Dr Radu Cimpeanu researches fluid dynamics at all scales, exploring the value and beauty of computational mathematics.

Direct numerical simulations, also known as fully resolved computations, are highly accurate numerical solutions to mathematical equations. These simulations can help to solve the Navier-Stokes equations, which govern the motion of fluids. Dr Cimpeanu, from Imperial’s Interfacial Fluid Dynamics group, headed by Professor Demetrios Papageorgiou, explains what drew him to fluid dynamics in the first place:

“It's an area of research that offers you the benefit of being able to visualise what you’re doing; I can easily get a feeling for how the physical models work and have a sense of seeing what I’m working toward. This was definitely part of the attraction.”

Dr Cimpeanu explains that there can be three approaches to realising a scientific proof: experimental, analytical and computational. Each of these has their role to play; they all have advantages and disadvantages:

“Experiments allow you to examine what is physically there in front of you, but they can be expensive, requiring access to equipment and manpower. It’s also difficult to isolate certain components; if you want to delve into the centre of a droplet of water during fast impact, this would be close to impossible with current technological capabilities. You can be extremely rigorous in analysis, but with the restrictive assumptions one has to make due to the inherent physical complexity, you can only describe effects at isolated scales. The computational work offers a kind of bridge between the experimental and analytical approaches.”

How can these visual simulations, that expose fluids in such intricate detail, impact our everyday lives?

Dr Cimpeanu’s research focuses on the area of multi-phase flows. Multi-phase flows contain more than one fluid, for example, a gas and a liquid, or oil and water. The interface and instabilities between the fluids can be manipulated and controlled to produce advantageous results with far-reaching applications, such as fabrication techniques for microchips and drug delivery systems. Understanding multi-phase flows also gives researchers exciting opportunities to work with industry; examining the nature of drops and jets of fluids can be of interest to pharmaceutical and oil companies, and those working in anything from aeronautics to Formula 1 racing.

How to make a splash: how a single drop can create a big impact 

Major improvements in imaging techniques and computational power in recent years have contributed to a resurgence of interest in drop impact, an area of fluid dynamics with broad appeal. Drop impact is a fundamental phenomenon that governs applications such as inkjet printing, combustion and pesticide distribution.

Liquid impact onto a solid surface

Dr Cimpeanu provides an example of how studying liquid drops on solid surfaces can be applied to aerodynamics; as a plane flies through cloudy areas, known as high liquid water content regions, drops hit the aircraft surfaces. Liquid accumulates on these surfaces and can freeze, potentially causing problems if it gets into the engine. Radu and his collaborators study the various stages of impact, from the first microseconds as the drop falls, hits and disperses upon an aircraft surface, to the later dynamics of the droplets that form as a result of a splash. He elaborates:

“This type of computation provides detailed understanding of what happens as part of the splash dynamics itself. At the early stages you can compare the results to classical analytical models that are well-regarded in the field, and at later stages this technique also allows you to quantify the number of drops being shed by the impact, their distributions and so on. This practical information is of interest to the aeronautics industry, who might want to know how much of the water stays on the surface [of an aircraft] and how much blows off.”

Liquid impact onto a liquid pool

The image above shows a three-dimensional simulation of a water droplet onto a water surface. Figure a) illustrates the whole scene, showing what happens to the drop at a particular point of impact; b) removes the liquid pool, showing just the contour of the drop itself. c) removes the drop, showing the area of impact in the liquid pool; the red area shows the pressure field where the drop presses into the pool, indicating a region of increased pressure.

This research can be applied to situations like oil spills. Imagine raindrops hitting the surface of polluted water, potentially breaking up the liquid sheet into tiny droplets and spreading contaminants. The very smallest drops might fly out into the atmosphere and could be carried by wind onto shore regions; drop impact provides information on the trajectories and distribution of droplets and how this affects the surrounding environment.

Dr Cimpeanu explains why these computations are a necessary part of this research:

“The beauty of doing this computation is that you can isolate certain variables of interest, for example, the drop itself, finding out the velocity at any given point. You can also exclude the drop from the system to see the crater and visualise the effect of the impact on the liquid pool. You could achieve this experimentally, but you’d need an extremely talented experimentalist with extensive time and resources to do so. With the right computational tools you have access to the results and can extract most of the information you need relatively quickly.”

Find out more about the group's drop impact research

Controlling fluids using electric fields

Electrohydrodynamics combines the study of fluid motion with the effect of electric fields. Dr Cimpeanu continues:

“In an unstable system, where you have a dense fluid on top of a lighter fluid, when perturbed the denser fluid would simply fall in a typical mushroom shape, but you can completely arrest this growth using horizontal electric fields (see image above). You can put electrodes on either side of your fluid system, turn the electric field on, and because of its effect on the fluid-fluid interface it essentially competes with gravity and alongside surface tension; depending on how powerful your electric field is you can either decelerate this growth or completely stop it. This is useful in applications such as coating, to create a flat film of liquid paint on a surface.”

Sometimes, instead of wanting to stabilise the liquid (as when applying coats of paint), you want to de-stabilise the system to your advantage. Mixing fluids is one such context where destabilising might be useful. The computations above and below show a droplet of liquid, like blood or ethanol, in two surrounding liquids that have an interface. By manipulating the interface up and down, whatever you want to mix is steered around the domain efficiently, despite the entire fluid environment being highly viscous. Dr Cimpeanu continues:

“…you encourage the mixing to occur via the use of electric fields by applying it perpendicularly to the interface of two liquids. The interface then moves up and down in what are called induced interfacial oscillations, and this movement smears the fluid that you want to mix all over the place and within a reasonable time scale you go from a perfectly round drop (a) to something that’s almost homogeneously mixed (c) using nothing (no moving parts or imposed flow) but the strength of the electric field.”

Electrohydrodynamics can be used in lab-on-a-chip devices, where varied reactions, such as creating droplets from films, or mixing fluids, must take place within a single confined region using a very small volume of liquid. Everything happens efficiently within the small local geometry of the chip without the need to take elements from one device to another, risking contamination and distortion of results.

Find out more about the group's research into electrohydrodynamics

The art of the splash

The simulation above looks at first glance like the crest of a wave. Dr Cimpeanu explains:

“This image came about when I was inspecting the curvature of what’s called a corona, after drop impact. A corona splash forms when a drop hits a liquid surface and splashes; the crater that evolves has liquid shooting from the sides. The details of this corona splash look suspiciously like an ocean wave breaking. My inspiration for this image was the famous Hokusai woodblock print ‘The Great Wave off Kanagawa’; blue and white mimicking the foam of the waves and the colour of the ocean, and a sunset background.”

The collaborators submitted this image to the 2017 Imperial Innovations Art of Research Competition, where it reached the final exhibition. Pondering on the significance of this computation, Dr Cimpeanu concludes:

“This image shows how ubiquitous the equations that govern certain systems are. What you’re looking at here is a one millimetre drop hitting a liquid surface, but you can use the same type of equations to describe what happens with a wave metres high in an ocean. The scales and a few of the parameters change, but if you zoom in on just the right type of dynamics you see that the equations of fluid motion, and the tools you need to use – analytical, computational, experimental – are quite powerful. They can screen so many length scales, so many systems. It’s part of the attraction of the field actually, you can solve many problems with a single beautiful set of techniques.”

The research described here was supported by EPSRC grants The Mathematics of Multilayer Microfluidics and Multiscale Analysis of Complex Interfacial Phenomena, as well as Innovate UK Project 113001 (SANTANA).

Find out more on the Fluid Dynamics group website