Drop Formation by Thermal Fluctuations at an Ultralow Surface Tension

Abstract

We present experimental evidence that drop breakup is caused by thermal noise in a system with a surface tension that is more than 10 6 times smaller than that of water. We observe that at very small scales classical hydrodynamics breaks down and the characteristic signatures of pinch-off due to thermal noise are observed. Surprisingly, the noise makes the drop size distribution more uniform, by suppressing the formation of satellite droplets of the smallest sizes. The crossover between deterministic hydrodynamic motion and stochastic thermally driven motion has repercussions for our understanding of small-scale hydrodynamics, important in many problems such as micro-or nanofluidics and interfacial singularities. DOI: 10.1103/PhysRevLett.97.244502 PACS numbers: 47.20.Dr, 47.55.df, 82.70.Dd Drop formation represents a basic phenomenon important in a wide variety of industrial and natural processes. For instance, all spraying processes, ranging from dispersing pesticides [1] to ink-jet printing, rely on controlling drop sizes for efficient application. Classically, two hydrodynamic mechanisms of drop formation are known: Surface tension always causes the breakup and is countered by either the viscosity or the inertia of the liquid [2 -6].In this Letter, we report on a different mechanism: drop formation when altered by perturbations of the interface. This leads to both qualitatively and quantitatively different behavior. It has been shown before that finite amplitude perturbations may trigger successive instabilities and qualitatively change the shape of the breakup [7,8]. In our experiments, however, the perturbations are an intrinsic property of the fluid interface: The thermal fluctuations of the interface lead to a new breakup mechanism [9,10]. Such thermal capillary waves are always present at all fluid interfaces due to the thermal energy k B T, with Boltzmann's constant k B and temperature T.To estimate at what length scales the thermal noise becomes dominant over capillary forces, a fluctuating stress S is added to the Navier-Stokes equation. Dimensional analysis gives the pressure gradient rp =L 2 , with the interfacial tension and L a characteristic length, and the gradient in the fluctuating stress tensorwhere is the viscosity, and the time t is proportional to L = . It now readily follows that at lengths L of the order of the thermal length L T k B T= p thermal noise dominates the capillary forces. This is also the typical roughness of an interface and results from the competition between surface tension that tends to keep the interface flat and thermal energy driving the fluctuations. For simple liquids, L T is typically nanometric. Consequently, the surface is flat at hydrodynamic scales, and free-surface flows such as the one occurring in droplet snapoff are very well described by the Navier-Stokes equation without fluctuations. This hydrodynamic description breaks down when the flow takes place at scales comparable to L T , which we are able to observe here by strongly decreasing the surface te...

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“…Note that the exponential regime is also observed for a colloidal suspension of 1.3 μm particles (Fig. 4), showing that the thermal (Brownian) fluctuations of the particles do not change the breakup dynamics qualitatively; this is nontrivial since in some cases the breakup can be altered by fluctuation forces [28,29].…”

Life at ultralow interfacial tension: wetting, waves and droplets in demixed colloid-polymer mixtures

“…They were able to account for their MD results by adding to the Navier Stokes equations a fluctuating stress first introduced by Landau and Lifshitz [41]. It is easy to estimate [42] that this fluctuating stress becomes dominant over capillary forces at length scales of the order of the thermal length L T = k B T /γ. Therefore one expects that these fluctuating stresses become important on the nanoscale for atomic and molecular liquids as was indeed observed in the computer simulations by Moseler and Landman [40].…”

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