PACS numbers Eects of viscosity on liquid structures produced by in-air microuidics David BaumgartnerG unter Brenn and Carole Planchette

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PACS numbers:

Eﬀects of viscosity on liquid structures produced by in-air microﬂuidics

David Baumgartner,∗G¨unter Brenn, and Carole Planchette

Institute of Fluid Mechanics and Heat Transfer, Graz University of Technology, A-8010 Graz, Austria

(Dated: October 11, 2022)

This study experimentally investigates the eﬀect of viscosity on the outcomes of collisions between

a regular stream of droplets and a continuous liquid jet. A broad variation of liquid viscosity of

both the drop and the jet liquid is considered, keeping other material properties unchanged. To

do so, only two liquid types were used: aqueous glycerol solutions for the drop and diﬀerent types

of silicone oil for the jet liquid. Combining these liquids, the viscosity ratio λ=µdrop/µjet was

varied between 0.25 and 3.50. The collision outcomes were classiﬁed in the form of regime maps

leading to four main regimes: drops-in-jet,fragmented drops-in-jet,encapsulated drops, and mixed

fragmentation. We demonstrate that, depending on the drop and jet viscosity, not all four regimes

can be observed in the domain probed by our experiments. The experiments reveal that the jet

viscosity mainly aﬀects the transition between drops-in-jet and encapsulated drops, which is shifted

towards higher drop spacing for more viscous jets. The drop viscosity leaves the previous transition

unchanged, but modiﬁes the threshold of the drop fragmentation within the continuous jet. We

develop a model that quantiﬁes how the drop viscosity aﬀects its extension, which is at ﬁrst order

ﬁxing its shape during recoil and is therefore determining its stability against pinch-oﬀ.

I. INTRODUCTION

The large number of recent scientiﬁc publications dedicated to encapsulation shows the increasing need for reliable,

precise and scalable technologies. This demand is mainly motivated by the biomedical and pharmaceutical industries,

which strive to deliver actives as eﬃciently and safely as possible [1–4]. The development of cell culture and tissue

engineering requires, beyond the necessity of cell feeding and harvesting, a mean, to manipulate and assemble the cells,

which can be achieved by their regular and controlled encapsulation into a matrix [5–8]. The need of encapsulation

is also rising in less demanding applications such as in the production of cosmetic, food-products, agricultural inputs,

and in depollution tasks [9–14].

To tackle these challenges, several methods have been proposed. For the production of well controlled spherical

capsules, the technology of choice is microﬂuidics. Indeed, since researchers have been using this toolbox, many micro-

droplet based applications emerged, including chemical micro-reactors, multiple emulsions and cell capsules [15–18].

Yet, while present in the scientiﬁc community since decades, microﬂuidics has barely made it to industries. Beside the

need for precise chips requiring appropriate design and manufacture, the risk of clogging remains, the main issue which

considerably limits scale-up possibilities [19–21]. Regarding the production of ﬁbers, which are especially desirable

for medical and biomedical applications [22–24], the state of the art relies on coaxial or emulsion electrospinning. The

former, however, enables only the production of core-shell structures, and the latter does not oﬀer the control on the

size and position of the inclusions [25–27].

The previously mentioned drawbacks of these existing technologies call for innovative approaches. Inspired by the

important knowledge about drop impacts, which include drop impacting onto a wall [28–33], a thin liquid ﬁlm [34–36],

a liquid bath [37, 38] or another drop [39–43], the so called in-air-microﬂuidics, has recently been proposed [44, 45].

This promising approach consists in solidifying the liquid microstructures resulting from the collision in air of drop

streams and jets [46]. Binary drop collisions involving two or three drops of one or more liquids [40, 47, 48], and the

collision of a stream of drops with a continuous jet, count to this rather new encapsulation method. The structures

produced by the drop-jet collisions enable to form both spherical capsules and regular ﬁbers containing periodic

encapsulation of monodisperse spheres. The collisions taking place in air, it suppresses the need for the additional

carrying liquid phase which must be used in microﬂuidics. Most importantly, the absence of channels eliminates the

critical risks of clogging. Finally, the alignment requirements are much more moderate than for drop-drop collisions.

Beside these obvious advantages, in-air-microﬂuidics remains to date largely unexplored, and its potential and limits

must still be described and understood. Indeed, not much happened since the pioneering work of Chen et al., who

used water for both the drops and the jet [49]. In that study, several behaviours were identiﬁed, which were named

with increasing inertia as bouncing, coalescence, segmenting, separation and splashing. The next study was performed

∗david.baumgartner@tugraz.at

arXiv:2210.04501v1 [physics.flu-dyn] 10 Oct 2022

by Planchette et al., who used immiscible liquids [44]. The outcomes were classiﬁed according to the fragmentation

of the drops or the jet, both or none providing fragmented drops in jet, capsules, mixed fragmentation and drops in

jet. The fragmentation of the jet was attributed to a capillary instability, while the one of the drop was associated

to an excess of its kinetic energy, which leads to its excessive deformation and thus its fragmentation. The proof of

concept regarding the solidiﬁcation of the produced structures was provided about the same time by Visser et al.

[46]. More recently, the eﬀects of liquid wettability and miscibility have been investigated [50]. It was shown that

replacing total wetting by partial one, or exchanging immiscible liquids against miscible ones, do not signiﬁcantly

modify the outcomes, as long as the surface tension of the jet remains lower than the one of the drops. Questions

about the role of the liquid viscosities have not been addressed yet. Our experimental study aims to ﬁll this gap and

bring the knowledge of in-air microﬂuidics one step forward. To do so, we investigate six diﬀerent liquid combinations

consisting of two liquid types, namely three aqueous glycerol solutions for the drops and four silicone oils for the jet

liquid. These liquids provide total wetting of the jet on the drop, promoting their encapsulation, and diﬀer only by

their viscosity. First, a wide range of collision parameters are screened for each combination, and the corresponding

outcomes are classiﬁed in four regimes, following the analysis by Planchette et al. [44]. Regime maps are built to

evidence the eﬀects of viscosity on these regimes and their occurrence. The results are further interpreted by focusing

on the capillary fragmentation of the jet and on the inertial fragmentation of the drop. For the latter, the description

of the drop extension and recoil is enabled by the use of two cameras and aliasing stroboscopic illumination.

The paper is organized as follows. The experimental set-up and problem description are ﬁrst introduced. The

experimental results are then presented, and the shifts in regime boundaries are discussed. The paper ends with the

conclusions.

II. MATERIAL AND EXPERIMENTAL METHODS

A. Experimental set-up and problem description

The present study focuses on head-on collisions of a regular stream of monodisperse droplets and a continuous

immiscible liquid jet. These collisions are realized by adjusting the trajectory of the droplets and the jet into the same

plane to avoid oﬀ-plane eccentricity. A sketch of the set-up used to generate this kind of collisions is shown in ﬁgure

1(a). Two pressurized and independent tanks supply the liquids for the drops and the jet, which are produced with a

droplet generator [51] and a nozzle, respectively. Micro traverses enable the accurate adjustment of their trajectories.

The drops and jet diameters range between Dd= 205 ±25 µm and Dj= 290 ±20 µm, respectively. Here, as well as

in the rest of this manuscript, the subscript drefers to the drop parameters and the drop liquid properties, while jis

used for the jet and the jet liquid properties. The drop generator and the illumination system (stroboscopic LED) are

connected to a signal generator in order to supply both devices with the same frequency (8000 Hz < fd<26000 Hz).

This allows the recording of frozen collision pictures. The imaging of one collision is then performed with two cameras

providing orthogonal (Camera 1) and front (Camera 2) views for all experiments. The drops are dyed and the

jet remains transparent, providing a strong contrast to easily distinguish them. All needed collision parameters are

extracted from collision pictures using the public-domain software ImageJ (https://imagej.nih.gov/ij/) shown in ﬁgure

1(b). These parameters include the drop diameter Ddand the jet diameter Dj, the spatial period of the drops Ld

(300 −1100 µm) and of the jet Lj(300 −800 µm), the collision angle α(15◦−60◦), and the velocities of the drop

~ud(4 −15 ms−1) and the jet ~uj(3 −15 ms−1). The magniﬁcation is larger than in our previous study [50] with not

more than 6 µm per pixel providing uncertainty below 3% for all measured diameters and velocities. Further detailed

information about the methods applied to obtain these parameters is shown elsewhere [50]. The relative velocity ~

(2 −10 ms−1) between drop and jet is deﬁned as the impact velocity and is calculated as ~

U=~ud−~uj. Note that in

this study the component of the relative velocity parallel to the jet trajectory, Uk=udcos(α)−uj, is set to zero with

even stricter conditions than in [50] (Uk<0.04Uand even Uk<0.01Uclose to the transitions instead of Uk<0.1U).

As a consequence, the relative velocity ~

Ucorresponds to the component perpendicular to the jet trajectory whose

norm U⊥=udsin(α) is independent from Lj/Dj=uj/(fdDj). This adjustment can be realized by varying ~ud,~uj

and αto obtain udcos(α) = uj, which is the condition ensuring head-on collisions.

For this work focusing on the viscosity role, we further introduce the viscosity ratio λ=µd/µj. It relates the

dynamic viscosity of the drop liquid µdto the dynamic viscosity of the jet liquid µjand lies between 0.25 and 3.50.

FIG. 1. (a) Experimental set-up for the drop/jet collision experiments. (b) Geometric and kinetic parameters of the collisions.

Figure adapted from [50].

B. Liquids

We use three aqueous glycerol solutions as the drop liquids and four silicone oils as the jet liquids. These two liquids

are immiscible and provide total wetting of the jet on the drop. The interfacial tension between the drop liquids and

the jet liquids can be speciﬁed as σdj = 32 ±3mNm−1[52–54]. The values for the surface tension σ, the density ρ,

the dynamic viscosity µand the range of Ohnesorge number Oh =µ/√ρσD of all liquids used are shown in table

I. Oh is calculated using either the drop or the jet diameter and the corresponding liquid properties. The density is

measured by weighing an exact volume of 100 ml, the viscosity is determined with a glass capillary viscometer, and

the surface tension is measured with the pendant drop method. To obtain aqueous solutions of diﬀerent viscosities for

the drops, the mass fractions of glycerol (≥98%, Carl Roth GmbH, Germany) in water are 12%, 50% and 68% in case

of G1, G5 and G20, respectively. The viscosity of the jet liquid is varied by using diﬀerent silicone oils (SO3, SO5,

and SO20 are pure liquids supplied by Carl Roth GmbH, Germany). SO1 is a mixture of SO3 and SO0.65 (supplied

by IMCD South East Europe GmbH, Austria) with a mass ratio of 70%:30%. In addition, the drop liquid is dyed

with Indigotin 85 (E 132, BASF, Germany) at a concentration of 1g/l. The dye is added to the aqueous glycerol

solutions before the liquid properties are measured.

TABLE I. Liquid properties. All measurements were carried out at an ambient temperature of Tamb = 23 ±1◦C

Abbreviation Density Dynamic viscosity Surface tension Ohnesorge number

ρ(kg ·m−3)µ(mP a ·s)σ(mN ·m−1)Oh(−)

G1 1024±5 1.33±0.05 70±1 0.011±0.001

G5 1118±5 5.05±0.10 68±2 0.041±0.004

G20 1169±5 17.14±0.05 67.5±1 0.137±0.007

SO1 846±5 1.45±0.03 17±1 0.023±0.001

SO3 887±5 2.73±0.05 18.5±0.5 0.034±0.001

SO5 915±10 5.10±0.05 19.5±0.5 0.071±0.004

SO20 949±5 19.15±0.05 20.5±0.5 0.263±0.002

III. RESULTS: REGIME MAPS

The ﬁrst set of experiments using G5 as the drop liquid and SO5 as the jet liquid is deﬁned as the reference case

with a viscosity ratio of λ=µd/µj≈1. It establishes the starting point for investigating viscosity eﬀects. The results

FIG. 2. (a) Collision outcomes of the reference case G5/SO5 classiﬁed in the form of a regime map with W edand Lj/Djas the

scaling parameters. (b) Recorded collision pictures (front view - camera 2) of the structures produced by drop-jet collisions.

A, B, C and D correspond to the data marked in red in (a). (c) Schematic illustration of the structures. Adapted from [50].

are represented in ﬁgure 2(a) in the form of a regime map, similar to the ones already introduced in [44] and [50].

Collision pictures recorded in front view (camera 2) are shown in ﬁgure 2(b). For clarity, a schematic illustration is

added in ﬁgure 2(c). Further details about the observed regimes and the reference case can be found in [50]. For

consistency, we brieﬂy recall the four regimes:

•(A) drops-in-jet: The drops are totally engulfed by the jet, which remains continuous. This regime is marked

with ﬁlled, but diﬀerently coloured circles in all regime maps.

•(B) fragmented drops-in-jet: In this case, the drops fragment, but the jet remains continuous. Often all drop

fragments remain inside the continuous jet, but sometimes parts of them may be expelled. This regime is marked

with black empty triangles.

•(C) encapsulated drops: The droplets do not fragment, but the jet breaks up. The result is a regular stream of

droplets, which are encapsulated with the jet liquid. This regime is marked with black empty diamonds.

•(D) mixed fragmentation: Here, both the drops and the jet fragment. This regime is marked with black crosses.

The regime maps used for the classiﬁcation of the collision outcomes is based on two scaling parameters. The ﬁrst

scaling parameter Lj/Dj, a purely geometric one, is used to predict the jet break-up. The fragmentation mechanism

can be primarily attributed to a capillary-driven instability, similar to the one of Plateau Rayleigh [44]. The geometric

term Ljdescribes the distance between two consecutive impacting droplets (see ﬁgure 1(b)), which is normalized by

the diameter of the jet Dj. By exceeding a critical value of Lj/Dj, the jet breaks into a regular stream of encapsulated

droplets [44, 50, 55, 56]. The critical value of the reference case G5/SO5 is approximately 2, as indicated by the solid

line in ﬁgure 2(a). Note that our previous study [50] associates the transition between drops-in-jet and encapsulated

drops to a unique critical value of Lj/Dj, whereas the present work reveals a moderate inﬂuence of inertia on this

critical value. Several reasons can explain the slight deviations observed in the data. First and most likely, the

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PACSnumbers:Eectsofviscosityonliquidstructuresproducedbyin-airmicrouidicsDavidBaumgartner,GunterBrenn,andCarolePlanchetteInstituteofFluidMechanicsandHeatTransfer,GrazUniversityofTechnology,A-8010Graz,Austria(Dated:October11,2022)Thisstudyexperimentallyinvestigatestheeectofviscosityontheoutcomeso...

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PACS numbers Eects of viscosity on liquid structures produced by in-air microuidics David BaumgartnerG unter Brenn and Carole Planchette

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