One-step formation of polymorphous sperm-like microswimmers by vortex turbulence-assisted microfluidics

Microswimmers are considered promising candidates for active cargo delivery to benefit a wide spectrum of biomedical applications. Yet, big challenges still remain in designing the microswimmers with effective propelling, desirable loading and adaptive releasing abilities all in one. Inspired by the morphology and biofunction of spermatozoa, we report a one-step formation strategy of polymorphous sperm-like magnetic microswimmers (PSMs) by developing a vortex turbulence-assisted microfluidics (VTAM) platform. The fabricated PSM is biodegradable with a core-shell head and flexible tail, and their morphology can be adjusted by vortex flow rotation speed and calcium chloride solution concentration. Benefiting from the sperm-like design, our PSM exhibits both effective motion ability under remote mag/netic actuation and protective encapsulation ability for material loading. Further, it can also realize the stable sustain release after alginate-chitosan-alginate (ACA) layer coating modification. This research proposes and verifies a new strategy for the sperm-like microswimmer construction, offering an alternative solution for the target delivery of diverse drugs and biologics for future biomedical treatment. Moreover, the proposed VTAM could also be a general method for other sophisticated polymorphous structures fabrication that isn’t achievable by conventional laminar flow.


Figures S1-S16
Table S1-3 Note 1-Droplet formation Note 2-Demulsification Note 3-The description of COMSOL model setup Note 4-Solidification Note 5-The explanation of physical principles and simulation Note 6-The dynamic model of sperm liked microswimmer Note 7-The numerical calculations of propulsion Note 8-The swelling behavior of ACA coated PSMs

Note S1-Droplet formation
As the microfluidic cross-junction shown in Fig. 2a, where the alginate-oil droplets form via three inlets, i.e., one for the dispersed flow phase (alginate) and two others for continuous flow phases (oil).Normally, according to the low Reynolds number in such microfluidic chip, the fluid flows are laminar.Therefore, the Navier-Stokes and Cahn-Hilliard equations can be utilized to describe the hydrodynamics of the fluid flows 23,24 : where u is the fluid velocity,  is the fluid density,  is the dynamic viscosity,  is the normalized density difference of two fluid flows, M is the Cahn-Hilliard mobility, and  is the chemical potential.p and I are the fluid static pressure and unit tensor respectively, which can be derived through the Gibbs-Duhem relation 42 : where the total density Define the thickness of alginate-oil interface  , which can be defined as: where b is the constant coefficient.Define the spatial location normal to the interface z , the thickness of alginate-oil interface  be represented as: Assuming the interfacial tension in equilibrium on the plane interface, which can be calculated through 43 : Therefore, the thickness of alginate-oil interface  can be obtained: The Navier-Stokes and Cahn-Hilliard Equation 1 for alginate-oil droplet formation dynamic description can be solved through lattice Boltzmann scheme 44,45 : where ( ) represents the particle distribution at position x and time t for the fluid with ith velocity direction.i e represents the particle velocity in ith velocity direction, and ( ) x represents the collision operator.

Note S2-Demulsification
During the demulsification, the fabricated alginate-oil droplet is imported to the vortex flow generated via magnetic stirrer in a beaker (Supplementary Fig. 2).And then, the droplet exerts large deformation and demulsificates in the vortex flow.In this process, the vortex flow need to be characterized in the first place.Through the applied magnetic field with adjustable frequency, the magnetic stirrer is controlled to rotate and generate strong stirring fluid motion.
The vortex flow is modelling in cylindrical velocity components, i.e., radial velocity ( vr v ), tangential velocity ( vt v ), and axial velocity ( vz v ), which can be expressed as Burgers vortex 46 : where v f is the vortex frequency, g is the gravitational acceleration.v  , v  , and v  are fitting parameters can be obtained in reference 47 .As shown in Supplementary Fig. and v R represent the length of the stirrer, the halfwidth of the vortex, the height of the stirrer, the height of still solution, the distance between the vortex's deepest point and the bottom of the beaker, the radius of the beaker.The radius of the cylinder v c can be obtained through: ( ) Therefore, radial velocity, tangential velocity, and axial velocity of the vortex can be investigated.After that, the droplet mechanics need to be determined during the alginate-oil capsule large deformation and burst process.Consider the fabricated alginate-oil droplet with unstressed geometry in the initial state.We assume that the oil membrane is isotropic and hyperelastic with surface elastic modulus Consider the thickness of alginate-oil interface  is much small that can be negligible, the droplet deformation gradient d F can be given as: where d X is a material point of the unstressed state, and d x is the position vector after deformation.According to the neo-Hookean constitutive law related to the strain energy function d w , the surface elastic modulus o E can be expressed as: ( ) where 1  and 2  are the principle extension ratios.The Cauchy stress tensor d T can be calculated as: where d e is the Green-Lagrange strain tensor, define the tangential projection operator d I , d e can be represented as:

Note S3-The description of COMSOL model setup
The mechanism of drop deformation is regulated by the value of the capillary number, Ca .The critical value of the capillary number at which the states transits from the stable to the deformation states is found to be approximately～ 0.015 [52][53][54] .In this case, the Under the effect of gravity, hydrogel droplets with a density higher than that of the oil fluid flow along in the channel as they simultaneously flow to the right together with the oil flow.A clear shaping can be captured on the oil-water interface, and the oil film can break after vortex flow impact.The Supplementary Fig. 5 shows the droplets are in a turbulent fluid and are being impacted from all directions.The demulsification are shown in Video S1.
For the geometric parameters, the droplet diameter, oil thickness, and inner diameter of the glass tube is set as 50 μm, 0.5 μm, and 100 μm, respectively.These parameters are set based on the measurements in the experiments.The detailed material parameters and physic field boundaries conditions are given in Supplementary Table S3.
These simulations are performed in 2D planar, which aimed to study 1: the demulsification process of the hydrogel-oil droplets 2: the formation process of the microswimmer (alginate droplet concentration diffusion process).We utilize COMSOL Multiphysics to simulate these two processes.Generally, we use "Turbulent Flow" to simulate the flow, and set up two inlet conditions to represent the flow in the bottle (Supplementary Fig. 4, inlet1) and the flow induced by alginate dropping into the calcium mixture solution (Supplementary Fig. 4, inlet2).
The velocity are 0.6-1 m s^-1 and 0.0212-0.0255m s^-1, which are based on experimental values 47 .The inserted capillary glass tube is defined as the "interior wall", while all walls in the flow model arte assumed to have a no slip "wall condition", which consistent with the experimental situation.The outlet condition (Supplementary Fig. 4, outlet) is set with an static pressure '0 Pa'.
To simulate the demulsification process of the hydrogel-oil droplets, we use "Ternary Phase Field" to couple with the "Turbulent Flow", while setting up "Three Phase Flow, Phase Field" in multiphysics.In this three-phase flow field, we can simulate flow of three immiscible fluids separated by moving interface.The phase field variables vary between 0 and 1 and are a measure of the concentration of each phase.At each point, the phase field variables satisfy the following equation: To simulate the formation process of the microswimmer (alginate droplet concentration diffusion process), we use "Transport of Diluted Species" to couple with the "Turbulent Flow", while setting up "Reacting Flow, Diluted Species" in multiphysics.In transport of diluted species field, we set the initial concentration of alginate droplet, the concentration boundaries was c=740.33molm^-3 (Malg=216.121gmol^-1), which are based on experimental values.
We set the condition c=0 on the boundary which is set the inlet in "Turbulent meaning the inflowing liquid is CaCl2 mixture.The use of "Transport of Diluted Species" is to characterize the alginate-oil shape, because there is a short concentration diffusion process between demulsification and gelation, since the concentration contours can be used to characterize the microswimmer's deformation 55,56 .

Note S4-Solidification
When the alginate-oil droplets burst in the vortex flow, the inside alginate phase will outflow and solidify in the calcium chloride solution via cross-linking reaction.
Therefore, the dimensionless formed structure s   obeys a law of the form: ( ) Considering the different demulsification positions with various flow acceration values in the vortex flow, the helix, regular, irregular head polymorphous microswimmers can be fabricated.

Note S5-The explanation of physical principles and simulation
The tail formation of the microswimmer can be divided into three processes, i..e, (1) vortex flow generation, (2) droplet deformation, and (3) demulsification.To elucidate the principle and find out the key factors determining these processes, we conduct research through theoretical analysis, simulations, and experiments, where the simulation is crucial.Briefly: The purpose and significance of the simulations in each step are explained below: (1) Vortex flow generation: We have established a mathematic model to investigate this process, which suggests that the shear velocity is the critical parameter (Eq S11).Yet, it's difficult to calculate the shear velocity at the demulsification position due to the complex parameters in the model.Therefore, we conduct simulation to investigate the range of the shear velocity.Our simulation suggests that when the rotation speed of magnetic stirrer increases from 800-1000 rpm, the shear velocity increases from 0.6 m s^-1 to 1 m s^-1 at the demulsification position in the vortex flow.These values are important for the following droplet deformation modeling and simulation analysis.
(2) Droplet deformation: In this process, one key challenge is to figure out the droplet deformation in the vortex flow and the droplet burst state, which is also hard to obtain analytical solutions through modeling calculations (Eq S14).Therefore, we further delved into the mechanics of the droplet during the large deformation and burst process of the alginate-oil capsule through the simulation.Our simulation suggests that when the shear velocity reach the 0.6 m s^-1 (corresponding to magnetic stirrer rotation speeds of 800rpm), the droplet would burst and generate a tiny tail.These values are important for the following demulsification analysis.
(3) Demulsification: After obtaining the trigger value of shear velocity that can generate the microswimmer with tail structure, we need figure out the polymorphous-tailed microswimmer generation progress, where the transient demulsification process of hydrogel-oil droplets is the key challenge.Therefore we have simulated the demulsification process with a 50 μm diameter sphereshaped alginate droplet (0.5 μm oil thickness), which allowed us to observe the transient demulsification process of hydrogel-oil droplets.We have observed the hydrogel droplets' behavior in tandem with the oil flow, capturing the shaping on the oil-water interface and the subsequent oil film breakage due to the impact of the vortex flow.These outcomes consistently aligned with our theoretical analyses and experimental observations.
The simulation environment we employ in this manuscript is 2D planar.The reason is that our goal is to investigate the influence of shear velocity on the fabrication process of microswimmers, where 2D planar simulation can take all key factors into consideration while maintaining a low time and computing resource consuming.The experimental observation showcases that the demulsification and deformation process is confined to micrometer size and milli-seconds, which is orders of magnitude smaller than the dimension of the simulation environment.Therefore, the shape of the simulated domain and the shape of the vial would not influence the results significantly.

Note S6-The dynamic model of sperm liked microswimmer
As shown in Supplementary Fig. 7, when a rotating magnetic field with a tilt angle θ about the locomotion direction OO' is applied, the head of microswimmer will revolve around locomotion direction OO' and rotate along its own helix axis AA' simultaneously.Following the revolving of head, the slender tail forms into a spiral shape.According to the mechanical analysis, both the rigid head and flexible tail make the contribution during the sperm locomotion.
As shown in the general model, the propulsion of helical element with a unit length can be expressed as: In which, where β is the pitch angle of spiral, d  and d  are normal and tangential resistance force respectively during rotation which related to the helical radius  , rotation speed  and coefficients resistance τ.
For the revolving of head, the helix head can be considered as a whole unit with a long axis  ℎ and equivalent body width  ℎ , where  = ,  ℎ′ =   ,  ℎ′ = 2 ℎ′

𝑡𝑎𝑛𝛽
. Since the ratio < 10, we adopt the resistive force theory to calculate the coefficients resistance: Where,  1 and  1 are tangential and normal coefficients resistance of helical head respectively, μ = 1.0 mpa • s is the dynamic viscosity of water.Then, the propulsion of the revolving of head under rotation speed ω can be expressed by integrating along the axis length  ℎ : For the rotating of helical head, it has a small helix radius R ℎ and pitch angle β ℎ .The helix pitch  ℎ can be calculated by Since the ratio ϵ =  ℎ  ℎ < 10, where  ℎ is the half wavelength of helical head and  ℎ is the cross-sectional radius of the element, we adopt the resistive force theory to calculate the coefficients resistance: Then, the propulsion of the helical head along its helix axis can be expressed by integrating: Where  ℎ is the straightened length of helical head and can be given by: Considering the tilt angle  between head and locomotion direction, then the contributed propulsion force from head rotation can be further delivered as: In which, Then, the propulsion of the flexible tail can be expressed by integrating: Hence, the total propulsion of the microswimmer can be expressed as:

Note S7-The numerical calculations of propulsion
As shown in table S1 are the parameters of different types of microswimmer for numerical calculations.The parameters, including total length, helix radius, and average pitch angle, are obtained through sample observations in both static and dynamic states.While the determination of the helical shape of the flexible tail under rotation is intricately fitted through mathematical simulations, harmonizing with other observed parameters.Besides, the controllable actuation frequency and the liquid viscosity add a dynamic dimension that can be easily adjusted.
Since the axisymmetric of the regular head and the equivalent helix angle is 90°, the propulsion force from head is equal to the propulsion from the revolving of head, which can be calculated as: And the propulsion of tail can be calculated as: Therefore, the total propulsion of the microswimmer with regular head can be expressed as: Where the propulsive force from regular head and flexible tail contributes 9.3% and 90.7% to their total propulsive force respectively.
Similar to the regular head, the rotation of irregular head also doesn't contribute to the propulsion and mainly come from its revolving.The propulsion force from irregular head can be calculated as: And the propulsion of tail can be calculated as: Then the total propulsion of the microswimmer with irregular head can be expressed as: Where the propulsive force from irregular head and flexible tail contributes 13.8% and 86.2% to their total propulsive force respectively.
For the microswimmer with helix head, the propulsion force from head including the rotation and revolving, which can be calculated as: The volume swelling degree of the PSMs with different membrane thicknesses was quite different as below.The PSMs with ＜6 µm membrane thickness exhibit the greatest swelling degree of 187.76% among the five groups.The result indicated that strength of ACA PSMs decreased with thinning membrane (Supplementary Fig. 10).
We found that suitable thickness can perform preferable sustain release ability, as shown in Fig. 4e.However, if the thickness is too thick or thin, the release properties of the microswimmer cannot be maintained, because too thin or too thick thickness will respectively result in not fully crosslinked between chitosan and sodium alginate amide bonds or the swelling reaction.For example, when thickness＜6 μm, the cumulative release value reaches approximately 88-95% within 2 hours presents burst releasing due to rupture of thinner membrane.On the other hand, when thickness≥6 μm, the cumulative release value increase and reach around 35-50% before 2 hours, indicating a thicker membrane enables effectively alleviating the burst release.Yet in the following several hours, the cumulative release of thickness 8 μm to 10 μm, their release presents continuously increase and reach around 88%.
Comparatively, the curve of release with a thickness ~ 6 μm is relatively flat around 60%, and presents the sustainable release property.The membrane with ~ 6 μm thickness demonstrates sustainable release ability to maintain a constant drug concentration in a period.
where s c is the lattice speed of sound.Considering the difficulty for evaluation of   when take the fluid-solid interaction into account, such equation can be reformed as: pressure.Considering the incompressible two-phase system (alginate-oil) with fluid densities h  and o  , through the Ginzburg-landau free energy function, the thermodynamics can be represented as: energy.Based on Equation3, the chemical potential  can be calculated as: fluid viscosity in the beaker.The vorticity is assumed to distribute in a cylinder (central line v z ) with radius v c , and v C is circulation constant.The vortex strength v C can be calculated through:

oE
, which follows the neo-Hookean constitutive law.According to previous analytical researches, the deformation of such spherical droplet mainly depends on two parameters, i.e., capillary number Ca and viscosity ratio of the interior droplet to exterior d  .In the steady state, when the flow strength increase, the droplet remains unburst until a critical capillary value b  reached, which can be expressed as 48-51 : is the dynamic viscosity of oil membrane, d d is the droplet diameter.Therefore, the shear velocity ve v is the critical parameter that influence the demulsification process.

b
～0.0032- 0.0128.The result presents b  ＜ Ca , which reasonably close to the theoretical in the experiments.In our model 50 μm sphere shaped alginate droplet (with 0.5 μm oil thickness) is dropped into a 0.3 mm width and 3 mm length of vortex liquid channel (calcium chloride solution).The aim of the simulation is to predict the demulsification process of hydrogel-oil droplets in a transient manner.The geometry of the experimental set-up is shown in Supplementary Fig. 4. The motions of the hydrogel-oil droplets, injected from the upper-left inlet, are simulated and plotted in 2D planar simulation.
choose the boundaries which is set the inlet in "Turbulent Flow" as inlet of "Ternary Phase Field".The boundaries condition of setting these boundaries, we finally get the demulsification process of the hydrogel-oil droplets, as shown in Maintext Fig.2band Supplementary Movie 1.
36)For the rotation of flexible tail, assuming the radius of amplitude is   and the cross-sectional radius of the element changes from  0 to   evenly.If the original straightened length of the tail is   and the axial length of tail after forming spiral is   .Then we can get the crosssectional radius and pitch angle of the arbitrarily point x in the tail: where   is the half wavelength of helical tail and   is the cross-sectional radius of the element at point x, we adopt the slender body theory to calculate the coefficients resistance: 6 × 10^− 4 + 15.9 × 10^− 4 = 33.5 × 10^− 4  (50)And the propulsion of tail can be calculated as: 3 = ∫   ( 3 () −  3 ())    total propulsion of the microswimmer with helix head can be expressed as: ℎ =  ℎ3 +  3 = 97.3× 10^− 4 (52)Where the propulsive force from irregular head and flexible tail contributes 34.4% and 65.6%to their total propulsive force respectively.Note S8-The swelling behavior of ACA coated PSMs'Swelling behavior' is an intrinsic property of hydrogels, where the PSMs enlarge due to solvent penetration into the void space between the polymeric chain network (ACA coating process).The PSMs enlarge which affects their locomotion under the magnetic field.Therefore, we need to analyze the relationship between the swelling degree and coating time to optimize membrane thickness, thereby reducing the locomotion obstruction at micro scale.In this experiment, we have obtained difference thickness PSMs by changing coating time, and used an optical microscope to measure the uncoated PSMs's head diameter and PSMs's head diameter respectively.According to our previous research 47 , swelling degree (Sw) is expressed as follows:

Table S2 . The comparison of sperm-like microswimmers
*R-head means regular head, I-head means irregular head, H-head means helical head; **BW means beating waves, BP means biological propulsion, HP means helical propulsion, DHP means dual-helical propulsion.