Reducing Spatial Heterogeneity of MALDI Samples with Marangoni Flows During Sample Preparation

Supporting Information

Reducing Spatial Heterogeneity of MALDI Samples with Marangoni Flows during Sample Preparation

Yin-Hung Lai,1 Yi-Hong Cai, 1 Hsun Lee,1 Yu-Meng Ou,1,2 Chih-Hao Hsiao,1 Chien- Wei Tsao,1,3 Huan-Tsung Chang,2 Yi-Sheng Wang*,1

1Genomics Research Center, Academia Sinica, Taipei 115, Taiwan, ROC

2Chemistry Department, National Taiwan University, Taipei 106, Taiwan, ROC

3Department of Chemical Engineering and Biotechnology, National Taipei University of Technology, Taipei 106, Taiwan, ROC A. Region of interest (ROI) analysis Five concentric ROIs with equal annular width within a sample spot. The regions from the center to the periphery are sequentially defined from ROI 1 to ROI 5.

B. Semi-empirical hydrodynamic analysis The rate of droplet evaporation (, in kg/s) is along the normal of droplet surface. The velocity of outward capillary flow (VC, in m/s) induced by droplet evaporation is 2 derived on the basis of fundamental formulae of evaporation flux (Js, in kg/s m ). The formulae were proposed by Lebedev and Deegan et al.[1, 2], and further developed by Hu et al.[3]: (S1) in which  is the density of solvent, R is the contact line radius,  is the contact angle, and h is the height of the droplet. According to literature, we obtain:

Combining Eqs. 1-3, VC becomes: (S4) where . Integrating Eq. S4, one can obtain the general form of VC. (S5) in which and are fitting parameters, and D, H, and Cv stand for the vapor diffusivity, relative humidity, and saturated vapor concentration of solvents, respectively. In order to obtain J0(), the proposed in literature is integrated in the present study to obtain the average evaporation rate (, in kg/s) under the quasi-steady-state condition [3-5], and the result is subsequently used to derive J0(): (S6)

From Eq. S7, the general expression of VC becomes:

(S8) Notably, even for complex systems, can be determined by measuring the drying time of the droplet. In the current study, the typical sample area is circular shaped with an R of 1 mm and an initial contact angle of 30°. The droplet drying processes are monitored using a CCD camera (C525 HD WEBCAM, Logitech, Lausanne, Switzerland). The spatial resolution and frame rate of this imaging system is 50 m and 5 frames per second (0.2 second per frame). Such specifications ensure precise determination of droplet drying times.

C. Boundary conditions and thermodynamics in simulation

The boundary condition of droplets can be analyzed using the cross section of a droplet showed above. The figure is axially symmetric about the axis to the left. The free surface of the spherical cap droplet can be expressed as [3]:

In this simulation, the contact radius (R) and the initial contact angle (0) are set to be 1.0 mm and 30°, respectively. The Marangoni boundary is applied to the interface between air and liquid,

(S10) where , ur, uz, , T stand for the viscosity, horizontal component of flow velocity, vertical component of flow velocity, surface tension, and temperature, respectively. The top boundary is set at 1 mm above the substrate, and the temperature at this boundary is determined experimentally. The boundary at the bottom represents the substrate, which is regulated by a programmed constant temperature circulator. Table S1 lists the boundary and substrate temperatures used in the calculations.

Table S1 Boundary and substrate temperatures boundary temperature 18.0°C 19.3°C 24.4°C 35.0°C substrate temperature 5.0°C 15.0°C 25.0°C 45.0°C

The thermodynamic properties of water under different temperatures are used to calculate the Marangoni vortex by COMSOL Multiphysics v5.0. The properties include heat capacity (Cp, in J/kg K), thermal conductivity (k, in W/m K), temperature coefficient of the surface tension (, in N/m K), viscosity (, in Pa s), and the density ( in kg/m3). The values of the properties are listed below: D. Results of theoretical and semi-empirical analysis Figure S1 The temperature gradients within a droplet when keeping substrates at 5, 25, and 45°C. The results represent the result at the instants the drying processes start. The temperatures measured 1-mm above droplets are used as the boundary conditions for theoretical calculations. The simulations are performed by using COMSOL Multiphysics v5.0. Figure S2 Comparison of average velocities of Marangoni and outward capillary flow within the effective contact region under different substrate temperatures.

s Marangoni flow / outward capillary flow m -4

y t i -5 c 10 o l e

V -6 10 e g

a -7 r 10 e v

A 10-8 5 25 45 Substrate Temperature (oC)

References 1 N. N. Lebedev, Special Functions and Their Applications. Courier Corporation: 1972. 2 R. D. Deegan, O. Bakajin, T. F. Dupont, G. Huber, S. R. Nagel and T. A. Witten, Contact line deposits in an evaporating drop. Phys. Rev. E 2000, 62, 756-765. 3 H. Hu and R. G. Larson, Evaporation of a sessile droplet on a substrate. J. Phys. Chem. B 2002, 106, 1334-1344. 4 S. M. Rowan, M. I. Newton and G. McHale, Evaporation of microdroplets and the wetting of solid-surfaces. J. Phys. Chem. 1995, 99, 13268-13271. 5 K. S. Birdi, D. T. Vu and A. Winter, A study of the evaporation rates of small water drops placed on a solid-surface. J. Phys. Chem. 1989, 93, 3702-3703.