1
Bubble guidance of tubular growth in reaction–precipitation systems

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj1

2
Numerous types of reaction–precipitation systems involve the growth of tubular structures similar to those formed in “silica gardens”.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac1

3
As a model case for this phenomenon, we investigate the rapid growth of hollow tubes in the reaction between sodium silicate and cupric sulfate.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj2

4
The latter solution is injected hydrodynamically at constant flow rates of 1–20 mL h−1 into a large reservoir of waterglass.

Type: Method | Advantage: None | Novelty: New | ConceptID: Met1

5
In this study, the growth is templated and guided by single, buoyant gas bubbles.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res1

6
The resulting tubes can be several decimetres long and have constant radii in the range of 100–600 μm.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs1

7
Systematic measurements show that bubble size governs the tube radius.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res2

8
According to this radius, the system selects its growth velocity following volume conservation of the injected solution.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res3

9
Moreover, scanning electron microscopy reveals intricate ring patterns on the tube walls.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs2

10
We also show evidence for the existence of a minimal and a maximal tube radius.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res4

11
Finally, we report an intriguing collapse of tubes created at high silicate concentrations, which yields twisted ribbon-like structures.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs3

12
Critical radii and tube collapse are discussed in terms of simple competing forces.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj3

Introduction

13
Self-organization in reaction–precipitation systems often leads to the formation of permanent tubular structures.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

14
Some of the most striking ones are 30 m high, black “smokers” growing at hydrothermal vents on the ocean’s floor.1

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

15
As hot acidic, mineral-rich water from below the earth’s crust surges into the cool, alkaline ocean the dissolved minerals precipitate and aggregate in a ring-shape area at the jet’s boundary.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

16
Another geological example, soda-straw stalactites result from the periodic detachment of calcium carbonate-saturated water droplets in caves.2,3

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

17
The pH increases during the drops’ hang-time and precipitation of CaCO3 occurs at the rim.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

18
This rhythmic deposition of material creates meter-long tubes of small but constant diameter.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

19
Similarly, capillary forces can create helictites, gravity defying structures, which grow along curved, spiral-like paths.4

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

20
On a microscopic scale, hollow fibers form in setting Portland cement5,6 as well as in certain corrosion systems.7–9

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

21
More recently, Goldstein et al. studied “ferrotubes” in an electrochemical system.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

22
In their experiment, small tubes are templated by successive detachment of gas bubbles formed at a steel cathode.10

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

23
All of these phenomena share similarities with precipitation tubes in chemical (or silica) gardens which can be considered a prototypic case of gradient-induced tube formation in reaction–precipitation systems.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

24
Descriptions of the latter system are found as early as the 17th century.11,12

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

25
Today, chemical gardens are known to many as a demonstration experiment that readily creates colorful, plant-like precipitation structures.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

26
Their formation is observed for many inorganic salts (e.g., CuSO4, MnCl2, FeCl3), crystals of which are placed into concentrated solutions containing anions such as silicate, phosphate or borate.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

27
Moreover, recent investigations of the properties of the material synthesized have contributed to a renewed scientific interest in chemical gardens.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

28
For example, Collins et al. reported evidence of surprisingly strong catalytic activity and discovered hierarchical nano- to micrometre structures in overall amorphous aluminosilicate precipitates.13,14

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

29
Fig. 1 shows a typical landscape generated from cupric nitrate crystals seeded into 1 M silicate solution (waterglass).

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs4

30
The surface of the seeds dissolves and reacts to form an insoluble metal hydroxide membrane.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

31
As the concentration of metal ion increases, osmotic pressure builds up and inflow of water across the membrane causes it to yield and rupture.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

32
The resulting release of buoyant solution into the surrounding waterglass creates hollow, vertical structures (see left-hand side of Fig. 1).

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

33
Their initiation and growth occurs in a matter of seconds to days depending on the salts employed.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

34
In some instances, small air bubbles are attached to the surface of the colloidal membrane.15,16

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

35
The detachment and rise of a bubble entrains the inner solution in its wake, thus, directing the rapid growth of a thin, hollow needle.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

36
Several examples of tubes formed in this fashion are seen in Fig. 1.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs4

37
A magnified view of a bubble still attached to the stalk is shown in the inset.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs4

38
The variation in the diameter and length of the needle-like structures is related to the size of the bubble drawing the inner solution along.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac5

39
Large bubbles moving along straight trajectories create wide precipitation tubes that taper as the supply of solution is depleted.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac5

40
More erratic paths are sometimes observed for thin tubes created by smaller bubbles.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac5

41
Here, we present a systematic investigation of bubble-guided tube growth.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj4

42
To allow quantitative variations of relevant control parameters, we have modified a recent method developed by Thouvenel-Romans et al.17,18

Type: Method | Advantage: None | Novelty: New | ConceptID: Met2

43
In both cases, the seed crystals are replaced by a seed solution which is injected hydrodynamically at well-defined flow rates and concentrations.

Type: Method | Advantage: None | Novelty: New | ConceptID: Met2

Experimental

Synthesis

44
A solution of 0.5 M cupric sulfate (CuSO4·5H2O; Fisher) is injected into sodium silicate solutions (Na2SiO3·5H2O; Fisher) of various concentrations at 25 ± 1 °C.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp1

45
All solutions are prepared using nano-pure water (18 MΩ cm; EASYpure® UV, Barnstead).

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp1

46
The injection rate of the aqueous cupric sulfate solution is controlled by a syringe pump (KD Scientific 200) and varied between 1–20 mL h−1.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp1

47
A glass capillary (length = 15 mm; inner diameter ≈ 1.1 mm) is used as a nozzle and delivers the cupric sulfate solution into a large, waterglass-filled cylinder (height ≈ 28 cm, inner diameter = 2.2 cm).

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp1

48
A stainless steel needle (23G, Bevel B-D Yale) is introduced into the capillary with its tip slightly protruding out.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp1

49
The needle is connected to an air-filled syringe used to manually inject single air bubbles into the flow of cupric sulfate solution.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp1

50
Each bubble entrains the buoyant solution upward, forming a single tube of precipitate in its wake.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp1

51
Optical micrographs of the growth are acquired with a monochrome charged-coupled device camera (COHU 2122) connected to a PC via a frame grabber board (Data Translation, 640 × 480 pixels at 8 bit pixel−1).

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp2

52
During the experiment, image sequences are captured using HLImage++97 software at a rate of typically 10 frame s−1.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp2

53
The images are then analyzed using in-house software.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp2

54
All measurements are corrected for optical deformations caused by the cylindrical geometry of the main reaction vessel.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp2

Microscopy

55
Samples are synthesized at a pump rate of Q = 7 mL h−1 using [CuSO4] = 0.5 M and [Na2SiO3] = 1.0 M. Collapsed tubes are produced at Q = 10–15 mL h−1 using [CuSO4] = 0.5 M and [Na2SiO3] = 2.5 M. The tubes generated are collected in a Petri dish filled with nano-pure water.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp3

56
The pieces of the tube are then rinsed three times and excess water is removed.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp3

57
The samples are dried at 45 °C overnight.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp3

58
Higher temperatures induce the degradation of the copper hydroxide precipitate to black copper oxide.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs5

59
The specimens are placed in a vacuum desiccator to remove remaining moisture.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp3

60
Then, they are either carbon coated or gold sputtered prior to acquiring micrographs using a JEOL JSM-5900 scanning electron microscope (SEM).

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp3

Results and discussion

61
In a recent publication, two of us have reported that the injection of cupric sulfate solution into sodium silicate solution leads to the formation of tubular structures.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac6

62
Three different growth regimes are distinguished.17

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

63
(1) Jetting growth: At low concentrations of cupric sulfate solution, hydrodynamics dominates the formation of precipitation tubes by templating the membrane at the interface between the jetting fluid and the outer, denser liquid.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

64
The tube radii are described quantitatively by the Poiseuille-flow characteristics of the buoyant jet of injected solution.18

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

65
(2) Popping growth: At intermediate concentrations, tubes grow in an oscillatory fashion.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

66
The tip of the tube is sealed by a colloidal membrane which stretches into a buoyant, membrane-bound droplet as solution delivery continues.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

67
When the material ruptures, this small solution-filled envelop is released and rises to the surface.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

68
This sequence repeats continuously with oscillation periods of approximately 1–12 s causing tube growth at speeds of 0.05–0.35 mm s−1.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

69
(3) Budding growth: For high concentrations of cupric sulfate, buoyancy forces are not large enough to remove the membrane-bound droplet from its hollow stalk.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

70
New growth appears through random breaches on the freshly formed membrane without ejection of material.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

71
Nonetheless, budding growth tends to be periodic yielding bulging but unbranched, hollow structures.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

72
Under budding conditions, the introduction of an air bubble at the interface between the two reactants emulates the bubble-guided growth shown in Fig. 1.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

73
As the bubble detaches from the syringe tip, it is released into the reaction zone between the two fluids and the air is trapped by a very thin colloidal copper hydroxide membrane.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

74
The buoyancy of the gas directs the growth upward.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

75
Fig. 2 shows an image sequence of a bubble rising in 1.0 M sodium silicate solution.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs6

76
In its wake, an initially translucent tube is rapidly forming.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs6

77
The bubble travels upward but remains anchored to the mouth of the structure.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs6

78
Sometimes, however, the bubble detaches and the system switches to its natural growth regime.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs7

79
We note that the gradual change between the upper translucent zone and the non-transparent blue stalk corresponds to fast formation of colloidal copper hydroxide and slower silica precipitation, respectively.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res5

80
This is in agreement with preliminary results from micro-Raman and EDS studies of the tube material, which detect predominantly copper hydroxide on the interior of the wall surface and amorphous silica on the outside.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res5

81
Our experiments show that the growth velocity of a tube is remarkably constant.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs8

82
This observation is exemplified by the data shown in Fig. 3 where the vertical coordinate h of three bubbles is plotted as a function of time.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs8

83
The bubbles’ velocities are obviously identical to the growth velocity of the tubes but smaller than the terminal velocity of free-rising bubbles.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs9

84
Notice that the height increases linearly over 4 to 6 cm which is approximately 100 times larger than the bubble and tube diameters.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs10

85
The origin h = 0 in the graph is situated 2 cm from the capillary outlet.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs8

86
At closer distances, transient fluctuations occur that are caused by momentum imparted to the bubble during its release.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res6

87
Moreover, as the bubble reaches the last few centimeters below the silicate solution/air interface, the growth velocity is no longer constant but increases rapidly and the radius of the tube decreases noticeably.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs11

88
This acceleration is possibly caused by a gradient in fluid viscosity close to the meniscus of the silicate solution and/or the effects of the interface on the flow field.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con1

89
Systematic measurements are carried out to obtain insights into the dependencies of the growth velocity v and the tube radius rtube on the injection rate Q and the bubble radius Rbubble.

Type: Goal | Advantage: None | Novelty: None | ConceptID: Goa1

90
A key question is whether the injected solution remains within the growing tube or leaks into the surrounding liquid without contributing to the volume increase of the structure.

Type: Hypothesis | Advantage: None | Novelty: None | ConceptID: Hyp1

91
In the absence of such leaks, the flow rate Q should equal the tube’s rate of volume change.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod4

92
This yields the simple equation v = Q/πrtube2.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod4

93
Fig. 4 compares this relation with experimental data obtained for flow rates between 2 mL h−1 (solid triangles) and 10.0 mL h−1 (solid squares), and various bubble sizes.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs12

94
We find an overall good agreement between the experimental data and the latter equation (see solid lines in Fig. 5A,B).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res7

95
Least-square fitting of the data (see dashed lines in Fig. 4B) yields observed flow rates that are about 8% smaller than the pump rates employed (−7.0%, −8.0%, −4.4%, −12.5% and −8.3% for Q = 2.0, 3.0, 5.0, 7.0, and 10.0 mL h−1, respectively).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res7

96
These relatively small deviations indicate that most of the injected solution stays within the growing tube.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con2

97
Consequently, the formation of new membrane material is sufficiently fast to avoid significant leakage.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con2

98
Under our experimental conditions, the rate-determining factor of tube growth is therefore the inflow of seed solution and not the kinetics of membrane formation.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con2

99
Visual inspection readily shows that tube growth occurs in close vicinity to the bubble rather than at the tube’s base.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res8

100
We characterize this crucial reaction zone by measuring the radii of both the bubble and the tube that forms in its trail.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj5

101
In this context, it is important to note that, within the resolution of our experiments, all bubbles had a simple spherical shape.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs13

102
Fig. 5A–D show the tube radii as a function of bubble size for four different silicate concentrations.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs14

103
Each plot presents data from experiments at flow rates of Q = 3, 5, 10 mL h−1 as solid circles, open squares and solid squares, respectively.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs14

104
For each data set, we find a nearly proportional dependence of rtube on Rbubble.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res9

105
We will therefore continue our discussion in terms of the corresponding radii ratio.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res9

106
Fig. 6 shows this ratio for four different silicate concentrations and three different flow rates.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs15

107
The concentration of cupric sulfate is kept constant at 0.5 M. We note that the radii ratio has a simple geometrical interpretation as it corresponds to the angle α between the boundary of the tube and the bubble surface (cos α = rtube/Rbubble); hence, the smaller the angle, the deeper the bubble sits in the mouth of the tube.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod5

108
Examples of small and large angles are shown in the left and right inset of Fig. 6, respectively.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod5

109
The data span the entire range of silicate concentrations (1.0–2.5 M) for which the bubbles are consistently creating simple tubes.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs16

110
Below 1.0 M, the membrane is tenuous and it is difficult to generate a bubble that drags the copper solution upward.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res10

111
Silicate concentrations above 2.5 M yield collapsing tubes.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res11

112
Fig. 6 shows that tube radii are only 5–20% smaller than the radii of their guiding bubbles.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs17

113
Within this range, the smallest ratios are found for the lowest flow rate of Q = 3 mL h−1.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs17

114
At this value, no significant dependence on silicate concentration is found.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res12

115
For Q = 10 mL h−1, however, the ratio increases with increasing silicate concentration and the contact angle decreases accordingly from about 30° to 20°.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res13

116
Moreover, we find that for a given silicate concentration, the radii ratio increases with increasing flow rate.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res14

117
This dependence is most pronounced for the highest silicate concentration (2.5 M).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res14

118
Our experiments also show that only bubbles of certain sizes are capable of guiding tubular growth.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res15

119
We only succeeded in creating tubes for bubbles with radii in the range of 150–600 μm.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res15

120
Moreover, our experiments suggest that, with increasing flow rate, the minimal and maximal radii shift to larger values.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con3

121
Since the tube and the bubble radii are closely related, as we discussed in the earlier paragraphs, this trend is also reflected by the range of the data in Fig. 4.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res16

122
The existence of a minimal and a maximal radius can be qualitatively argued in the context of competing forces.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con4

123
The buoyancy acting on the air bubble scales as Rbubble3.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con4

124
Two forces are counteracting buoyancy, namely a “sticking” force due to the contact between the membrane and the gas bubble and the Stokes force due to the viscosity of the silicate solution around the growing, bubble-guided tube.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con4

125
The Stokes force is proportional to ηoRbubblev = ηoRbubbleQ/(πrtube2) where ηo denotes the viscosity of the silicate solution.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod6

126
Therefore, this force roughly scales as 1/Rbubble while the sticking force is likely to scale as Rbubble.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con4

127
Accordingly, the buoyancy of very large bubbles is greater than the combined contributions from “sticking” and Stokes forces and the bubble detaches.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con4

128
For very small bubbles, the Stokes force is dominant and the bubble cannot act as a sufficiently strong guide for the growing tube.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con4

129
While this discussion motivates the existence of a finite range of radii in bubble-guided tube growth, more insights into the nature of the sticking force are needed.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con4

130
We also note that the size, the shape and the position of the injection needle might affect measurements of minimal and maximal radii.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con5

131
The delicate force balance needed for bubble-guided tube growth can be easily upset.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res17

132
In Fig. 7A, a second smaller air bubble is injected deliberately into the growing tube.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp4

133
This bubble rises up the hollow tube and eventually collides with the leading bubble.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs18

134
When the two coalesce, the force balance is disturbed and the bubble is engulfed by the colloidal membrane.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res18

135
As more copper solution is delivered by the pump, the system transitions to its natural growth regime (budding) and the tube widens into the expected bulging structure.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res18

136
The bubble has lost its ability to guide the tube’s growth.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con6

137
An example of a different outcome is shown in Fig. 7B.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs19

138
Here, the zone underneath the bubble begins to inflate, thus, stretching the sides of the tube.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res19

139
Nonetheless, the bubble is still attached to the top of the tube while the inflow of solution moves it from side to side.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs20

140
The lighter shades of gray at the thickest part of the bulge indicate thinning of the membrane or some newly produced material.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res20

141
It appears that in this case the growth zone moved away from the bubble, thus, rendering the guide ineffective.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con7

142
For the conditions of this particular experiment, the resulting structure is growing in the popping regime and, consequently, the top portion of the stalk and the attached bubble are released shortly after the time of the last snapshot.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con7

143
Additional features of bubble-guided tube growth are unveiled by examining the tubes’ micrometre-scale features.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj6

144
We investigate the morphology of the tube walls using scanning electron microscopy.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj6

145
Samples are prepared according to the procedures described in the experimental section.

Type: Method | Advantage: None | Novelty: New | ConceptID: Met3

146
Fig. 8A shows a typical tubular structure attached to the dark background of a carbon tape.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs21

147
In this example, the tube radius is approximately 250 μm.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs21

148
The micrograph reveals stripes of different texture along the tube.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs21

149
For the given experimental parameters, the wavelength of the stripe pattern varies between 200 μm and 250 μm.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs21

150
We emphasize that these stripe patterns are also discernible on the inside surface as we observed numerous times during SEM studies of broken tube segments.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs21

151
At higher magnification (Fig. 8B), we can clearly discern two distinct surface textures that alternate within this stripe pattern.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res21

152
One appears dark and smooth (see upper left-hand corner of Fig. 8B) while the other one is lighter with a coarse, grainy appearance (lower right-hand corner).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res21

153
Additional features include blister-like structures (typical diameter 50 μm), most of which flank the transition regions within the stripe pattern.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs22

154
One can envision a variety of different mechanisms that may cause the observed stripe patterns on bubble-guided tubes.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con8

155
These include oscillatory phenomena within or around the primary reaction zone (e.g., periodic rupturing of the freshly formed membrane material), Liesegang-like processes that influence the relevant precipitation reactions, and shape oscillations of the guiding gas bubble.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con8

156
Any oscillatory mechanism acting during the growth process corresponds to a characteristic frequency that can be calculated from the growth velocity of the tube and the wavelength of the stripe pattern.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con8

157
For the example shown in Fig. 8, the growth speed of 1.0 cm s−1 and the stripe distance of about 250 μm correspond to a frequency of approximately 40 Hz.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res22

158
Inspection of several other samples yields frequencies in the range of 30–90 Hz.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res23

159
However, further interpretations require more systematic measurements and a thorough characterization of compositional variations throughout the striped wall material.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con9

160
Another intriguing phenomenon is observed for high silicate concentrations (≥2.5 M), which correspond to large density differences between the dense silicate and the lighter cupric sulfate solution.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs23

161
Under these experimental conditions, we observe that the bubble-guided tubes collapse.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs23

162
This process yields twisted ribbon-like structures.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs23

163
A typical example for these collapsed tubes is shown in Fig. 9A.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs23

164
The ribbon is approximately 1.5 mm wide and has five well-defined twists within the field of view.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs23

165
Accordingly, the structure has a pitch of about 6 mm.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs23

166
Fig. 9B and 9C show scanning electron micrographs of a collapsed tube.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs24

167
The overall morphology of the sample is more rugged than in the case of the uncollapsed structures (cf., Fig. 8).

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs24

168
Also the characteristic stripe pattern appears to be absent although very coarse ring-like ridges are found.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs24

169
The outer wall surfaces of the collapsed tube also reveals numerous blisters and the twist is easily discernible as a large fold.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs24

170
Some of the barnacle-like blisters feature little spirals such as the very left one in Fig. 9C.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs25

171
Tube collapse occurs after several centimetres of ordinary, cylindrical growth, but our experiments did not reveal a well-defined critical length.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs26

172
Typically the structure flattens and twists nearly simultaneously with the entire collapse requiring only a few seconds.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs27

173
In the following, the bubble-guided growth process continues but the resulting precipitation structure forms as a twisted ribbon.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs28

174
This observation reveals that the collapsed state still allows internal flow of solution.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res24

175
We also observed that stopping and restarting of the pump can induce a transition back to the cylindrical or a near cylindrical state.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs29

176
This phenomenon of “re-inflation” indicates that the growth of the collapsed structure is actually cylindrical in close vicinity of the bubble.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con10

177
The collapse of precipitation tubes is obviously related to an increased density difference Δρ = ρo − ρi between the outer silicate (‘o’) and the inner cupric sulfate solution (‘i’).

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con10

178
Assuming mechanical equilibrium at the top of the growing tube, one obtains the hydrostatic pressure difference Δp = Δρgh across the membrane, where g and h denote earth’s acceleration and the vertical distance from the growth zone, respectively.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con10

179
This transmural pressure difference exerts a compressive force on the cylindrical tube.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con10

180
In the actual growth experiment, flow within the structure contributes an opposing pressure that follows the Hagen-Poiseuille equation Δp = (8ηihQ)/(πrtube4) where ηi is the viscosity of the cupric sulfate solution.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con10

181
If one further assumes that the freshly formed wall does not resist a possible collapse, one obtains the simple stability criterion (8ηiQ)/(πΔρgrtube4) > 1.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con10

182
We therefore expect that collapse occurs for low flow rates, large density differences and large radii.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con10

183
This conclusion is in qualitative agreement with the observation that structures grown at Q = 10 mL h−1 are stable if the tube radii are less than approximately 450 μm whereas wider tubes collapse.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con10

184
However, the predicted critical radius for Q = 10 mL h−1, ηi = 1.21 cP, and Δρ = 0.2 g cm−3 is 250 μm and, hence, smaller than the observed value.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con10

185
This difference could be the result of a certain rigidity of the tube material and/or indicate a small but non-zero pressure difference between the inner and outer solutions at the reaction zone.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con10

186
While our qualitative discussion motivates some of the dependencies relating to tube collapse, it does not explain the occurrence of the striking helical twist that accompanies the flattening of the structure.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con11

187
However, this feature is observed for nearly all collapsing tubes.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con11

188
We suggest that the twisting motion is a secondary aspect of the collapse that reflects the mechanical characteristics of the tube material; in particular, its gradient-like vertical and radial composition as well as the specific boundary conditions that immobilize the lower end while allowing unconstrained motion of the upper extremity.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con11

Conclusions

189
In summary, this study provides the first quantitative insights into the rapid growth dynamics of tubular precipitation structures guided by buoyant gas bubbles.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con12

190
The tube radii are controlled primarily by the radius of the rising bubble.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con13

191
Based on this simple radius selection, the system determines its growth velocity following volume conservation of the injected reactant solution.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con13

192
Moreover, cylindrical tubes collapse to helical ribbons if the density difference across the tube wall is large enough to cause compressive pressure that outbalances flow-induced and other stabilizing forces.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con14

193
A key question that remains unanswered concerns the nature of the adhesive contact between the gas bubble and the forming copper hydroxide membrane at the tip of the tube.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con15

194
Failure to establish or maintain a proper contact results in slow tubular growth that is not templated by the bubble.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con15

195
Our experiments suggest that such a situation occurs outside of a finite range of bubble radii.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con15

196
In particular, large bubbles are lifted out of the reaction zone due to their pronounced buoyancy.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con15

197
This process appears to be related to the pinning of bubbles to solid walls or interfaces between immiscible liquids.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con15

198
In our experiments, however, this situation is complicated by the unknown flow and concentration fields around the upper portion of the growing structure.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con15

199
Nonetheless, it appears likely that bubbles stick to the reaction zone due to surface tension.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con15

200
Consequently, more detailed measurements of the upper, critical radius might allow the characterization of transient surface tensions.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con16

201
Such measurements could provide useful data concerning the early stages of the formation of colloidal membranes.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con16

202
Our findings are of additional importance as they relate to a wide class of precipitation systems in which radial gradient fields orchestrate the formation of permanent, tubular structures.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con16

203
As described in the Introduction, these systems span through a diverse range of fields including electrochemistry, materials science, geology and also biomineralization.19,20

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con16

204
Our investigation is the first step towards the development of methodologies that will allow us to template, guide, and control the formation of precipitation structures in diverse systems.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con16

205
Such approaches not only will reveal underlying universalities but could potentially lead to novel materials and devices.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con16