1 Three -Dimensional Printed Liquid Diodes with Tunable Velocity Design Guidelines and Applications for Liquid Collection and Transport

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Three-Dimensional Printed Liquid Diodes with Tunable Velocity: Design Guidelines and

Applications for Liquid Collection and Transport

Camilla Sammartino,¶ Michael Rennick, ¶ Halim Kusumaatmaja,* Bat-El Pinchasik **

C.S and B.-E.P.

Tel-Aviv University

School of Mechanical Engineering

Faculty of Engineering

6997801

Tel-Aviv, Israel

M.R and H.K

Department of Physics

Durham University South Road

Durham DH1 3LE

United Kingdom

¶ These authors contributed equally to the work.

Keywords

Capillarity, directional flow, liquid diodes, open microfluidics, biomimetics

Corresponding Authors

* halim.kusumaatmaja@durham.ac.uk

** pinchasik@tauex.tau.ac.il

Abstract

Directional and self-propelled flow in open channels has a variety of applications, including

microfluidic and medical devices, industrial filtration processes, fog-harvesting and condensing

apparatuses. Here, we present versatile three-dimensional (3D)-printed liquid diodes that enable

spontaneous unidirectional flow over long distances for a wide range of liquid contact angles.

Typically, we can achieve average flow velocities of several millimeters per second over a distance

of tens to hundreds of millimeters. The diodes have two key design principles. First, a sudden

widening in the channels’ width, in combination with a small bump, the pitch, ensure pinning of

the liquid in the backward direction. Second, an adjustable reservoir, the bulga, is introduced to

manipulate the liquid velocity with differing expansion angles. Using a combination of

experiments and lattice Boltzmann simulations, we provide a comprehensive analysis of the flow

behavior and speed within the channels with varying contact angles (CA), pitch heights and bulga

angles. This provides guidelines for the fabrication of bespoke liquid diodes with optimal design

for their potential applications. As a feasibility investigation, we test our design for condensation

of water from fog and subsequent transport uphill.

1. Introduction

Many industrial applications rely on directional transport of liquids, such as microfluidics,1

printing,2 filtering3 and lubrication apparatuses,4 water-harvesting,2 medical devices5 and precise

irrigation systems.6 While existing technologies feature external energy sources such as

micropumps and moving parts to drive the flow, they also increase production and operating costs

and add potential for malfunctions.7 However, passive solutions to this problem, including fluid

rectifiers such as Tesla valves,8 require high Reynold’s numbers or non-Newtonian fluids.9

In recent years, the fabrication of devices that are capable of spontaneous unidirectional liquid

transport attracted much attention. Such devices, named liquid or fluidic diodes in analogy with

the electronic counterpart,10 exploit capillary action as the driving force. The key is to create a

pressure difference that favors flow in one direction, while halting it in the opposite one. This can

be done by introducing surface wettability gradients, leading to so-called slip-mode11 liquid

diodes. Alternatively, we can harness the geometry of the solid surface, in particular by employing

asymmetric structures, to design spreading-mode11 liquid diodes. For example, sudden openings

that increase the liquid interfacial area can halt motion due to the increased energy required to

overcome these features, while inducing motion in the opposite direction. Indeed, liquid motion in

spreading-mode diodes often demonstrate stick-slip behavior12 where an advancing liquid front is

paused until these geometric features are overcome. It is also worth noting that several of the works

conducted on liquid diodes are inspired by nature,13 exhibiting passive unidirectional transport of

liquids with remarkable efficiency and precision. These include fleas,14 insects,15 lizards,16

butterflies,17 spider silk,18 cacti,19 pitcher plants20 and the beak of shorebirds.21

Despite the continuous growth of this field, further developments are needed to improve the

performance of these passive devices in terms of flow rate and directionality, and provide general

design guidelines that are adaptable to multiple use cases.2 To this end, we present 3D printed

spreading mode liquid diodes with a highly modifiable design. Importantly, we demonstrate for

the first time how the two structural features, the pitch and the bulga, can be exploited to separately

control the unidirectionality and velocity of the liquid flow. Our design allows long distance

transport of tens to hundreds of millimeters, with a typical speed of several millimeters per second.

3D printing has been on the rise over recent years in several fields for large-scale production.22

Here, the use of 3D printing allows us to easily adjust key structural features in the diode design.

This economic and accessible choice may replace other frequently employed techniques such as

laser cutting,14 self-assembled monolayers 23,24 lithography,25 etching26 or additional delicate post-

treatments.27 These methods are more expensive and laborious, with potential for irregularities and

durability problems in the long term.28

We use a combination of experiments and lattice Boltzmann simulations to provide a

comprehensive, systematic analysis on the performance of the liquid diodes as we vary the

aforementioned structural features and the surface tension (or the contact angle) of the liquid used.

We demonstrate that the pitch, designed as an elliptic cylindrical bump, widens the working

window of contact angles by introducing more degrees of freedom in the system, and that the bulga

allows fine control over the velocity by controlling the volume of an additional reservoir. Finally,

we test our design for condensation of water from fog and subsequent horizontal transport or uphill.

2. Results and Discussion

2.1. Design

Fig. 1 shows an overview of the diode design. Each diode typically consists of a unit cell, repeated

14 times, and 2 reservoirs, one at each end (Fig. 1a, i). Longer diodes, consisting of 30 unit cells

with total length of 146.4 mm, were also printed and successfully tested (see ESI, Video S1). Each

unit cell features a central triangular area, the bulga, and entrance and exit paths, the hilla and the

orifice, respectively. The pitch is located at the exit of the bulga (Fig. 1a, ii). Lattice Boltzmann

simulations allowed us to compare the performance of different pitch shapes. The elliptic cylinder

provides the best compromise between diodicity and ease of fabrication (Fig. S1, ESI).

Fig. 1. (a) Design of the liquid diodes, showing (i) full channel, with unit cell highlighted

in dashed red line, (ii)the main components of a unit cell. (b) Confocal microscope images

of unit cells with increasing pitch height, (i) 0%, (ii) 40% and (iii) 80% and (c)

corresponding profile images of the pitches from the unit cells shown in (b).

Fig. 1b shows laser confocal micrographs of unit cells with (i) 0%, (ii) 40% and (iii) 80% pitch

heights. The corresponding profiles of the pitches are shown in Fig. 1c. One advantage of this

design is that the geometry leading to pinning is now only a small section of the channel. This

allows us to use the angular expansion of the bulga, shown in Fig. 1a, ii, to adjust velocity with a

minimal effect on diode behavior. Both the hilla and the orifice are fixed in length. The length of

the hilla is chosen to allow room for varying the bulga angle. The length of the orifice is chosen to

ensure that the pinning behavior at the pitch is not influenced by the sloped wall of the hilla.

Diode geometry was identical in both experiments and simulations, with the simulations allowing

for finer control over the pitch height and contact angle, and experiments allowing for tests

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1Three-DimensionalPrintedLiquidDiodeswithTunableVelocity:DesignGuidelinesandApplicationsforLiquidCollectionandTransportCamillaSammartino,¶MichaelRennick,¶HalimKusumaatmaja,*Bat-ElPinchasik**C.SandB.-E.P.Tel-AvivUniversitySchoolofMechanicalEngineeringFacultyofEngineering6997801Tel-Aviv,IsraelM.RandH....

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