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Efficient mixing method at the microscale for Time-Resolved Serial Femtosecond Crystallography

Periodic Reporting for period 2 - X-MIXING (Efficient mixing method at the microscale for Time-Resolved Serial Femtosecond Crystallography)

Reporting period: 2021-03-01 to 2022-02-28

Liquid mixing is an intriguing physical phenomenon across the scales, attracting the scientific community's attention not only for its open questions but also for its crucial role in technological applications. One of them is Time-Resolved Serial Femtosecond Crystallography (TR-SFX), a revolutionary multidisciplinary method to record molecular movies with an atomic resolution of biochemical reactions by utilizing x-ray free-electron lasers (XFEL) and the diffraction-before-destruction concept. The way of triggering these biochemical reactions is critical to control the process. An instant triggering would be ideal for initiating and mapping their spatio-temporal evolution. Unfortunately, many of them are not light sensitive and need hydrodynamic mixing to start the process correctly.

On the one hand, the length scales should be at the micro or even submicron-scale to avoid the backscattering of the liquid that is not ideal for obtaining cleaner diffraction patterns. On the other hand, the temporal scales should be as fast as possible and controllable. State-of-the-art methods utilized in this field take advantage of diffusion mechanisms to produce mixing. In this project, we propose a microfluidic mixing method to overcome the spatio-temporal limitations of diffusion and potentially obtain even 1000 faster mixing rates than current methods can produce. Besides, the versatility of our microfluidic arrangement can address the triggering of reactions by PH or temperature jumps.

In this project, we have elucidated the physical mechanisms the interplay between temperature gradients, electrical stresses and mixing in singularity fluid processes and pinch-off dynamics. Precise control of microfluidic mixing and their features is crucial to increase the temporal resolution of time-resolved biomolecular studies with XFEL, which potentially will offer new capabilities for the pharma industry in the design and customization of efficient drugs to cure dangerous diseases. With potential regional and national funding, the ideas conceived in this project will be extended to develop a commercial microfluidic device to address the above crucial challenges in a proper way for the society.

These are the overall objectives of the action:

. To analyse experimentally the influence of the input parameters on the mixing time.
. To analyse numerically the role of both the electro-migration of charges and thermal effects.
. To determine the scaling laws for the mixing time as a function of the governing parameters.
. To characterize experimentally how temperature affects the capillary cone-jet physics laws.
Understanding the underlying physical mechanisms behind any phenomenon, particularly our method, turns out critical to better exploit all its features. In this period, as part of the contemplated Contingency Plan, we have mainly focused on addressing theoretical and numerical aspects of our micromixing arrangement. In particular, it is of specific interest for our method to approach the interfacial dynamics of liquid entities and their topological transformation, particularly liquid jets. The split of a fluid filament into droplets inherently entails crossing tiny scales, eventually reaching the characteristic interface's thickness and then the continuum limit. However, we realized that there is no attention to the interface’s nature in the literature of pinch-off of liquid jets and only infinitely narrow models for the interface are assumed. Indeed, it is not found an interfacial model even at those tiny scales at which bulk fluctuations might emerge and become dominant. Essentially, we filled this gap and discovered how the deterministic, non-symmetric, self-similar inertia-viscous-capillary fragmentation can talk with a new symmetric set of self-similar breakup profiles that we found by adding a finite-thickness interface modeling. Symmetry within the breakup is crucial for obtaining clean and smooth fragmentation into mother drops without daughter satellite droplets. These theoretical features open a window to scaling down the periodic generation of droplets, which is linked to our mixing arrangement and can widen its possibilities and even produce much faster mixing than expected initially.

Published research articles:
1. The Natural Breakup Length of a Steady Capillary Jet: Application to Serial Femtosecond Crystallography. Crystals 2021, 11(8), 990. Authors: Gañán-Calvo, A. M., et al.
2. Pinch-off of liquid jets at the finite scale of an interface. Phys. Rev. Fluids 7, L012201. Authors: F. Cruz-Mazo & H. A. Stone
Comments: this paper is currently under embargo until Jan. 18th 2023. Unfortunately, we did realize after acceptance that we did not have enough budget to afford. We will be happy to pay the open-access fees and mitigate this problem once the oncoming regional project is finally granted. In any case, EU acknowledgment is visible in the article and compliant with the grant agreement.
Future research articles directly related to this action:
3. “Submicronsized periodic droplet trains”. Authors: F. Cruz-Mazo & A. M. Gañán-Calvo.
4. “Unconditional liquid jets”. Authors: A. M. Gañán-Calvo, F. Cruz-Mazo et al.
5. “Viscous-capillary liquid fragmentation and thermal effects”. Authors: F. Cruz-Mazo (H. A. Stone & A. M. Gañán-Calvo will be invited).
6. “Electrohydrodynamic evaporation”. Authors: F. Cruz-Mazo & A. M. Gañán-Calvo.
7. “Evaporative streams”. Authors: F. Cruz-Mazo, A. M. Gañán-Calvo & Gañán-Calvo’s students.
8. “Megahertz pulse trains enable multi-hit serial crystallography experiments at XFELs”. Authors: Holmes, S. et al. (under review)
9. X-MIXING, an electrohydrodynamic disintegration of miscible fluid flows. Authors: F. Cruz-Mazo & A. M. Gañán-Calvo

Press release: local and regional newspapers published that F. Cruz-Mazo is beneficiary of a Marie Sklodowska-Curie Individual Fellowhisp. Social media: Talk on Youtube from the European Researchers’ Night 2021. Website: Participation to a Conference: American Physical Society, Division of Fluid Mechanics (2019, 2020). Participation to a Workshop: Challenges in Microfluidic Sample Delivery, European XFEL 2022.. Participation in activities organized jointly with other EU projects: the European Researchers’ Night 2019.
This project introduces a novel microfluidic mixing method that itself is a jump over the state-of-the-art of the field. We have demonstrated faster mixing (from ten to a hundred times faster) and a potential to achieve one-thousand much faster mixing than current methods by the miniaturization of this concept. Its versatility to induce biochemical reactions by jumping either PH or temperature is also an asset. The potential short-term impact of this project concerns offering a new tool for taking full advantage of recent massive investment on the European XFEL, enabling challenging TR-SFX studies that in some cases could not even be approachable without our microfluidic mixing method. The long-term impact embraces the expected effects of TR-SFX and the use of biomolecular movies for studying chemical reactions to gain insight and open new horizons in pharma. A good example is the design of novel specific drug targets based on G protein-coupled receptors (GPCRs), under a current tendency for their application to cure diseases that affect the World population massively as Cancer and Diabetes.