Abstract

The wide applications of plug flows in microscale in science and engineering help them attract a great deal recent interest. An analytical study is undertaken here to study the impacts of a transversely applied external uniform magnetic field affecting the motion of liquid in the plug in terms of hydrodynamic mixing properties. The well-known symmetric vortex structure occurring in a long plug with moderate aspect ratio is observed to be preserved, while the recirculation phenomenon is highly affected by the action of the magnetic field. The decelerating feature of Lorentz force on the liquid motion is illuminated by reducing the strength of the recirculating vortex moving towards the upper and lower walls. The effects of magnetic field on the flow resistance of the liquid plug as well as on the plug circulation rate and on the axial flux are also clarified. The liquid plug considered here is shown to be fully consistent with the continuous liquid flow in a channel whose exact solution is further extracted.

References

References
1.
Stone
,
H. A.
,
Stroock
,
A. D.
, and
Ajdari
,
A.
,
2004
, “
Engineering Flows in Small Devices: Microfluidics Toward a Lab-on-a-Chip
,”
Annu. Rev. Fluid Mech.
,
36
(
1
), pp.
381
411
.10.1146/annurev.fluid.36.050802.122124
2.
Cassidy
,
K. J.
,
Gavriely
,
N.
, and
Grotberg
,
J. B.
,
2001
, “
Liquid Plug Flow in Straight and Bifurcating Tubes
,”
ASME J. Biomech. Eng.
,
123
(
6
), pp.
580
589
.10.1115/1.1406949
3.
Sista
,
R.
,
Hua
,
Z.
,
Thwar
,
P.
,
Sudarsan
,
A.
,
Srinivasan
,
V.
,
Eckhardt
,
A.
,
Pollack
,
M.
, and
Pamula
,
V.
,
2008
, “
Development of a Digital Microfluidic Platform for Point of Care Testing
,”
Lab Chip
,
8
(
12
), pp.
2091
2104
.10.1039/b814922d
4.
Kreutzer
,
M. T.
,
Kapteijn
,
F.
,
Moulijn
,
J. A.
, and
Heiszwolf
,
J. J.
,
2005
, “
Multiphase Monolith Reactors: Chemical Reaction Engineering of Segmented Flow in Microchannels
,”
Chem. Eng. Sci.
,
60
(
22
), pp.
5895
5916
.10.1016/j.ces.2005.03.022
5.
Walsh
,
P. A.
,
Walsh
,
E. J.
, and
Muzychka
,
Y. S.
,
2010
, “
Heat Transfer Model for Gas-Liquid Slug Flows Under Constant Flux
,”
Int. J. Heat Mass Transfer
,
53
(
15–16
), pp.
3193
3201
.10.1016/j.ijheatmasstransfer.2010.03.007
6.
Fuchiwaki
,
Y.
, and
Nagai
,
H.
,
2014
, “
Study of a Liquid Plug-Flow Thermal Cycling Technique Using a Temperature Gradient-Based Actuator
,”
Sensors
,
14
(
11
), pp.
20235
20244
.10.3390/s141120235
7.
Mitroo
,
D.
,
Sun
,
Y.
,
Combest
,
D. P.
,
Kumar
,
P.
, and
Williams
,
B. J.
,
2018
, “
Assessing the Degree of Plug Flow in Oxidation Flow Reactors (OFRs): a Study on a Potential Aerosol Mass (PAM) Reactor
,”
Atmos. Meas. Tech.
,
11
(
3
), pp.
1741
1756
.10.5194/amt-11-1741-2018
8.
Che
,
Z.
,
Wong
,
T. N.
, and
Nguyen
,
N.-T.
,
2012
, “
Heat Transfer Enhancement by Recirculating Flow Within Liquid Plugs in Microchannels
,”
Int. J. Heat Mass Transfer
,
55
(
7–8
), pp.
1947
1956
.10.1016/j.ijheatmasstransfer.2011.11.050
9.
Sivasamy
,
J.
,
Che
,
Z.
,
Neng Wong
,
T.
,
Nguyen
,
N.-T.
, and
Yobas
,
L.
,
2010
, “
A Simple Method for Evaluating and Predicting Chaotic Advection in Microfluidic Slugs
,”
Chem. Eng. Sci.
,
65
(
19
), pp.
5382
5391
.10.1016/j.ces.2010.06.017
10.
Che
,
Z.
,
Wong
,
T. N.
, and
Nguyen
,
N.-T.
,
2011
, “
An Analytical Model for Plug Flow in Microcapillaries With Circular Cross Section
,”
Int. J. Heat Fluid Flow
,
32
(
5
), pp.
1005
1013
.10.1016/j.ijheatfluidflow.2011.06.009
11.
Shojaeian
,
M.
,
Yildiz
,
M.
, and
Koşar
,
A.
,
2014
, “
Heat Transfer Characteristics of Plug Flows With Temperature-Jump Boundary Conditions in Parallel-Plate Channels and Concentric Annuli
,”
Int. J. Therm. Sci.
,
84
, pp.
252
259
.10.1016/j.ijthermalsci.2014.05.014
12.
Cao
,
Y.
, and
Li
,
R.
,
2018
, “
A Liquid Plug Moving in an Annular Pipe—Flow Analysis
,”
Phys. Fluids
,
30
(
9
), p.
093605
.10.1063/1.5050258
13.
Hu
,
Y.
,
Romano
,
F.
, and
Grotberg
,
J. B.
,
2020
, “
Effects of Surface Tension and Yield Stress on Mucus Plug Pupture: A Numerical Study
,”
ASME J. Biomech. Eng.
,
142
(
6
), p.
061007
.10.1115/1.4045596
14.
Bozkaya
,
C.
, and
Tezer-Sezgin
,
M.
,
2007
, “
Fundamental Solution for Coupled Magnetohydrodynamic Flow Equations
,”
J. Comput. Appl. Math.
,
203
(
1
), pp.
125
144
.10.1016/j.cam.2006.03.013
15.
Hunt
,
J. C. R.
, and
Stewartson
,
K.
,
1965
, “
Magnetohydrodynamic Flow in Rectangular Ducts
,”
J. Fluid Mech.
,
23
(
03
), pp.
563
581
.10.1017/S0022112065001544
16.
Hussam
,
W. K.
, and
Sheard
,
G. J.
,
2013
, “
Heat Transfer in a High Hartmann Number MHD Duct Flow With a Circular Cylinder Placed Near the Heated Side-Wall
,”
Int. J. Heat Mass Transfer
,
67
, pp.
944
954
.10.1016/j.ijheatmasstransfer.2013.08.081
17.
Alshare
,
A.
,
Tashtoush
,
B.
, and
El-Khalil
,
H. H.
,
2013
, “
Computational Modeling of Non-Newtonian Blood Flow Through Stenosed Arteries in the Presence of Magnetic Field
,”
ASME J. Biomech. Eng.
,
135
(
11
), p.
114503
.10.1115/1.4025107
You do not currently have access to this content.