1
Vapor-Driven Propul
sion of Catalytic
Micromotors
Renfeng Dong
a,b
†
, Jinxing Li
a
†
, Isaac Rozen
a
, Barath Ezhilan
c
, Tailin Xu
a
, Caleb Christianson
a
, Wei
Gao
a
, David Saintillan
c
, Biye Ren
b*
, Joseph Wang
a*
a
Department of Nanoengineering, University of California,
San Diego, La Jolla, California 92093, United States.
b
Research Institute of Materials Science, South China Un
iversity of Technology, Guangzhou 510640, P. R. China
c
Department of Mechanical and Aerospace Engineering, Unive
rsity of California, San Diego, La Jolla, California
92093, United States.
*Corresponding Author: josephwang@ucsd.edu, mcbyren@scut.edu.cn, dstn@ucsd.edu
†
R.D. and J.L. contributed equally to this paper
Supporting Videos
SI Video 1. Large scale micromotor motion remotely triggered by placing a hydrazine fuel
droplet (concentration 30%) at a distance
of 1.0 cm from the micromotor droplet.
SI Video 2. Behavior of two
micromotors before and after the
remote placement of a hydrazine
droplet (concentration 20%) 0.5 cm away from the micromotor droplet. .
SI Video 3.
Micromotor motion 5 min after placing droplets containing 10%,
20%, and 30%
hydrazine at a distance of 0.5 cm over 2 second periods.
SI Video 4.
Micromotor motion 5 min after placing droplets of 20% hydrazin
e at different
distances from the micromotor droplet: 1.0 cm, 2.0 cm, and 3.0c
m over 2 second periods.
SI Video 5. 3D simulations of the normalized hydrazine concentr
ation within the sample droplet
for the first 4 minutes after exposure to the hydrazine fuel dr
oplet. The videos are 6 times faster
than real time.
2
Supporting Figure
Figure S1
Dependence of the speed of Ir-Au
Janus micromotors upon the hydrazine
concentrations over the 0.0000001
−
10% range.
Diffusion model and simulation.
The dynamics of the new system can be described using the following mathematical model.
We assume the source and motor dropl
ets to be hemispherical in sh
ape. Let be the radius of
the droplets and be the source-sample separati
on distance. Evaporation of hydrazine from the
source droplet creates a vapor-phase hydrazine concentration
c
s
at the surface of the droplet. The
source droplet surface concentrati
on is directly proportional to the percentage of hydrazine inside
the source droplet.
Vapor phase hydrazine diffuses from the surf
ace of the source droplet driving the formation of
concentration gradients in air. Hydrazine transport
in air is modeled using the diffusion equation
in spherical coordinates.
(1)
subject to boundary conditions,
3
(2)
(3)
and initial condition,
(4)
where is the radial distance from the center from the source droplet and
= 0.4164 cm
2
/s is
the diffusion coefficient of hydrazine in air. This
equation can be solved analytically to obtain
the vapor phase hydrazine concentration in the atmosphere:
1
.
(5)
At long times (t >> 2.4s), the concentration of vapo
r-phase hydrazine in air reaches a steady state
given by:
(6)
When the distance of separation between the drop
lets is larger than the radius of the droplet
(L>>R), the vapor phase hydrazine concentration
near the surface of the motor droplet can be
considered to be uniform to leading order. Whil
e hydrazine diffuses in air with a timescale
= 2.4s, it diffuses inside the water dropl
et with a much slower timescale of
=
822s (where
=1.9e-005 cm
2
/s is the diffusivity of hydrazine in water). Because of the
separation of timescales, the vapor phase hydra
zine concentration immediately surrounding the
motor droplet can be approximated by the steady s
tate concentration at the center of the motor
droplet
c
a
(L)
given by:
(7)
This equation suggests that th
e vapor-phase hydrazine concentration surrounding the motor
droplet has a linear relationship with the
surface concentration of the source droplet
(c
s
) (and
hence with the hydrazine concentration insi
de the source droplet) and an inverse linear
relationship with the source-sample droplet separa
tion distance ( ). Therefore, the average speed
within the motor droplet follows a similar relationship with these variables.
4
The dissolution of vapor-phase hydrazine into
the motor droplet and the subsequent transport are
modeled as a diffusion problem within a
hemisphere according to the equation
(8)
subject to boundary and initial conditions
(9)
(10)
where now refers to the radial position within
the motor droplet measured from its center.
is
proportional to
and both are related by Henry’s Law.
The solution to this equation can be obtained numerically using finite differences and is
shown in Figure 4(B-C) of the main text.
Reference:
1.
Haberman, R.
Applied Partial Differential Equations with Fourier Series and Boundary
Value Problems (5th Edition);
AMC(2013).