Dynamics of 2-Dimensional Soft Particle Flow Through Hopper Open Access

Abstract

I study the quasi-2d hopper flow of oil-in-water emulsions as they exit an orifice in two

scenarios. First, I look at many particle flow of droplets with diameters smaller than the

opening width For many particle flow, prior work on hopper dynamics has focused on the flow

rate, which is defined as the number of oil droplets exiting per unit time. This has shown a

general power law dependence between flow rate, Q, the ratio of the opening width, w, to the

average diameter of droplet size, d, and the fitting constant κ as such: Q ∼ (w/d−κ)β. Prior

work has seen various values for the exponent β, corresponding to different experimental

conditions. Recent work has suggested that the range of values for the exponent β can

explained by the ratio of the viscous drag force of particles moving in their medium to the

kinetic friction of two particles sliding past each other. In two dimensions, for the low kinetic

friction limit, this exponent should be 1/2. We experimentally verify this claim by studying

the flow rate of silicon oil-in-water emulsions as they pass through an orifice over a range

of w/d values. We find that the flow rate collapses to the general curve with β = 0.49 and

κ = 1.47. I then extend this work to examine the flow of a oil droplet with a diameter

larger than the opening width of the orifice. If the volume of oil is high enough, I find that

droplets can flow through this opening by deforming, even when the droplet diameter is 3°ø

the size of the opening. In this scenario, I compare my results with the common approach to

modelling soft particles: the Durian bubble model. This model predicts that once the droplet

is half-way through the opening, the wall-droplet repulsion assists in pushing the droplet

out of the hopper, so much so that the droplet overshoots its terminal velocity. I find that

my experiment is unable to replicate the velocity overshoot predicted by the Durian bubble

model. I suggest that this occurs because of a regime where viscous dissipation is capable

of depleting the energy required to overshoot, as well as the presence of a non-negligible

depletion force.

Table of Contents

1. Introduction

1.1 Many Particle Flow and the Wandering Exponent . . . . . . . . . . . . . . . 2

1.1.1 Beverloo Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Single Particle Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.1 Surface Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2. Methods

2.1 Emulsion Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.1 Snap Off Through Direct Syringe Injection . . . . . . . . . . . . . . . 10

2.1.2 Microfluidic Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Chamber Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.1 Hopper Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.2 Hopper Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3 Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4 Computational Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4.1 Particle Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4.2 Measuring Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3. Multiple Particle Results and Analysis

3.1 Trajectory of Droplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2 Velocity Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.3 Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3.1 Flux for Soft Particles . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3.2 Experimental Data on Flux . . . . . . . . . . . . . . . . . . . . . . . 27

3.4 Fitting to the Beverloo Equation . . . . . . . . . . . . . . . . . . . . . . . . 29

3.5 Summary of Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4. Single Particle Results and Analysis

4.1 Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.1.1 Durian Bubble Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.1.2 Surface Energy and Velocity . . . . . . . . . . . . . . . . . . . . . . . 39

4.1.3 Center of Mass Velocity . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.1.4 Leading and Trailing Edge . . . . . . . . . . . . . . . . . . . . . . . . 45

4.2 Summary of Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Conclusion 48

Bibliography 51

About this Honors Thesis

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School	Emory College
Department	Physics
Degree	Ph.D.
Submission	Honors Thesis
Language	English
Research Field	Physics, Condensed Matter Physics, General
Keyword	Hopper flow Emulsions
Committee Chair / Thesis Advisor	Weeks, Eric, Emory University
Committee Members	Mitchell, Andrew, Emory University Bing, Tom, Emory University

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