 And it's on oscillatory motion of whiskolastic polymer drops on celebrity lubricated surfaces and you are already there Okay, thank you. Thank you very much and I would like to start by thanking all the organizers for getting back here in presence the community working on dissipation and nanotribology and tribology in general and In this cross course Triturization with different topics and different competencies I would also thank for the opportunity to share what we did in Padua So the work has been done in Padua in Charlie in Padua and it has been done in close Collaboration with Jean-Paul Mistura who is very sorry He missed this conference, but he's looking forward to come to the next and he's reading all co-workers and colleagues and The idea has started with some with some thesis with some masters and We would like to thank in particularly Paolo Sartori who has performed a lot of work also in the collecting the final data and organizing all the material Okay, let us start with a couple of words about the motivation Controlling and predicting the mobility of the drops is a is a major goal Okay, it's a major scientific challenge, which is relevant also Not only for science but also for a lot of practical application including self cleaning coatings digital microfluidics drop-wise condensation and for collection Well, the mobility of the drops is Actually deeply affected by the subject heterogeneities So if we look quickly look to the nature, for instance, water drops can roll very easily retaining a nearly spherical shape On the super hydrophobic surface is like the lotus leaves instead a partial impregnation of a surface texture Can cause a strong pinning of the drops like in the petal in the in the in the rose petal and in some picture plants Very in addition another phenomenon and other effect that surface section Surface texturing can be impregnated by an immiscible fluid so that the drop can float on that So the main point is that From a static point of view all of these configuration are pretty are pretty similar one each other But the mobility the motion of a drop is completely different in these three cases And the why it happens it is related to not the Equilibrium contact angle, but the dynamic contact angle If we start from equilibrium configuration and we increase the volume of a drop We have that the contact angle is increasing up to a value where the contact line is moving and if we Decrease the volume have a similar phenomenon But the two angles are different and the difference of a contact angle is called contact angle hysteresis and it is accounting for the morphological and chemical heterogeneities and defects Okay, so if you want to study the sliding of a drop over the surfaces where we of course we have different contact angles Bouncing part of the other drop and in the receding part We have to consider at least three forces mainly three forces Of course the gravitational pull which is given by the down plane component of the drop weight And then we have the viscous track which is proportional to the viscosity of a drop to the speed of a drop and To the volume of a drop to a one third a power Which is a relative cost of a perimeter of the drops advancing or sliding into the plane and The coefficient of proportionality it is Keeping account about the distribution of a contact angle around the perimeter of the drops and the fact that the dissipation is associated It is smaller for It is it is smaller for It's more in the wedge. Okay as the as the contact angle is lower it the dissipation is Increased and it so in this particular configuration. It is higher than for example the bulk of a drop It the bug dissipation is really smaller than the dissipation close to the contact line And finally, of course, we have the interfacial forces interfacial forces as of course proportional to the surface tension between the liquid in the and the and the gas Again to the one third power of a volume and then we have a Parameter a coefficient which is again keeping into account a distribution of a contact angle around the perimeter of the drops But in the farmage formulation, this is proportional to the contact angle hysteresis in the form of a difference of a cosine Okay, the difference between the advancing and the receding contact angle does not necessarily vanish For small velocities and this is a manifestation of a hysteresis above Above a certain A certain threshold, which is a call that critical angle below which the drop the result spin it above that threshold the force balance among the Different forces can be expressed in terms of dimensionless quantity That is the capillary number and the bond number and the critical bond number It is accounting. It is keeping into account the wetting hysteresis So given that the surface tailoring Has been proven to an effective strategy to try the drops on the tilted surfaces Drops can undergo a stick-as-leap motion across different hydrophilic and hydrophobic patterns on can be deviated by a chemical steps for example Well, if you had a look to the posture of Sebastian cremascini, you know now that the deviation can be also Achieve it by using optical path and the chemical step can also be bent it well to play a game With interfacial forces in order to reduce as much as possible the contact angle hysteresis Inspired by the nifantis picture plans Effective strategies has been developed to produce very slippery surfaces that hardly pins aside drops They involve the trapping of a suitable low surface tension lubricating liquid inside the texture and The lubricant if it is chosen correctly and sweetably allows a drop of another liquid to float on the And so a new class of materials Of material is defined it and they are known as liquid-infused surfaces and their results hemiliquid and hemisolid and They intercalate a lubricant It is trapped by the solid cavities by capillaries and therefore there is no direct contact between the drop and the solid surfaces behind and Since the lubricant it is intrinsically flat and chemical homogeneous The contact angle hysteresis the pinning due to the contact angle hysteresis is expected to reduce Really a lot for these futures All these futures all these characteristics This kind of surfaces has been used in various applications including bio Biomedical device by that my biomedical devices, sorry and sanitation heat exchanges and also food dispensers So in this study we realize it two different Liquid impregnated surfaces following two different routes for silicone oil Noil a silicone oil is spread into a glass slide and then bake it at 300 degrees for several minutes Back to the room temperature the excess of the oil has been washed away with acetone and the results of this Thermal process is a thin porum solidified silicone layer of about 200 nanometer of thickness that we can impregnate with silicone oil conversely with for fluorinated oil We use another technique so we use 20 micron thickness filter Teflon filter made of Teflon and we applied We applied that on the microscope slide and wetted with ethanol in order to Get an addition a kind addition by capillarity Once the ethanol evaporates the membrane it is impregnated with fumbling, which is basically a fluorinated lubricant So the control The control That the memory is pigmented with the system and the control of a withdrawal velocity of a deep coating He controlled essentially the thickness of the oil in this case of fumbling that it is retained by the surfaces With this technique. It is usually common to to get A thickness of the oil over over the order of 0.5 micron So currently we cannot measure directly the thickness of the oil but In this kind of study we had a very high reproducibility of a drop motion indicating that the Lubricants the lubricant layer it is very stable indeed if we try to use the second process Also to use the the filter with silicone oil the Reproducibility is much worse because mainly And a not good chemical affinity within the silicone oil and the different filter So now the goal it is to address the motion of non-Newtonian drops Non-Newtonian drops because on this kind of surfaces and this is particularly important because non-Newtonian drops are in Generally very viscous and hardly can move on solid surfaces We consider a couple of polymers the polyacrylamide PAA a flexible polymer and exanthangam Which is a steep road like polysaccharide and both of them are prepared in ultra pure water A different concentration and different molecular weight in particular different molecular weight for the PAA With respect to the concentration all the polymers are falling in the either the dilute or the semi dilute regime And since the fact since the surface tension of a polymer solution is very similar to that of pure water It is expected that the drop are clocked by a thin thin layer of a lubricant So for non-Newtonian fluid the viscosity is not a coefficient But it is a function of a shear rate that is the rapidity at which the formation takes place So in a complete geometry we measure the viscosity of a polymers as a function of a shear rate and as commonly reported both polymers Exhibit a shear thinning a shear thinning Behavior meaning that the viscosity is reduced as the shear rate is increased And as expected And as expected, okay, we saw we have also for reference we have also indicated here the glycerol the glycerol Water solution and the silicon oil viscosity We also measure the shear dependence of the first normal stress difference and one which is related to the vertical force exerted by the polymer Upon the rotating plate and with respect to the stress tensor the n1 it is the Difference between the diagonal term and it is of course it is of course zero for a Newtonian fluid and positive for an elastic fluid and In agreement with literature to n1 increases Quadratically with a shear rate and increases of course with the polymer concentration Okay, as for the wetting properties, they are quite similar to the The contact angle of the pure of the pure water So the motion of the drops is acquired using a custom made setup and the sample is mounted on a rotating Support was inclination can be set with an accuracy of 0.5 degree The drops of a volume which is in the rent between 10 and 40 micro liters Can be are those away with a micro pipette and are illuminated by a white lead backlight The lateral profile of the drop is imaged in time by a fast camera Mounted along the rotational axis of a stage and with respect to a title plane we indicate the Front contact point the one which is down here the drop. So let's have a look to the motion of this draw So the movie clearly show that An Oscillatory behavior of a instantaneous speed and the periodical motion of a deformation around the semi circular profile and since we are in Trieste to pay tribute we prepare the polymeric coffee and The The ground coffee particles added to the solution I like the internal rolling motion of the drop So it is not a pure sliding. Well a sequence of the snapshot extracted from the movie is that the drop profile It is not stationary and there is a budge moving around the drop perimeters during the motion So let's go ahead and just study the time evolution of the front position of the contact line of different drops Most of the data are taken with silicone oil With a nominal with a nominal lubricant thickness of approximately 3 micron The blue course it is the the glycerol water mixture the glycerol the Newtonian fluid and Is expected as expected it is linear like the other Newtonian liquids But one important thing that it is despite the much higher static viscosity meaning at zero shear the average speed of polyacrylamide at 10 with a molecular weight of 10,000 gram per moles 10 One to the one to the to the seven gram per moles a concentration below 2000 and 2500 ppm is comparable to that over this little water drops and this is because Basically due to the shear finning The what it is happening that is the viscosity of the oil it is resulting greater than the one of the polymer and In this kind of motion if the viscosity of the oil it is greater with respect to the drop the dissipation It is taking place into the lubricant oil and that's why all these course are more or less the same and the noise It is just because we use different Surfaces, so maybe it is related to the presence of different thickness of a lubricant oil and the uniform motion of Glycerol and also the polyacrylamide at low molecular weight is better shown by subtracting the linear trend and blocking the instantaneous variation of a front and the rear cotton points with respect to the feet as Expected from the logical characterization This kind of drop exited the same uniform motion as glycerol However as the molecular weight of a polyacrylamide is increased oscillation starts to appear and The most evident oscillation are the one related to the concentration the intermediate molecular weight for the polycylamide and the concentration of the 5000 ppm This is by the way the situation where we extracted the Snapshot that you see just before Obviously if the molecular weight is further increased it oscillation appear damped and irregular For the xanthan xanthan displays a weak yet non-null oscillation as well And here we want to stress that this kind of non-uniform motion It is very unlikely due to the surfaces, which is a homogeneous perfectly homogeneous surfaces To complete the story we did the same with orinated oil and to make the story short We just recovered more or less the same the same results confirming that there is no a rule a role played by by the surface the surface is pretty homogeneous independently from the kind of a realization for different surfaces and so this kind of oscillation are basically due to the Properties of the polymer itself For both polymers we have plotted the frequency of a periodic oscillation as a function of the mean drop speed having different volumes on surface titled for different angles and It emerges a clear proportionality between the frequency and the speed and this confirms that the oscillation are related to the motion of a bulge of the drop in the in the drop profile a The inverse of the slope of interpolating dash of an important interpolated usher line Yes, it's a characteristic length and this length. It is surprisingly very very similar to the Free perimeter of the drop it if we plot not the frequency but the product of the frequency times the perimeter as a function of a speed we get a master curve and a Mastercoupe with a slope which is equal to one with no free parameter So basically the time law it is the one that it can be Observed by a mechanical system, but of course the Explanation it is completely different and it is related to the Beisenberg effect Very very quickly Here in the in the it is the last slide here in the rear in the wedge of the of the drop The shear rate it is particularly great Particularly important and so the elastic effect which is n1 It is important as well. And so there is the formation due to the elasticity of the polymer There is an extra tension Which is Forming the bulge in the rear and then when the bulge it is formed the Periodical emotion it is just a matter of conversion of a kinetical and potential energy during the motion so I have concluded and Just to resume the take-home messages Oscillations have been detected in the presence of defect free surfaces elastic properties and also The presence of the homogeneous surfaces are important to observe this phenomena But of course the story it is not complete and so we will we would be happy to collect the idea to to to give a comprehensive and definitive explanation of Thank you very much all of you for that Thank you very much indeed for this clear presentation Which I hope has answered most of the questions we may have had because we used up our time And we will sort of postpone all questions to the coffee break. Thank you very much Okay, our next speaker is Thomas Heimlich. He's coming to us from a Sort of different field. We have not heard about membranes today and yesterday and but there is of course fluctuations