Liao Mai-Jia1, 2, Wei Ming-Tzo3, Xu Shi-Xin4, Daniel Ou-Yang H2, 3, ‡, Sheng Ping1, §
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(a) Drag coefficients calculated at various spherical surfaces at distance r outside the solid particle are represented by solid curves. Measured drag coefficients are plotted as open symbols. The inner/outer interface position is denoted as the dashed vertical blue line at log2. The solid symbols at r = a indicate the values of
(
4
π
a
2
)
η
/
λ
D
/
γ
S
which is an estimation for electrophoresis drag coefficient in previous literature.[14,21] (b) Values of
κ
Δ
, which indicates the reference surface position Δ normalized by λ
D, are plotted as a function of
κ
a
.
Solid symbols indicate the inner/outer interface position as determined by the peak values in
U
/
v
∞
as shown in Fig. 3(a). Open symbols indicate
κ
Δ
values as determined by using the measured drag coefficients as the inputs to find the resulting interface position on which the calculated drag coefficient exactly yields the experimental value. The proximity and the trend give no doubt that, as far as drag coefficient is concerned, the inner/outer interface is the relevant reference surface at which the drag force is being acted on. The dashed line is a guide to the eye, it follows the relation
Δ
=
0.87
a
0.3
λ
D
0.7
.
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