Dripping to Jetting Transitions in Coﬂowing Liquid Streams Andrew S. Utada, 1 Alberto Fernandez-Nieves, 1,2 Howard A. Stone, 1 and David A. Weitz 1,3, * 1 Harvard School of Engineering and Applied Sciences, Cambridge, Massachusetts 02138, USA 2 INEST Group, Philip Morris USA, Richmond, Virginia 23224, USA 3 The Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA (Received 21 October 2006; published 28 August 2007) A liquid forced through an oriﬁce into an immiscible ﬂuid ultimately breaks into drops due to surface tension. Drop formation can occur right at the oriﬁce in a dripping process. Alternatively, the inner ﬂuid can form a jet, which breaks into drops further downstream. The transition from dripping to jetting is not understood for coﬂowing ﬂuid streams, unlike the case of drop formation in air. We show that in a coﬂowing stream this transition can be characterized by a state diagram that depends on the capillary number of the outer ﬂuid and the Weber number of the inner ﬂuid. DOI: 10.1103/PhysRevLett.99.094502 PACS numbers: 47.61.Jd, 47.20.Dr, 47.27.nf, 47.55.db A liquid forced through an oriﬁce will ultimately break into drops through one of two mechanisms. At slow ﬂows, the emerging liquid drips from the oriﬁce, whereas at faster ﬂows, the liquid forms a thin stream that breaks into drops away from the oriﬁce; these are the dripping and jetting regimes. This behavior is familiar to anyone who has slowly increased the ﬂow rate of water at a kitchen faucet. In this case, dripping occurs at low ﬂow rates where surface tension causes the water to form drops at the tap; the hanging drops detach when the gravitational force exceeds surface tension forces. At higher ﬂow rates jetting occurs when the inertial forces of the water exceed surface tension forces [1,2]. The dripping-to-jetting transition is sharp if the liquid viscosity is large compared to water [2], whereas the transition initially becomes chaotic [1,3 – 5] before jet- ting for lower viscosity ﬂuids. The jets eventually break into drops due to the Rayleigh-Plateau instability [6,7]. While both dripping and jetting must occur when a liquid is injected in a second immiscible liquid [8 –10], the mechanism of droplet formation changes due to the presence of the surrounding viscous liquid [11–14]. Drop formation has rich dynamics [15,16] that are affected by many parameters such as the average velocities of both liquids, their viscosities and densities, surface tension, and the surface chemistry and device geometry [17]. Two- phase drop formation is important to applications in micro- ﬂuidics [18,19] such as ﬂow focusing [15,20] and in liquid- gas systems [21], selective withdrawal for coating particles [22], and extrusion emulsiﬁcation [23]. Because of its importance, drop formation in two ﬂuids has been widely studied [8 –10,24,25]; however, complete control over the two-phase ﬂow behavior requires a detailed understanding of the dripping-to-jetting transition, and a uniﬁed view of this transition is still lacking [26]. In this Letter, we use a microcapillary device to study the transition between dripping and jetting in a two-phase coﬂowing stream. The behavior is characterized by a state diagram that depends on both the capillary number of the outer ﬂuid, C out , and the Weber number of the inner ﬂuid, W in ; these parameters describe, respectively, the magni- tude of the viscous shear forces from the outer liquid and the inertial forces from the inner liquid compared to sur- face tension forces. We observe two distinct jetting re- gimes with signiﬁcant differences in jet shape and the mechanism controlling drop size. Our experimental device is made of two coaxially aligned capillary tubes. The inner capillary tube is cylin- drical, with a tip tapered to an inner diameter of d tip ’ 20 m and an outer diameter of 30 m. The outer capil- lary tube is square; coaxial alignment of the tubes is achieved by matching the outer diameter of the untapered portion of the inner capillary to the inner dimension of the square capillary, D  1 mm, as shown in Fig. 1(a). At this length scale, which is below the capillary length, the effects of gravity are negligible. Although the ﬂow in the square tube is not axisymmetric, since the tip is centered and d tip =D  0:02, the local ﬂow around the tip should be approximately axisymmetric. For experiments requiring a larger velocity of the outer ﬂuid, we place a second cylin- drical capillary with inner diameter of 200 m inside the outer square capillary, surrounding the tip; since this extra capillary has a smaller cross section than the square one, the outer ﬂuid achieves a higher average velocity. Although the surrounding walls are closer in this case, the jet diame- ter is  d tip , and d tip =D  0:1; thus, we expect wall effects to be small. We use deionized water and different viscosity polydimethylsiloxane (PDMS) oils; interchanging the oil and water enables us to vary the viscosity ratio,  in = out , from 0.01 to 10, where  in and  out are the viscosities of the inner and outer ﬂuids, respectively. The surface tension between PDMS oil and water can be lowered from 40 to 4 mN=m by adding 60 mM sodium dodecyl sulfate (SDS) to the water. This high concentration of SDS reduces surface tension gradients across the jets. In coﬂowing ﬂuids, dripping occurs at low ﬂow rates of both ﬂuids and is characterized by the periodic formation of individual drops that pinch-off from the tip [Fig. 1(b)]. We observe two distinct classes of transitions from drip- PRL 99, 094502 (2007) PHYSICAL REVIEW LETTERS week ending 31 AUGUST 2007 0031-9007= 07=99(9)=094502(4) 094502-1  2007 The American Physical Society