Slide 35
Slide 35 text
Rigid body motion of active colloids
T T
ij
·Vj
T R
ij
· ⌦j + FP
i
+ ˆ
Fi
1
X
l =1s
(T, l )
ij
· V(l )
j
= 0,
RT
ij
·Vj
RR
ij
· ⌦j + TP
i
+ ˆ
Ti
1
X
l =1s
(R, l )
ij
· V(l )
j
= 0.
Propulsion tensors
relate modes of
slip to rigid body motion
White noises
Mobility matrices
connectors for forces
and torques
Vi = µT T
ij
· FP
j
+ µT R
ij
· TP
j
+
q
2kBTµT T
ij
· ⌘T
j
+
q
2kBTµT R
ij
· ⇣R
j
+
1
X
l =2s
⇡(T, l )
ij
· V(l )
j
+ VA
i
⌦i = µRT
ij
· FP
j
+ µRR
ij
· TP
j
| {z }
Passive
+
q
2kBTµRT
ij
· ⇣T
j
+
q
2kBTµRR
ij
· ⌘R
j
| {z }
Brownian
+
1
X
l =2s
⇡(R, l )
ij
· V(l )
j
+ ⌦A
i
| {z }
Active
⇡(T, l )
ij
= µT T
ik
· (T, l )
kj
+ µT R
ik
· (R, l )
kj
,
⇡(R, l )
ij
= µRT
ik
· (T, l )
kj
+ µRR
ik
· (R, l )
kj
.
Invert for rigid body motion
RS and Adhikari, EJCM 2017, JPC 2018