Generation and Observation of Long-Lasting and Self-Sustaining Marangoni Flow

When solute molecules in a liquid evaporate at the surface, concentration gradients can lead to surface tension gradients and provoke fluid convection at the interface, a phenomenon commonly known as the Marangoni effect. Here, we demonstrate that minute quantities of ethanol in concentrated sodium hydroxide solution can induce pronounced and long-lasting Marangoni flow upon evaporation at room temperature. By employing particle image velocimetry and gravimetric analysis, we show that the mean interfacial speed of the evaporating solution sensitively increases with the evaporation rate for ethanol concentrations lower than 0.5 mol %. Placing impermeable objects near the liquid–gas interface enforces steady concentration gradients, thereby promoting the formation of stationary flows. This allows for contact-free control of the flow pattern as well as its modification by altering the objects shape. Analysis of bulk flows reveals that the energy of evaporation in the case of stationary flows is converted to kinetic fluid energy with high efficiency, but reducing the sodium hydroxide concentration drastically suppresses the observed effect to the point where flows become entirely absent. Investigating the properties of concentrated sodium hydroxide solution suggests that ethanol dissolution in the bulk is strongly limited. At the surface, however, the co-solvent is efficiently stored, enabling rapid adsorption or desorption of the alcohol depending on its concentration in the adjacent gas phase. This facilitates the generation of large surface tension gradients and, in combination with the perpetual replenishment of the surface ethanol concentration by bulk convection, to the generation of long-lasting, self-sustaining flows.


Pendant drop experiments
To simulate the influence of ethanol in the gas phase, a petri dish filled with ethanol was placed directly under a freshly generated drop of sample liquid, as illustrated in Figure S1. Due to the close distance of the drop to the evaporating surface, fast equilibrium between the gas and liquid phase was achieved. For each experiment, the mean of six measurement values was taken. All measurement values are provided in Table S1.

Calculation of dissipated viscous energy
The amount of dissipated kinetic energy per unit time can be calculated from the velocity field where is the dissipation function for an incompressible fluid with the general form Here, , and denote the velocity components in x, y and z-direction, respectively. The bulk viscosity of SCS (17.5 mol% NaOH solution) mixed with 0.5 mol% of ethanol = 12.64 mPa s was determined by rheometry. For flows with velocity components only in the xand z-direction, the dissipation function simplifies to To calculate the dissipated kinetic energy from PIV velocity fields, Equations 1 and 2 were implemented in discretized form in MATLAB (r2020a, The MathWorks Inc.). The code is available on request. The dissipation functions for the flows generated by vapor trap geometries 2 and 3 for SCS mixed with 0.5 mol% of ethanol are provided in Figure S2.

Viscosity measurements
To determine the influence of ethanol on the bulk viscosity of SCS, three samples with ethanol concentrations of 0, 0.5 and 1 mol% were tested. As visible in Figure S3, all samples showed approximately Newtonian behavior, i.e., constant viscosity as a function of the shear rate. This allows determination of viscosity simply via averaging over datapoints, yielding the values provided in Table S2. For the sample without ethanol, the value is in good agreement with data reported in the literature 2 .

Conductivity measurements
To validate that concentrated sodium hydroxide solution can store small amounts of ethanol, the electrolytic conductivity was measured using a custom setup employing the method of moving electrode electrochemical impedance spectroscopy (MEEIS). In contrast to conductivity sensors with static electrodes, MEEIS uses two parallel, oppositely arranged electrodes, with one of them being mounted on a motorized linear stage. This enables precise adjustment of the electrode distance and allows determination of the conductivity by a modified version of Pouilett's law, where is the slope of the impedance as a function of the electrode distance and the (homogenous) cross section of the sample. Due to capacitive effects at the electrode-liquid interface, the measured impedance is frequency dependent and selection of the right value is crucial to obtain accurate results. Therefore, impedance spectra are recorded in a large frequency range (10 Hz to 5 MHz), and the measurement frequency is chosen based on a minimal-phase criterion 3 . Since conductivity is not determined from the absolute impedance value but the impedance increment as a function of the electrode distance, (quasi-)constant contributions to the impedance are eliminated, enabling accurate conductivity measurements of chemically aggressive, highly conducting and heterogenous media, as demonstrated in previous studies of our research groups 4-6 . Furthermore, this method allows locally probing the sample properties, enabling the analysis of individual phases, e.g., of a phase-separating sample.
separation was observed but conductivity drastically decreased, as shown in Figure S4.

Influence of reduced salt concentration
To investigate the influence of salt concentration on interfacial flow speeds, a sample with reduced (10 mol% NaOH) and a sample without NaOH, each mixed with 0.5 mol% of ethanol, were investigated. At this ethanol concentration, flow speeds reached a maximum for the most concentrated sample (SCS + 17.5 mol% NaOH , cf. Figure 2(a)), whereas flow speeds for the sample with 10 mol% NaOH were already significantly lower and less sustained, as shown in Figure S5. When no salt was added (0 mol% NaOH), flows were entirely absent, although a similar mass loss due to evaporation was measured for all three samples ( Figure S6).

Calculation of molar ethanol fraction and evaporation rate
First, each measurement curve was fitted with an appropriate function (dashed lines in Figure   3(a)). For concentrations ≤ 2 mol%, a quadratic function of the form = + 2 was used to account for the slightly positive curvature, whereas for the 3 mol% samples, a linear function of the form = was used. Assuming ethanol being the only evaporating component, the ethanol mass in the sample as a function over time is given by where ( 0 ) is the mass of ethanol in the sample before evaporation takes place, and ∆ ( ) where , and 2 are the molar mass of ethanol, sodium hydroxide and water, respectively, = 0.32 is the weight fraction of NaOH in SCS, and = 16.42 g is the initial sample mass, calculated as the product of the initial sample volume (12.25 ml) times the sample density ( = 1.34 g cm -1 ).
Evaporation rates as a function of time were determined by differentiating the line fits over time using the Python's numpy package.