 90 degree that means we should say here that theta is in between 0 and 90 degree. So that is favorable wetting and it is more towards the wetting characteristics we can also put this way the value of theta that means it is somewhere between this two and this is actually the sign of non wetting. So absolute wetting very satisfactory wetting totally non wetting this is a favorable wetting and this is unfavorable or say it is more towards non wetting. Now here if we consider the equilibrium of this liquid with this solid surface we can find out identify three interfaces one is here between this liquid and this vapour then we have one with solid and vapour and another one between this liquid and solid. So what we see here that this film is equilibrium on this solid surface under the action of various forces which are known as interfacial tension force. Now here along the line of tangent we have one force that is actually the surface interfacial energy per unit area at this vapour liquid interface and that we can put as gamma L v. Similarly in this direction along this surface we can also have gamma S v that is the interfacial surface energy per unit area at this vapour solid interface which is gamma S v. Also we can see another force very much prevalent at this liquid surface interface and that is known as gamma S L. Now under the action of these three forces of course there is some gravity force this whole thing is in equilibrium. Now we can balance this force in the horizontal direction and from there we can find out that gamma S v minus gamma S L that is equal to gamma L v cos theta. Here we can see that to have satisfactory weighting or spreading this liquid film has to be stretched in this direction and for that there must be a driving force and this happens to be the driving force which is balanced with this cosine component of the interfacial tension between the liquid and vapour. However considering the dynamic state and if we want this continuous spreading of this film this part should be greater than gamma L v cos theta. So, this is actually known as Young's equation. Now this equation gives us a clear message that means or we can write cos theta is equal to gamma S v minus gamma S L by gamma L v. So, this is the term. Now when we have to have a spreading leading to 0 theta then obviously this value should be very high and under that condition this gamma S L should be as low and gamma S v should be quite high. So, in this case when we consider this as a favourable case of weighting we can write gamma S v is greater than gamma S L and that is greater than gamma L v. So, that is the condition which must be made in order that this liquid has a good or favourable weighting characteristics. Now here one thing also we understand that this gamma L v that is the surface tension of the liquid that is actually the resisting force which opposes this spreading or weighting and the numerator is the driving force. Now when it is non-weighting we have little different situation this will be gamma L v and in this case this is gamma S v this is gamma S L and this is theta. So, in this case what happens just the situation changes this way gamma S L and gamma L v that means in this case liquid tension is quite high compared to the surface energy of the solid surface though the interfacial tension is in between these two extreme values. Now with that we can find out another term apart from contact angle that is called work of adhesion. Now this work of adhesion means that when we create this interface which is having a contact angle which may be obtuse or we can have a contact angle which may be also acute the main thing here is that if we like to break this interface then certain change in free energy will take place this can be expressed this way. So, we can have gamma S v plus gamma S L v minus gamma S L that is given as W ad. Now this we can see in the form of change of free energy per unit area of this interface that means this is the final state this is the initial state that means the change is taking place from splitting of the interface and transforming it to two surfaces that means one liquid solid interface is now changed to a solid surface and that of liquid surface and in this process a change in free energy is taking place and that is given by this term work of adhesion. Now lower this value of this interfacial energy higher will be the work of adhesion that means this is actually the energy per unit area one may require to break this bond. So, this is actually known as Dupres equation and putting this Young's and Dupres equation one can find out that gamma S v this gamma S v minus gamma S L is plus gamma L v that is equal to W ad, but this can be substituted for by substituted by gamma L v cosine theta plus gamma L v is equal to W ad or finally, we are we arrive at this relation gamma L v is equal to 1 plus cos theta. So, this one this is an index of cohesion and this is the index of adhesion. So, by looking at this surface tension of the liquid and that of the contact angle some estimation on the work of adhesion or the adhesive force which is prevailing between this liquid solid or this liquid solid interface that can be estimated. Now contact angle on a heterogeneous surface now so far what we have discussed that is the contact angle on a homogeneous surface, but the surface may also have two phases say if we consider this as the unit area there we can have two phases and this is just like a dispersion in a matrix. So, if this is A that is the dispersion and B is the matrix then we can also make some attempt to find out what could be the resulting contact angle that means equivalent when we have a heterogeneous phase consisting of A and B. So, basic equation is say W we write W as work of adhesion into 1 plus cos theta. Now this can be also written as W A as into had it been totally the dispersion material that means the material which is dispersed if it contains 100 percent then we can write it is like this 1 plus cos theta A where theta A is the contact angle had it been 100 percent of A. Now following the same logic we can also write gamma L v plus 1 plus cos theta B and this is considering that the matrix is actually 100 percent over this unit area. Now let us consider that over this unit area q 1 fraction that is occupied by A and q 2 fraction that is occupied by B. So, in that case we can write that q 1 into W A that gives us q 1 W gamma L v into 1 plus cos theta A and q 2 W B that means the work of adhesion for A and work of adhesion for B. So, this will be is will be equal to gamma L v into 1 plus cos theta B. So, it is now apportionment by q 1 part and q 2 part. So, if we add then we get q 1 W A plus q 2 W B is equal to actually gamma L v which is the surface tension of the liquid plus into q 1 plus q 2 plus gamma L v into q 1 cos theta A plus q 2 cos theta B. So, it is cos theta A and cos theta B. Now this one q 1 plus q 2 equal to 1 because it is the fraction over this unit area. So, this is the equivalent work of adhesion. So, if we can replace it by W equivalent then we write here W L v this is also W L v and this is also equivalent to the resulting contact angle which we can write as theta equivalent what we have shown here and this is in this is in the same form as the combined form of Young-Dupre's equation that means 1 plus theta equivalent. So, this one actually this is coming as cos theta equivalent cos theta. So, from there we can write or cos theta equivalent is equal to q 1 cos theta A plus q 2 cos theta B. The summary of this whole exercise is that if we have component A and component B over a solid surface and if their proportion is q 1 and q 2 and if theta A is the contact angle for the surface A and if theta B is the contact angle for the surface B then the equivalent contact angle when we have a dispersion over a matrix that will be given by this relation. So, for a heterogeneous surface we can have one attempt we can try we try to find out the equivalent contact angle. Effect of roughness of the solid surface. Now, roughness of the solid surface can also affect wetting characteristics and this is actually given by Engels equation. Now, the equation states that this cos theta star that is given by R into cos theta O. Now, cos theta O is the normal wetting angle if the surface is absolutely flat and smooth. So, if it is a flat surface with sufficient smoothness then theta O will be the contact angle of a liquid over the surface. So, the liquid and solid they are same only according to Engels equations what happens now this surface is no more smooth, but it is slightly rough and this roughness is given by this factor R and this R is actually it is given by A R by A A suffix. So, A R means the real area of contact. So, if the surface is rough it can be machining mark or grinding mark or can be scratch over the surface. So, naturally real area of contact with the liquid that will increase and obviously, this ratio will increase. So, if it is a advancing liquid that means, there is a spreading normal spreading or there is normal wetting that means, in a situation where theta is in this zone that means, less than 90 degree that means, it is a favorable case of wetting under that condition if we have a rough surface then this rough surface favors wetting according to this law. So, because in this case cos theta star that means, the equivalent or apparent wetting angle this will be more than 1. So, naturally this value will be greater than that of cos theta O and naturally if it is a higher value of cos theta star. So, in this case this cos theta star is going to be more than cos theta O and therefore, this theta star will be less than theta O that means, wetting is improved by this roughness. However, if it is the non wetting situation that means, in that case what we see that value of so, this is for situation where we have normal wetting, but when it is non wetting and when it is non wetting in that case what happens this theta O this is normally it is negative that means, greater than 90 degree it is normally usually negative and by putting this equation here what we find that cos theta star will become more negative, more negative means it will approach more towards 180 degree. So, this will be more negative that means, theta star will be greater than that of theta O this is because of the simple reason that cos theta star is more negative than that of cos theta O. So, we also come to this conclusion that if the liquid drop is basically if it is non wetting in character then because of the surface roughness this angle will keep on changing and that value will keep on changing and it will be more towards non wetting. So, non wetting character will keep on increasing because of the surface roughness if originally the liquid is non wetting in nature. Effect of temperature on surface tension of liquid. Now, if we recall the basic equation of wetting which is given by this gamma s v minus gamma s l by gamma l v then we find that this gamma l v has a role to play though it is understood that the predominant role will be played by this surface energy of the solid and inter facial energy between this solid and liquid should be as low as possible, but at the same time if by some mechanism we can reduce this value of the surface tension of the liquid that will go in favorable direction. So, from this point of view we can consider the effect of temperature on surface tension of the liquid and here this is the common experience that means if we put in this differential form d t which is the temperature this happens to be a negative quantity that means with increase of temperature we have lowering of this value and by lowering this value we can have an effect positive effect on the value of cos theta that means the cos theta value will keep on increasing and as a result the theta value will also improve a lot that means more it will move towards wetting characteristics. So, this is the effect of temperature now surface tension of liquid solution. So, this is actually if we have one liquid l 1 we can add another liquid l 2 in certain proportion of course, these two are totally miscible. So, in that case we can find out that there is a resultant effect of this liquid and in this case what happens that this particular liquid can also reduce the surface tension of the original liquid and by this addition if we reduce the value of gamma l v. So, in that case we can also get a favorable value of cos theta that mean higher value of cos theta means a low value of theta. So, here the basic idea is to add one component in the parent liquid only to reduce is surface tension for example, in silver copper alloy if tin is added that can have a positive effect of reducing the surface tension of this parent liquid and that can have immediate effect a very positive effect on this value of theta. Now physical wetting so far the discussion we have made and the equations those governing equations whether it is Young's equation or Dupres equation or a combination of that. So, this is a guiding equation. So, what we have observed here that means it is actually the basic requirement of formation of interface and intimate contact that is the basic requirement to be met to have the wetting then comes a atomic level contact that must exist at the interface and that is only possible by van der Waals force of attraction and this is just a two phase system that means here we have. So, this is liquid and this is solid and at this interface there must be an intimate contact and this is this can happen by virtue of very presence of this van der Waals force of attraction and this is a two phase system that means liquid and solid and there is no presence of any third element in between. So, this is actually known as physical wetting. Now comes chemical wetting now in chemical wetting also we must have a true interface. However, in this case it is not only van der Waals force of attraction that promotes wetting, but more importantly here it is the diffusion across that boundary that means this is the solid and here we have the liquid. More importantly here you have transfer of the material either by the process of diffusion or by chemical reaction or alloying at the interface that means there is a chemical bridge that is established at the interface and as a result it is no longer a two phase system, but it becomes a three phase system. So, you have here a diffusion layer or a reaction layer or a layer because of the alloying this layer can be very thin or very thick it depends upon the chemistry of the liquid chemistry of the solid then the prevalent temperature. So, these are the three parameters which dictates what should be the reaction layer or the layer as a result of this alloy formation or because of the diffusion. The interesting thing here is that this equation that governing equation showing that this is gamma s v, gamma s l, s l and this is l v this just cannot be directly used in this case. So, here what is important to also consider this gamma s l that means this interfacial tension at this interface and that will be affected because of this chemical reaction that means this wetting angle that wetting angle is not just affected by van der Waals force of attraction, but the effect of diffusion cross diffusion or a reactivity or even alloying effect can have an overriding influence over the overall value of theta and this can be written rewritten little bit modified just by writing because of this chemical chemically augmented wetting we can write this as s v minus gamma s l minus delta g and that will go inside this parenthesis and l v. So, by this what we can achieve that original value of gamma s l that can be drastically reduced if we have some kind of reactivity between this liquid and this solid thereby changing the surface chemistry of the solid and as a result of this reactivity there will be a change in free energy which must be negative and this negative change in free energy that can act in a very favorable way by just reducing the value of the interfacial tension and thereby the net gain would be a very low value of theta and this is actually known as chemical wetting and this is extremely suitable or this is essential for wetting of ceramic surface ceramic surface by a liquid metal by liquid metal and unless this reactivity is there we cannot achieve a spreading or even a meaningful wetting otherwise this most of the metal they will act like a passive one and that will not lead to any meaningful wetting or spontaneous spreading. So, this reactivity is a must for wetting of those materials where there is a discontinuity in terms of mechanical discontinuity or physical discontinuity or even chemical discontinuity across this interface. Now, this can be well illustrated by one wetting characteristics and this can be illustrated here. Let us consider one binary system binary alloy and which forms one U-tectic at certain temperature. This is the melting point of the element M and this is the melting point of element N here M is 100 percent here N is 100 percent and this is actually the U-tectic composition and what we can have here say few cases. So, this is the prevailing temperature where we are going to examine the wetting characteristics. Now, what we have here four composition of this alloy it is 100 percent this is A this is B this is C and this is D that means, following this diagram we come to conclusion that A means 100 percent M and B means that is the limit that is the limiting temperature up to which B can hold itself in the solid form. Similarly, D is also one limiting position where it can also assume the liquid form and D is also in the liquid state. Now, what we can examine here very interesting thing say we have one solid which is B and we have a liquid which is C. Now, in this case participation of B or C in spreading the liquid that will not take place because of the simple reason that B is having a saturated composition and C liquid C that is the liquid C that is also having a saturated composition. However, angle theta that is acute and in this case gamma S V that is greater than gamma SL. So, this is called a passive interaction between B and C there is no sign of change of composition of C or B when they are brought in contact. Now, if we have another situation where C is in contact with A what is going to happen let us look into that in this case A will dissolve this compound this element N from C and so A serves A though it is a solid A here is acting like a solvent and this composition of the liquid at C that is like a solute. So, A will dissolve some component N from this composition C and as a result the chemistry of surface A that will change and because of this change what we can say here A is a active participant in this wetting activity and this active participant will reduce the value of theta drastically and it will lead to spontaneous spreading that means we can call it reaction spreading. So, A changes its surface composition just by dissolving some of the element N from this liquid which is at the composition C. Now we can consider another situation where this solid B that is in contact with D so liquid D and solid B now in this case also we do not see any active participation of the solid B though the liquid at D can dissolve some of the element M from B that means this D this D can dissolve some of the element M from the composition B however B composition as such it will not change because this is already saturated level. So, in this case also we can say that it is just a wetting case of wetting no reaction spreading however there is no reaction spreading. So, what we see here that considering this particular case and this case the first one number 1 this is number 2 and this is number 3 if we consider 1 and 3 only the difference is that D can dissolve some of the component M from B thereby its composition may change but the composition of B is not going to change its surface composition is not going to change because it is already saturated at that point. So, there will be no reaction spreading now come we take another example which is we consider another example which is actually two extreme situation here we have A as the solid and B as the liquid D as the liquid D as the liquid this is the liquid. So, what is the interesting thing that both A and D both are unsaturated. So, in this case what is going to happen A will dissolve some of N from D at the same time this liquid D can also dissolve some of the element M from A that means, there will be change in composition of both liquid and solid at the interface across this interface and in this case we can see that both liquid and solid both are actively participating in this wetting or spreading activity and we can call it reaction spreading. So, what is important what we find from this example that to have spontaneity in spreading there must be some kind of reaction and this reaction should lead to a change in surface chemistry of the solid surface unless that is done the liquid cannot be chemically activated towards the surface of the solid and we may not achieve the spontaneous spreading or wetting. Now this thing can be also extended this idea can be also extended in joining of ceramic where we find that a ceramic known for its ionic nature or covalent nature and it does not have the free electron to share and to bridge a continuity across this interface. So, when it becomes a ceramic and this is a liquid metal. So, unless this ceramic is reacted with this liquid that means, this liquid should be able to react on this surface of the ceramic to change its chemistry we cannot achieve this spreading over this also ceramic and that is why the conventional alloy must have some additive that means, this alloy must have some additive which can enhance the reactivity of this liquid over this ceramic and as a result this additive will be segregated towards this surface and change the chemistry of the ceramic making that surface wettable by the conventional metal M. So, this is also one of the very important aspect of metal ceramic joining by this activation of the conventional metal by this addition of a strategic material and this strategic materials are mostly we find from this transitional elements which are known as carbide former oxide former thank you or boride former or even nitride former. So, these materials are strategically chosen and added to the parent material to make this surface quite active and that can increase the wettability. So, what we see that in surface coating by wetting formation of an intimate contact at the solid liquid interface is the first requirement. The effectiveness of wetting process depends on the spontaneity of spreading of the liquid on solid surface. The reduction of interfacial tension by chemical activation of the liquid is one of the most important state for achieving this.