Evaporation of alcohol droplets on surfaces in moist air

Significance The evaporation of an alcohol droplet in moist air is more complicated than it seems due to condensation. We present a combined experimental and theoretical study of the evaporation of picoliter sessile droplets (isopropyl alcohol) under controlled relative humidity (RH). We report a series of morphological changes, including the formation of a pancake-droplet that suppresses the coffee-ring effect. We developed a quantitative model that captures the essential physics of the problem and shows good agreement with experiment. One unexpected feature from simulation is that water can evaporate and condense concurrently in different parts of the drop, providing fundamental insight into drying dynamics. We show that large compositional variations exist within drops with profound implications in formulation applications.


Thermal effect in drying IPA droplet
In Figures S2 and S3, we show the drying behavior on two substrates -glass and sapphire -which have very different thermal conductivities (sapphire: 46 W m −1 K −1 ; glass: 0.96 W m −1 K −1 (1)).
The drying behavior is the same on both substrates, showing that the substrate behaves as an isothermal heat source; there is no cooling of the substrate that leads to observable thermal effects in the drying of the droplets.
We have estimated the magnitude of thermal cooling of a pure IPA droplet in an earlier paper (2).
The average rate of heat loss in a droplet due to the latent heat of evaporation is J avg ∆H v , where the average evaporative mass flux J avg = 4RD v c a /(πR 2 ) ≈ 0.03 kg m −2 s −1 with vapour density c a ≈ 0.12 kg m −3 and R = 50 µm, and the latent heat of evaporation per unit mass of liquid ∆H v = 756 kJ kg −1 (3).Under quasi-steady conditions, evaporative heat loss is balanced by heat conduction from the substrate (assumed to be isothermal, see above), i.e.J avg ∆H v ≈ k L ∆T /h, where h is the thickness of the drop at the apex ∼ 3 µm and the thermal conductivity k L = 0.14 W m −1 K −1 (25 °C, (3)).The temperature difference between the bottom and top of the drop, ∆T ≈ J avg ∆ v Hh/k L ≈ 0.5 K (colder at the top).The ratio of the substrate to liquid thermal conductivities k R = k S /k L > 2, so the drop is coldest at the apex (4).Consequently, the thermal Marangoni effect opposes spreading.
Since Marangoni flows due to composition gradients enhance spreading under the conditions studied here, any thermal Marangoni effects would act to reduce the rate of enhanced spreading.The ratio of flow speeds from thermal Marangoni effects and evaporation is given (5) by the thermal

Marangoni number Ma
Ma T is not negligible, so we cannot a priori rule out thermal Marangoni flows making an observable contribution to the spreading dynamics.We note that studies on microlitre droplets have found that convection within drops typically leads to thermal Marangoni flow being 10 − 100 times weaker than predicted using scaling arguments (7,8).Our experiments show, however, that pure IPA evaporation displays the canonical spreading behavior for pure droplets on both glass and sapphire at both low RH (Fig. S2) and high RH (Fig. S3).We note that water condensation reduces thermal gradients in the droplet, so the largest thermal Marangoni effects would be expected in pure IPA.
The good agreement between our experiments and simulations, which do not account for thermal effects, provides additional evidence that thermal effects in our system are weak compared to solutal effects.

Condensation effect at the nozzle
The initial condition for an IPA droplet printed onto a glass substrate is not pure IPA due to absorption of water in the nozzle and, to a lesser extent, in flight.To provide a quantitative estimate of the effect of water absorption in the nozzle on the initial droplet composition, we treat the nozzle for simplicity as a cylindrical channel with a radius of 15 µm and a constant, uniform flow of pure IPA from a reservoir towards the nozzle plate to maintain the meniscus at a constant position as the IPA evaporates.We can then write down a steady-state 1-D solution to the convective-diffusion equation in the nozzle in which the liquid at the nozzle surface is in equilibrium with the vapor at the nozzle.Figure S8c shows the equilibrium volume fraction of IPA for different RH.For example, for RH = 60%, the liquid at the nozzle surface has composition (by volume) of 92% IPA and 8% water.The water concentration then decays exponentially into the liquid with a decay length given by D l /E, where D l = 6 × 10 −10 m 2 s −1 is the mutual diffusion coefficient in the liquid ( 9) and E is the flow rate in the nozzle (which is equal to the evaporation rate of the IPA, since at steady-state

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Lisong Yang, Amir A. Pahlavan, Howard A. Stone and Colin D. Bain there is no net condensation or evaporation of water).For a 92% IPA solution in a 15-µm diameter nozzle, E = 120µm s −1 , giving a diffusion length of 5 µm.The characteristic time to establish a steady-state profile is given by D/E 2 = 40 ms.Given that the delay before printing a drop is 40 ms, we can assume that the composition profile in the nozzle is close to steady-state.Again assuming a cylindrical nozzle for simplicity and plug flow during the droplet formation process, a 22-pL drop is formed from the 17-µm depth of liquid nearest the nozzle, the average composition of which is 2.4% water and 97.6% IPA.This is only an approximate calculation of the initial composition of the droplet because the nozzle is actually tapered (which will slightly increase the water concentration in the drop) and the flow velocity is non-uniform due to the non-slip boundary condition on the walls of the nozzle (which will decrease the water concentration in the drop).This estimate also neglects Marangoni effects in the nozzle.
To explore the effects of water condensation on the experimental results we carried out two control experiments.First, we compared the drying behaviour of IPA droplets printed after a delay of 500 ms and 2 s (See Fig. S4 and S5).We would expect on the basis of the scaling argument above that the initial droplet composition should be the same for both of these time delays and we do indeed observe nearly identical behaviour.This control experiment is also important in showing that we do not have to control the delay before printing a droplet with great precision.
Second, we studied the drying behaviour of a droplet with an initial (reservoir) composition of 95% IPA by volume -a solution that contains more water than the calculation above yields for pure IPA in the nozzle at all the RH that we studied, shown in Fig. S6.At very low RH, the 95% IPA droplet shows qualitatively different behaviour from pure IPA due to Marangoni contraction (10), because the water is evaporating faster than the IPA (which in turn arises from a combination of the well-known non-ideality of mixing of water and alcohol (11) and the higher vapor diffusion coefficient of water).Marangoni contraction is not observed with pure IPA since at low RH there is negligible water condensation in the nozzle.At RH = 61% we observe the same qualitative features as for pure IPA.We conclude that water condensation in the nozzle does not materially affect the behaviour of IPA droplets over the range of RH reported in this paper.

Storage and handling of IPA samples
The master bottle from the purchase is poured to fill 2/3 of a 100-mL borosilicate glass reagent bottle inside a fume hood.The master bottle is resealed immediately and used for analytical purposes within a month after being opened.The secondary bottle is used for the experiment within two On glass On sapphire

Fig. S1 .
Fig. S1.Profiles for (a) RH = 68% and (b) RH = 74% at earlier times (see later times in Fig. 1b).Symbols are experimental data, and lines are (a) parabolic fit for t ≤ 0.45t f , and (b) 4th-order polynomial fit for t = 0.2t f and 9th-order polynomial fit to t = 0.3t f and 0.4t f .(c) Droplet profile from side-view image (inset) for RH = 68%.Symbols are experimental data, and the line is fit to a circular arc.Scalebar for inset image is 20 µm.(d) Droplet volume as a function of time for RH = 68%.The volume at t = 1 ms is obtained from a side-view image of a droplet (error bar shown) and the rest are from the reconstruction of the profile (see Methods).

Fig. S3 .
Fig. S3.Contact diameter of IPA sessile droplet as a function of the elapsed time at various RH, printed on (a) glass and (b) sapphire from a nozzle with orifice diameter of 50 µm.Initial droplet volume is in the range of (a) 72 -83 pL, and (b) 87 -91 pL.

Fig. S4 .Fig. S5 .
Fig. S4.Droplet lifetimes, t f , and the lifetimes of the IPA-rich central cap, t f , as a function of RH.(a) Two independent measurements (with a two-month gap) on a glass substrate.Initial droplet volume is in the range of 72 -83 pL.IPA in the first experiment was from an IPA bottle opened 15 days before the experiment.IPA in the second experiment was from a freshly opened bottle.(b) Data for two consecutively printed droplets at 2 Hz on a sapphire substrate.The 1st droplet is generated from a nozzle with an idle time of ∼ 2 s after the previous drop is dispensed.The initial droplet volume is in the range of 87 -91 pL.