Supplementary:
Photochemically Induced Motion of Liquid Metal Marbles
Xinke Tang, Shi-Yang Tang, Vijay Sivan, Wei Zhang,
Arnan Mitchell and Kourosh Kalantar-zadeh, Khashayar Khoshmanesh
School of Electrical and Computer Engineering, RMIT University, Melbourne, Australia
Supplementary 1: Experimental setup
FIG. S.1. (a) Photo of the experimental setup. Liquid metal marbles are prepared by rolling a droplet
of liquid metal galinstan (Geratherm Medical AG, Geschwenda, Germany) on a WO3 nano-particle
powder bed until the surface of galinstan droplet is entirely covered by the particles. Aqueous
solutions of hydrogen peroxide (30% v/v, LabServe) with different concentrations are freshly
prepared by using deionized (DI) water as the solvent before the experiments. The WO3 coated
galinstan marble is placed in a 35 mm petri dish (LabServe) filled with 4 ml of H2O2 solution, and
placed on the stage of an inverted microscope (Eclipse Ti, Nikon). The stage was tethered to a linear
screw actuator with a velocity in the order of 0.1 to 50 mm/min which pulled the microscope stage at
the desired speeds. (b) The actuation path of the marble within the petri dish is defined by two stripes
with a thickness of 1 mm attached on both sides of the marble. UV radiation from a ultrahigh
pressure 130 W mercury lamp (Intensilight C-HGFI, Nikon) is focused onto the marble through a
UV filter (MBE41300 C-FL Epi-Fl Filter Cube DAPI, Nikon) using a 10× objective lens. Different
light intensities are accurately regulated through a neutral density filter installed in the illuminator
(Intensilight C-HGFI, Nikon).
Supplementary 2: Analytical model for prediction of marble’s speed assuming compressible
gas within the bubbles
Basic equations as described in the main text:

(S.1)
U marble  r bubble cos
mbubble  bubble 
4
3
 rbubble
3
(S.2)

(S.3)
The rate of bubble generation can be calculated as:


4
3
2
mbubble   bubble  3  rbubble  bubble  4  r bubble rbubble
Assuming bubbles behave like an ideal gas:
 bubble 
P
RT
(S.4)
in which P is the pressure of the bubble, R is the universal gas constant and T is the temperature.
When the bubble is generated under the marble, it experiences the weight of the marble, and
therefore its pressure is obtained as:
P
(S.5)
M marble g
 Patm
2
 rbubble
Combining equations (S.4) and (S.5) leads to the following equation:



M
g r bubble
 bubble  P  marble
3
RT
 RT
rbubble
(S.6)
Substituting equations (S.6) in (S.3) leads to the following equation:



M
g r bubble 4 3
M marble g
2
 mbubble  2 marble


r


4

r
bubble
bubble rbubble
3
2
 RT
3
rbubble
 R T rbubble


M
g 
8 M marble g 
r bubble  4 marble  r bubble
3
RT
RT
(S.7)
4 M marble g 
r bubble
3
RT
Assuming the marble droplet has a spherical geometry:
4
3
M marble   marble   Rmarble
3


16   marble g 3
 mbubble 
Rmarble r bubble
9
RT
(S.8)
On the other hand, the rate of bubble generation can be expressed as:



2
mbubble  I  CH 2O2   Rmarble
(S.9)
Combining equations (S.8) and (S.9) leads to the following equation:

r marble 
9
RT
16  marble g
I  CH 2 O2
Rmarble

I  CH 2 O2
(S.10)
Rmarble
Combining equations (S.1) and (S.10) results in:

U marble  r bubble cos   U marble 
I  C H 2O2
Rmarble
(S.11)
Supplementary 3: Calculated data
U marble 
I  CH 2 O2
Rmarble
U marble  I   U marble  k1  I 
where k1 is a constant
Predicted speed (mm/min)
α=1
α=0.5
I
12%
1.32
1.73
25%
2.75
2.5
50%
5.5
3.53
100%
11
5
U marble  CH 2O2  U marble  k2 CH 2O2
where k2 is a constant
Predicted speed (mm/min)
U marble 
1
Rmarble
 U marble 
CH2O2
β=1
β=0.5
3%
1.77
2.07
7.50%
4.425
3.286
15%
8.85
4.64
30%
17.7
6.57
k3
R
where k3 is a constant
1
Predicted speed
(mm/min)
9
2
4.5
3
3
R (mm)