Electrostatic Interactions Between Charged

Bubble Interface and Solid Wall

Jonathan C. Hui, Peter Huang

Binghamton University, State University of New York

COMSOL Conference Boston

October 3, 2019

Optical and Fluidic Technologies Laboratory Jonathan C. Hui © 2019 – 2

Background Problem Method Results Conclusion

Projected U.S. Natural Gas Consumption & Production

• Increase in production and consumption through next 30 yrs

• International Energy Agency: 2018 record high production of 139 tcf (4%

increase from 2017)

• Hydraulic fracturing has become predominant method of extracting gas since

2011 and accounted for most of all new wells drilled since late 2014

Source: U.S. Energy Information Administration Annual Energy Outlook 2019

0

20

40

60

80

100

120

140

160

0

10

20

30

40

50

60

2000 2010 2020 2030 2040 2050

Dry natural gas production

trillion cubic feet billion cubic feet per day (bcf/d)2018

history projectionsHigh Oil and

Gas Resource

and Technology

High Oil Price

High Economic

Growth

Reference

Low Economic

Growth

Low Oil Price

Low Oil and

Gas Resource

and Technology

Optical and Fluidic Technologies Laboratory Jonathan C. Hui © 2019 – 3

Background Problem Method Results Conclusion

Hydraulic Fracturing Overview

Source: U.S. Environmental Protection Agency

Source: M. K. Mulligan and J. P. Rothstein. Deformation and Breakup of Micro- and

Nanoparticle Stabilized Droplets in Microfluidics Extensional Flows. Langmuir,

27(16):9760–9768, July 2011

Optical and Fluidic Technologies Laboratory Jonathan C. Hui © 2019 – 4

Background Problem Method Results Conclusion

Problem

v

P

Channel Wall

Continuous

Phase

Bubble

Optical and Fluidic Technologies Laboratory Jonathan C. Hui © 2019 – 5

Background Problem Method Results Conclusion

Problem

Channel Wall

Continuous

Phase

Original

Bubble Shape

ΔP = 0

v = 0

Equilibrium

Bubble Shape

Optical and Fluidic Technologies Laboratory Jonathan C. Hui © 2019 – 6

Background Problem Method Results Conclusion

Problem

Channel Wall

Continuous

Phase

Original

Bubble Shape

ΔP = 0

v = 0

Equilibrium

Bubble Shape

Deformation and Contact Considerations:

• Surface Tension

• Disjoining Pressure

• Electrostatic Forces

Charged Particles

Optical and Fluidic Technologies Laboratory Jonathan C. Hui © 2019 – 7

Background Problem Method Results Conclusion

R

Outlet

Channel W

all

Water

50.2 µm

50 µm

62.75 µm

Outlet

Air

Channel W

all

z

r

Model – Geometry

Objectives:

• Find conditions of maximal electrostatic repulsion

between bubble interface and channel wall

• Simulate bubble morphology due to electric charge

effects from channel wall on spherical bubble

interface using the customized weak contribution in

COMSOL

• Spherical bubble in microchannel

• 2D axisymmetry & planar symmetry

• Initial bubble radius = 50µm

• Channel radius = 50.2µm

• Half channel height = 62.75µm

Optical and Fluidic Technologies Laboratory Jonathan C. Hui © 2019 – 8

Background Problem Method Results Conclusion

Model – Boundary Conditions

Fluid Transport of Dilute Species Electrostatic

Impermeable Barrier

Symmetry

Axisymmetry

No Ions

Concentration C1,C2

Concentration C1,C2

No Flux

Optical and Fluidic Technologies Laboratory Jonathan C. Hui © 2019 – 9

Background Problem Method Results Conclusion

Model – Module Implementation & Weak Formulation

Navier-Stokes Eqn

Boundary Condition at Fluid-Fluid Interface

Total Stress

With unit normal from gas B to liquid A Surface Tension Electrostatics

Time Deriv Advection Diffusion Surface Tension BC Electrostatic BC

Weak Form

Implemented as

Weak Contribution for E

Initial

Conditions TDS ES TPFMMCj E

u�

• Two Phase Flow Moving Mesh Method (TPFMM) – Multiphase, interfacial tracking

• Transport of Dilute Species module (TDS) – Ion concentration

• Electrostatics module (ES) – Electric field

f

Optical and Fluidic Technologies Laboratory Jonathan C. Hui © 2019 – 10

Background Problem Method Results Conclusion

Results – Electric Double Layer

Verify COMSOL Capability for Steady State EDL Profile

0 20 40 60 80 1000

5

10

15

20

25

30

35

40

45

50

55

Radial Distance From Wall (nm)

Ele

ctr

ic P

ote

ntial (m

V)

C = 0.001 M

C = 0.0001 M

Electric Potential Profile Away from Wall

Electric Potential Plot Near Wall

(Boltzmann distribution)

Numerical Debye Length

(Debye-Huckel approximation)

Theoretical Debye Length

(Univalent-Univalent, Symmetric Electrolyte)

Strong Theoretical & Numerical Agreement

Optical and Fluidic Technologies Laboratory Jonathan C. Hui © 2019 – 11

Background Problem Method Results Conclusion

Results – Repulsion/Attraction

Vi = +75 mV 𝜁 = +50 mV

• Repulsive behavior with like

electric potential

• Attractive behavior with unlike

electric potential

• Double layer overlapped and

updated through time

C = 0.01µM

Vi = –50 mV 𝜁 = +50

mV

C = 0.01µM

Optical and Fluidic Technologies Laboratory Jonathan C. Hui © 2019 – 12

Background Problem Method Results Conclusion

Results –Attraction/Repulsion

Final Displacement vs. Concentration at Various Interfacial Potential

While 𝜁 = + 50 mV• Unlike Potential

• Attractive behavior for low concentration

• Neutral behavior for high concentration

• Like Potential

• Repulsive behavior for low

concentration

• Attractive behavior for high

concentration

df

Optical and Fluidic Technologies Laboratory Jonathan C. Hui © 2019 – 13

Background Problem Method Results Conclusion

Conclusion

• Developed a customized model to couple electrostatic influence on bubble interfacial morphology

• Quantify repulsive and attractive interactions between charged bubble interface and charged channel wall

• Key parameters: Electric potential and ion concentration for a given geometry

• Below certain ionic concentration threshold, larger electric potentials of like polarity maintain thicker

lubrication layers

• Ability to create repulsive environments indicates strong possibilities for precluding bubble contact

Acknowledgements:

American Chemical Society

Binghamton University, State University of New York