The behavior of liquid drops in the retropulsive jet produced by a peristaltic wave is investigated computationally. The computational geometry consists of a tube which is closed at one end, with the peristaltic wave that deforms the boundary moving toward it. A modified solver with the capability to couple mesh deformation and adaptive mesh refinement around moving drops was developed and validated with experimental data, and good agreement was found. A parametric study was then performed to determine the effect of interfacial tension, viscosity ratio, relative occlusion, and initial drop position on the drop's behavior and breakup characteristics. In particular, breakup regimes on graphs of capillary number vs viscosity ratio were determined for each initial drop position and relative occlusion. It was found that these breakup regimes were bounded above and below, and an optimal capillary number for breakup was determined. The volume of the parent drop after breakup decreased linearly with capillary number for low capillary numbers and was independent of the viscosity ratio. For higher capillary numbers, this volume generally increased with the viscosity ratio. It was also found that a drop with lower interfacial tension reached the apex plane sooner than a drop with higher interfacial tension, but once there, took longer to pass through this plane and longer to breakup. The viscosity ratio had negligible influence on the drop transit times for viscosity ratios less than one, while the breakup time generally increased with the viscosity ratio.
References
1.
G. I.
Taylor
, “The viscosity of a fluid containing small drops of another fluid
,” Proc. R. Soc. London, Ser. A
138
, 41
–48
(1932
).2.
G. I.
Taylor
, “The formation of emulsions in definable fields of flow
,” Proc. R. Soc. London, Ser. A
146
, 501
–523
(1934
).3.
E.
Hinch
and A.
Acrivos
, “Long slender drops in a simple shear flow
,” J. Fluid Mech.
98
, 305
(1980
).4.
H. P.
Grace
, “Dispersion phenomena in high viscosity immiscible fluid systems and application of static mixers as dispersion devices in such systems
,” Chem. Eng. Commun.
14
, 225
–277
(1982
).5.
B. J.
Bentley
and L. G.
Leal
, “An experimental investigation of drop deformation and breakup in steady, two-dimensional linear flows
,” J. Fluid Mech.
167
, 241
–283
(1986
).6.
H. A.
Stone
and L. G.
Leal
, “A note concerning drop deformation and breakup in biaxial extensional flows at low Reynolds numbers
,” J. Colloid Interface Sci.
133
, 340
–347
(1989
).7.
J.
Li
, Y.
Renardy
, and M.
Renardy
, “Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method
,” Phys. Fluids
12
(2
), 269
–282
(2000
).8.
S.
Guido
, M.
Simeone
, and F.
Greco
, “Deformation of a Newtonian drop in a viscoelastic matrix under steady shear flow. Experimental validation of slow flow theory
,” J. Non-Newtonian Fluid Mech.
114
, 65
–82
(2003
).9.
D. P.
Panigrahi
, S.
Das
, and S.
Chakroborty
, “Deformation of a surfactant-laden viscoelastic droplet in a uniaxial extensional flow
,” Phys. Fluids
30
, 122108
(2018
).10.
D.
Wang
, D. S.
Tan
, and N.
Phan-Thien
, “A lattice Boltzmann method for simulating viscoelastic drops
,” Phys. Fluids
31
, 073101
(2019
).11.
D.
Wang
, D. S.
Tan
, Z.
Ouyang
, B. C.
Khoo
, and N.
Phan-Thien
, “A lattice Boltzmann modeling of viscoelastic drops' deformation and breakup in simple shear flows
,” Phys. Fluids
32
, 123101
(2020
).12.
Y.
Kruijt-Stegeman
, F.
van de Vosse
, and H.
Meijer
, “Droplet behavior in the presence of insoluble surfactants
,” Phys. Fluids
16
, 2785
–2796
(2004
).13.
K.
Feigl
, D.
Megias-Alguacil
, P.
Fischer
, and E. J.
Windhab
, “Simulation and experiments of droplet deformation and orientation in simple shear flow with surfactants
,” Chem. Eng. Sci.
62
, 3242
–3258
(2007
).14.
Z. Y.
Luo
, X. L.
Shang
, and B. F.
Bai
, “Effect of soluble surfactant on the motion of a confined droplet in a square microchannel
,” Phys. Fluids
31
, 117104
(2019
).15.
H. A.
Stone
, B. J.
Bentley
, and L. G.
Leal
, “An experimental study of transient effects in the breakup of viscous drops
,” J. Fluid Mech.
173
, 131
–158
(1986
).16.
H. A.
Stone
and L. G.
Leal
, “The influence of initial deformation on drop breakup in subcritical time-dependent flows at low Reynolds numbers
,” J. Fluid Mech.
206
, 223
–263
(1989
).17.
V.
Sibillo
, G.
Pasquariello
, M.
Simeone
, V.
Cristini
, and S.
Guido
, “Drop deformation in microconfined shear flow
,” Phys. Rev. Lett.
97
, 054502
(2006
).18.
R. D.
Egholm
, P.
Fischer
, K.
Feigl
, E. J.
Windhab
, R.
Kipka
, and P.
Szabo
, “Experimental and numerical analysis of droplet deformation in a complex flow generated by a rotor–stator device
,” Chem. Eng. Sci.
63
, 3526
–3536
(2008
).19.
M.
Mulligan
and J.
Rothstein
, “The effect of confinement-induced shear on drop deformation and breakup in microfluidic extensional flows
,” Phys. Fluids
23
, 022004
(2011
).20.
K.
Feigl
, A.
Baniabedalruhman
, and F. X.
Tanner
, “Numerical simulations of the breakup of emulsion droplets inside a spraying nozzle
,” Phys. Fluids
28
, 123103
(2016
).21.
B.
Nath
, G.
Biswas
, and A.
Dalal
, “Influence of electric field on deformation of a drop in shear flow
,” Phys. Fluids
31
, 042102
(2019
).22.
S.
Santra
, A.
Jana
, and S.
Chakraborty
, “Electric field modulated deformation dynamics of a compound drop in the presence of confined shear flow
,” Phys. Fluids
32
, 122006
(2020
).23.
A.
Zeeshan
, N.
Ijaz
, M. M.
Bhatti
, and A. B.
Mann
, “Mathematical study of peristaltic propulsion of solid–liquid multiphase flow with a biorheological fluid as the base fluid in a duct
,” Chin. J. Phys.
55
(4
), 1596
–1604
(2017
).24.
M. M.
Bhatti
, A.
Zeeshan
, and N.
Ijaz
, “Heat transfer analysis on peristaltically induced motion of particle-fluid suspension with variable viscosity: Clot blood model
,” Comput. Methods Prog. Biomed.
137
, 115
–124
(2016
).25.
K.
Connington
, Q.
Kang
, H.
Viswanathan
, A.
Abdel-Fattah
, and S.
Chen
, “Peristaltic particle transport using the lattice Boltzmann method
,” Phys. Fluids
21
, 053301
(2009
).26.
K. S.
Mekheimer
, E. F.
El-Shehawey
, and A. M.
Elaw
, “Peristaltic motion of a particle-fluid suspension in a planar channel
,” Int. J. Theor. Phys.
37
, 2895
–2920
(1998
).27.
J. C.
Misra
and S. K.
Pandey
, “Peristaltic transport of a particle-fluid suspension in a cylindrical tube
,” Comput. Math. Appl.
28
(4
), 131
–145
(1994
).28.
L. J.
Fauci
, “Peristaltic pumping of solid particles
,” Comput. Fluids
21
(4
), 583
(1992
).29.
L. M.
Srivastava
and V. P.
Srivastava
, “Peristaltic transport of a particle-fluid suspension
,” J. Biomech. Eng.
111
(2
), 157
–165
(1989
).30.
L. M.
Srivastava
and V. P.
Srivastava
, “Peristaltic transport of blood: Casson model–II
,” J. Biomech.
17
(11
), 821
–829
(1984
).31.
F.
Blanchette
, “The influence of suspended drops on peristaltic pumping
,” Phys. Fluids
26
, 061902
(2014
).32.
B.
Taghilou
, M.
Pourjafar
, and K.
Sadeghy
, “On the use of peristaltic waves for the transport of soft particles: A numerical study
,” Phys. Fluids
32
, 062108
(2020
).33.
D.
Dufour
, F. X.
Tanner
, K. A.
Feigl
, and E. J.
Windhab
, “Investigation of the dispersing characteristics of antral contraction wave flow in a simplified model of the distal stomach
,” Phys. Fluids
33
, 083101
(2021
).34.
N.
Scheuble
, J.
Schaffner
, M.
Schumacher
, E. J.
Windhab
, D.
Liu
, H.
Parker
, A.
Steingoetter
, and P.
Fischer
, “Tailoring emulsions for controlled lipid release: Establishing in vitro–in vivo correlation for digestion of lipids
,” ACS Appl. Mater. Interfaces
10
(21
), 17571
–17581
(2018
).35.
M. J.
Ferrua
and R. P.
Singh
, “Modeling the fluid dynamics in a human stomach to gain insight of food digestion
,” J. Food Sci.
75
, R151
–162
(2010
).36.
37.
S.
Alokaily
, K.
Feigl
, F. X.
Tanner
, and E. J.
Windhab
, “Numerical simulations of the transport of Newtonian and non-Newtonian fluids via peristaltic motion
,” Appl. Rheol.
28
(3
), 32832
(2018
).38.
S.
Alokaily
, K.
Feigl
, and F. X.
Tanner
, “Characterization of peristaltic flow during the mixing process in a model human stomach
,” Phys. Fluids
31
(3
), 103105
(2019
).39.
P.
Boulby
, R.
Moore
, P.
Gowland
, and R. C.
Spiller
, “Fat delays emptying but increases forward and backward antral flow as assessed by flow-sensitive magnetic resonance imaging
,” Neurogastroenterol. Motil.
11
(1
), 27
–36
(1999
).40.
K.
Schulze
, “Imaging and modeling of digestion in the stomach and the duodenum
,” Neurogastroenterol. Motil.
18
(3
), 172
–183
(2006
).41.
A.
Pal
, K.
Indireshkumar
, W.
Schwizer
, B.
Abrahamsson
, M.
Fried
, and J. G.
Brasseur
, “Gastric flow and mixing studied using computer simulation
,” Proc. R. Soc. B
271
(1557
), 2587
–2594
(2004
).42.
M. J.
Ferrua
and R. P.
Singh
, “Understanding the fluid dynamics of gastric digestion using computational modeling
,” Proc. Food Sci.
1
, 1465
–1472
(2011
).43.
D.
Dufour
, “Ultrasound Doppler flow measurement in food production and digestion processes
,” Ph.D.
thesis (Swiss Federal Institute of Technology, ETH Zurich
, 2018
).44.
F.
Kong
and R. P.
Singh
, “A human gastric simulator (HGS) to study digestion in human stomach
,” J. Food Sci.
75
(9
), E627
–E635
(2010
).45.
M. A.
Kwiatek
, A.
Steingoetter
, A.
Pal
, D.
Menne
, J. G.
Brasseur
, G. S.
Hebbard
, P.
Boesiger
, M.
Thumshirn
, M.
Fried
, and W.
Schwizer
, “Quantification of distal antral contractile motility in healthy human stomach with magnetic resonance imaging
,” J. Magn. Reson. Imaging
24
, 1101
–1109
(2006
).46.
R. I.
Tanner
, “A modified Oldroyd-b model for non-colloidal suspensions
,” Phys. Fluids
33
, 073105
(2021
).47.
T.
Sato
, Y.
Kwon
, Y.
Matsumiya
, and H.
Watanabe
, “A constitutive equation for Rouse model modified for variations of spring stiffness, bead friction, and Brownian force intensity under flow
,” Phys. Fluids
33
, 063106
(2021
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.
