The effect of uniform electric field on the cross-stream migration of a drop in plane Poiseuille flow

2016 ◽  
Vol 809 ◽  
pp. 726-774 ◽  
Author(s):  
Shubhadeep Mandal ◽  
Aditya Bandopadhyay ◽  
Suman Chakraborty
Keyword(s):  
Steady State ◽  
Electric Field ◽  
Numerical Simulations ◽  
Poiseuille Flow ◽  
Shape Deformation ◽  
Uniform Electric Field ◽  
Plane Poiseuille Flow ◽  
Stream Migration ◽  
The Cross ◽  
Transverse Position

The effect of a uniform electric field on the motion of a drop in an unbounded plane Poiseuille flow is studied analytically. The drop and suspending media are considered to be Newtonian and leaky dielectric. We solve for the two-way coupled electric and flow fields analytically by using a double asymptotic expansion for small charge convection and small shape deformation. We obtain two important mechanisms of cross-stream migration of the drop: (i) shape deformation and (ii) charge convection. The second one is a new source of cross-stream migration of the drop in plane Poiseuille flow which is due to an asymmetric charge distribution on the drop surface. Our study reveals that charge convection can cause a spherical non-deformable drop to migrate in the cross-stream direction. The combined effect of charge convection and shape deformation significantly alters the drop velocity, drop trajectory and steady state transverse position of the drop. We predict that, depending on the orientation of the applied uniform electric field and the relevant drop/medium electrohydrodynamic parameters, the drop may migrate either towards the centreline of the flow or away from it. We obtain that the final steady state transverse position of the drop is independent of its initial transverse position in the flow field. Most interestingly, we show that the drop can settle in an off-centreline steady state transverse position. Two-dimensional numerical simulations are also performed to study the drop motion in the combined presence of plane Poiseuille flow and a tilted electric field. The drop trajectory and steady state transverse position of the drop obtained from numerical simulations are in qualitative agreement with the analytical results.

Effect of transverse temperature gradient on the migration of a deformable droplet in a Poiseuille flow

2018 ◽  
Vol 850 ◽  
pp. 1142-1171 ◽  
Author(s):  
Sayan Das ◽  
Shubhadeep Mandal ◽  
Suman Chakraborty
Keyword(s):  
Thermal Conductivity ◽  
Steady State ◽  
Temperature Gradient ◽  
Numerical Simulations ◽  
Thermal Convection ◽  
Shape Deformation ◽  
Droplet Radius ◽  
Channel Height ◽  
State Position ◽  
Transverse Position

Intricate manipulation of droplets in fluidic confinements may turn out to be critically important for achieving their controlled transverse distributions. Here, we study the migration characteristics of a suspended deformable droplet in a parallel plate channel under the combined influence of a constant temperature gradient in the transverse direction and an imposed pressure driven flow. An outstanding question concerning the resultant non-trivial dynamical features that we address here pertains to the nonlinearity that results as a consequence of the shape deformation, which does not permit us to analyse the combined transport as a mere linear superposition of the results for the thermocapillary and imposed flow driven droplet migration in an effort to obtain the final solution. For the analytical solution, an asymptotic approach is used, where we neglect any effect of inertia or thermal convection of the fluid in either of the phases. To obtain a numerical solution, we use the conservative level set method. We perform numerical simulations over a wide range of governing parameters and obtain the dependence of the transverse steady position of the droplet on different parameters. In order to address practical microfluidic set-ups, the influence of a bounding wall as well as the effect of thermal convection and finite shape deformation on the cross-stream migration of the droplet is investigated through numerical simulations. Increase in the thermal Marangoni stress shifts the steady-state transverse position of the droplet further away from the channel centreline, for any particular value of the capillary number (which signifies the ratio of the viscous force to the surface tension force). The confinement ratio, which is the ratio of the droplet radius to the channel height, plays an important role in predicting the transverse position of the droplet and thus has immense consequences for the design of droplet-based microfluidic devices with enhanced functionalities. A large confinement ratio drives the droplet towards the channel centre, whereas a smaller confinement ratio causes the droplet to move towards the wall. Moreover, for a fixed droplet radius and constant imposed temperature gradient, an increase in the channel height results in an increase in the time required for the droplet to reach the steady-state position. However, the final steady-state position of the droplet is independent of its initial position but at the same time dependent on the droplet phase thermal conductivity. A larger droplet thermal conductivity compared with the carrier phase results in a steady-state droplet position closer to the channel centreline. A higher fluid inertia, on the other hand, shifts the steady-state position towards the channel wall.

scholarly journals Uniform electric-field-induced lateral migration of a sedimenting drop

2016 ◽  
Vol 792 ◽  
pp. 553-589 ◽  
Author(s):  
Aditya Bandopadhyay ◽  
Shubhadeep Mandal ◽  
N. K. Kishore ◽  
Suman Chakraborty
Keyword(s):  
Electric Field ◽  
Surface Charge ◽  
Tilt Angle ◽  
Shape Deformation ◽  
Uniform Electric Field ◽  
Lateral Motion ◽  
Drop Surface ◽  
Lateral Migration ◽  
Drop Velocity ◽  
Pressure Fields

We investigate the motion of a sedimenting drop in the presence of an electric field in an arbitrary direction, otherwise uniform, in the limit of small interface deformation and low-surface-charge convection. We analytically solve the electric potential in and around the leaky dielectric drop, and solve for the Stokesian velocity and pressure fields. We obtain the correction in drop velocity due to shape deformation and surface-charge convection considering small capillary number and small electric Reynolds number which signifies the importance of charge convection at the drop surface. We show that tilt angle, which quantifies the angle of inclination of the applied electric field with respect to the direction of gravity, has a significant effect on the magnitude and direction of the drop velocity. When the electric field is tilted with respect to the direction of gravity, we obtain a non-intuitive lateral motion of the drop in addition to the buoyancy-driven sedimentation. Both the charge convection and shape deformation yield this lateral migration of the drop. Our analysis indicates that depending on the magnitude of the tilt angle, conductivity and permittivity ratios, the direction of the sedimenting drop can be controlled effectively. Our experimental investigation further confirms the presence of lateral migration of the drop in the presence of a tilted electric field, which is in support of the essential findings from the analytical formalism.

scholarly journals Patterns in Wall-Bounded Shear Flows

2020 ◽  
Vol 52 (1) ◽  
pp. 343-367 ◽  
Author(s):  
Laurette S. Tuckerman ◽  
Matthew Chantry ◽  
Dwight Barkley
Keyword(s):  
Numerical Simulations ◽  
Couette Flow ◽  
Poiseuille Flow ◽  
Pipe Flow ◽  
Shear Flows ◽  
Plane Couette Flow ◽  
Plane Poiseuille Flow ◽  
Flow Focusing ◽  
Annular Pipe ◽  
Flow Plane

Experiments and numerical simulations have shown that turbulence in transitional wall-bounded shear flows frequently takes the form of long oblique bands if the domains are sufficiently large to accommodate them. These turbulent bands have been observed in plane Couette flow, plane Poiseuille flow, counter-rotating Taylor–Couette flow, torsional Couette flow, and annular pipe flow. At their upper Reynolds number threshold, laminar regions carve out gaps in otherwise uniform turbulence, ultimately forming regular turbulent–laminar patterns with a large spatial wavelength. At the lower threshold, isolated turbulent bands sparsely populate otherwise laminar domains, and complete laminarization takes place via their disappearance. We review results for plane Couette flow, plane Poiseuille flow, and free-slip Waleffe flow, focusing on thresholds, wavelengths, and mean flows, with many of the results coming from numerical simulations in tilted rectangular domains that form the minimal flow unit for the turbulent–laminar bands.

scholarly journals The motion of a deformable drop in a second-order fluid

1979 ◽  
Vol 92 (1) ◽  
pp. 131-170 ◽  
Author(s):  
P. C.-H. Chan ◽  
L. G. Leal
Keyword(s):  
Experimental Data ◽  
Shear Flow ◽  
Particle Velocity ◽  
Simple Shear ◽  
Poiseuille Flow ◽  
Second Order ◽  
Simple Shear Flow ◽  
Stream Migration ◽  
The Cross ◽  
Viscoelastic Rheology

The cross-stream migration of a deformable drop in a unidirectional shear flow of a second-order fluid is considered. Expressions for the particle velocity due to the separate effects of deformation and viscoelastic rheology are obtained. The direction and magnitude of migration are calculated for the particular cases of Poiseuille flow and simple shear flow and compared with experimental data.

Breakup of a conducting drop in a uniform electric field

2014 ◽  
Vol 754 ◽  
pp. 550-589 ◽  
Author(s):  
Rahul B. Karyappa ◽  
Shivraj D. Deshmukh ◽  
Rochish M. Thaokar
Keyword(s):  
Steady State ◽  
Numerical Analysis ◽  
Electric Field ◽  
Viscosity Ratio ◽  
Uniform Electric Field ◽  
Shape Prior ◽  
Capillary Stress ◽  
Electric Stress ◽  
Dc Electric Field ◽  
Axisymmetric Shape

AbstractA conducting drop suspended in a viscous dielectric and subjected to a uniform DC electric field deforms to a steady-state shape when the electric stress and the viscous stress balance. Beyond a critical electric capillary number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Ca}$, which is the ratio of the electric to the capillary stress, a drop undergoes breakup. Although the steady-state deformation is independent of the viscosity ratio $\lambda $ of the drop and the medium phase, the breakup itself is dependent upon $\lambda $ and $\mathit{Ca}$. We perform a detailed experimental and numerical analysis of the axisymmetric shape prior to breakup (ASPB), which explains that there are three different kinds of ASPB modes: the formation of lobes, pointed ends and non-pointed ends. The axisymmetric shapes undergo transformation into the non-axisymmetric shape at breakup (NASB) before disintegrating. It is found that the lobes, pointed ends and non-pointed ends observed in ASPB give way to NASB modes of charged lobes disintegration, regular jets (which can undergo a whipping instability) and open jets, respectively. A detailed experimental and numerical analysis of the ASPB modes is conducted that explains the origin of the experimentally observed NASB modes. Several interesting features are reported for each of the three axisymmetric and non-axisymmetric modes when a drop undergoes breakup.

scholarly journals On the Drift Velocity of Electrons in a Gas

1972 ◽  
Vol 25 (3) ◽  
pp. 329
Author(s):  
SL Paveri-Fontana
Keyword(s):  
Steady State ◽  
Electric Field ◽  
Drift Velocity ◽  
Isotropic Scattering ◽  
Uniform Electric Field ◽  
Present Communication ◽  
Steady State Distribution ◽  
State Distribution ◽  
Neutral Gas

In a recent paper, Crompton, Elford, and Robertson (1970; hereafter referred to as CER) considered certain questions concerning the steady-state distribution of electrons moving in a neutral gas under the influence of a uniform electric field E. The present communication comments on some aspects of the error discussion in the Appendix of the paper by CER. The analysis will be restricted to the case of isotropic scattering.

Cross-stream migration of drops suspended in Poiseuille flow in the presence of an electric field

2018 ◽  
Vol 97 (6) ◽  
Author(s):  
Binita Nath ◽  
Gautam Biswas ◽  
Amaresh Dalal ◽  
Kirti Chandra Sahu
Keyword(s):  
Electric Field ◽  
Poiseuille Flow ◽  
Stream Migration

scholarly journals NIMG-58. THE EFFECT OF CELL CONFLUENCE ON THE DISTRIBUTION OF TUMOR TREATING FIELDS

2020 ◽  
Vol 22 (Supplement_2) ◽  
pp. ii161-ii161
Author(s):  
Tal Marciano ◽  
Shay Levi ◽  
Zeev Bomzon
Keyword(s):  
Cell Membrane ◽  
Electric Field ◽  
Numerical Simulations ◽  
Membrane Permeability ◽  
Field Distribution ◽  
Membrane Integrity ◽  
Uniform Electric Field ◽  
Isolated Cells ◽  
Cell Membrane Integrity ◽  
Tumor Treating Fields

Abstract BACKGROUND Tumor Treating Fields (TTFields) are known to exert anti-mitotic effects on cells. Numerical simulations investigating the electric field distribution within isolated cells have been reported. These studies have shown that during metaphase a uniform electric field forms within the rounded cells. This field is thought to disrupt spindle formation through alignment of the tubulin dimers with the field. Simulations also show that during cytokinesis, a non-uniform electric field forms at the furrow, leading to strong dielectrophoretic forces that further disrupt cell division. Cells in the tumor are densely packed. We used numerical simulations to investigate how the clustering of cells influences TTFields distribution. METHODS COMSOL was used to numerically simulate delivery of TTFields to clusters of round cells placed in a hexagonal arrangement. The influence of the distance between the cells on field distribution was investigated. The effect of pores in the cell membrane on field distribution was also investigated. RESULTS Placing round cells in clusters resulted in regions of highly non-uniform fields within the cells. Strong gradients in the electric field were also observed around pores placed in the membrane. Non-uniformity and gradients in the field could result in strong dielectrophoretic forces capable of disrupting key cellular structures such as the cytoskeleton and mitotic spindle, as well as cell membrane integrity. CONCLUSIONS The placement of cells in close proximity to one another creates gradients in the electric field, which could be associated with very strong dielectrophoretic forces that enhance the effects of TTFields on cells. Strong dielectrophoretic forces were also observed around the membrane pores. Previous studies have reported that TTFields increases membrane permeability [Chang et al Cell Death Discovery. 2018]. The strong dielectrophoretic forces in the membrane may provide a physical mechanism by which TTFields enhance membrane permeability.

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