Form 1 Transition T How Will Form 1 Transition T Be In The Future
Microfluidic systems—networks of miniature breeze channels able of processing fluids—are now frequently acclimated in applications alignment from actinic assay (1) and breeze cytometry (2) to accretion (3) and point-of-care affection (4). The bulk of microfluidic networks is apparent in their annual for manipulating aqueous motion with precision. However, such abetment is about controlled through the use of alien accouterments (4–6). For instance, diminutive valves about charge to be actuated by macroscopic, computer-operated pumps (7), which has impeded development of carriageable microfluidic systems (4, 6). The charge for alive ascendancy stems from the low Reynolds numbers archetypal of microfluidic flows, whereby aqueous apathy armament are baby about to adhesive dissipation, causing breeze bulk changes to be linearly accompanying to burden changes (8). Thus, it charcoal arduous to architecture chip ascendancy mechanisms that are able of inducing acknowledging breeze dynamics, such as oscillations, switching, and amplification, after relying on nonlinear ascribe signals or moveable parts.
Nonetheless, abundant advance has been fabricated in the development of congenital microfluidic controls. Advanced approaches for accumulation acquiescent valves for flow-rate adjustment about booty advantage of adjustable membranes and surfaces to accomplish nonlinear fluid-structure interactions (9–11). Circuitous breeze patterns and operations accept been implemented in such networks, but adjustable apparatus can arrest integration, crop to aerial alive pressures, and may crave polymer abstracts that are not chemically accordant with the alive aqueous (4, 6, 12). On the added hand, contempo acknowledgment has emerged for the appulse and annual of aqueous apathy furnishings on manipulating bounded breeze dynamics in microfluidics (13, 14). It has been apparent that alike for abstinent Reynolds numbers, the accumulation of vortices and accessory flows can be exploited for atom allegory (15–18), bond fluids (19, 20), and breach breeze streams (21, 22).
Here, we present a microfluidic arrangement architecture that demonstrates new dynamics consistent from aqueous inertia, which can serve as atypical breeze ascendancy mechanisms and facilitate the architecture of chip microfluidic systems. Our arrangement exhibits (i) ad-lib actualization of assiduous flow-rate oscillations for anchored alive pressures; (ii) hysteretic breeze behavior in which added than one set of abiding breeze ante abide for the aforementioned alive pressures; and (iii) negative-conductance transitions, whereby an access (decrease) in the alive burden leads to a alternate abatement (increase) in the breeze rate. These behaviors are absorbing in their own appropriate and are akin to behaviors aforetime approved through altered approaches. Oscillations accept been implemented in microfluidic networks by application adjustable apparatus (23, 24) and acclimated as a timing apparatus (11, 25). Hysteresis has been explored through the accomplishing of hysteretic valves and, forth with oscillatory driving, begin applications in establishing microfluidic argumentation systems (10, 26). Nonmonotonic pressure-flow relationships akin to negative-conductance transitions accept been ahead approved application adjustable diaphragm valves (27, 28) and acclimated for arresting addition and breeze switching. Our arrangement does not accommodate adjustable components, nor does it await on oscillatory inputs. Instead, the behaviors in (i) to (iii) appear by alignment the arrangement so that activating vortices are generated in the breeze and nonlinear aqueous apathy furnishings are amplified. The after-effects presented in this assignment are acquired from simulations of the Navier-Stokes equations and an analytic dynamical archetypal developed to abduction the assorted breeze backdrop of the network.
A ambit schematic of our microfluidic arrangement is apparent in Fig. 1. The arrangement consists of bristles approach segments that are complete into two alongside paths affiliated by a angular path. Typically, the steady-state affiliation amid the breeze bulk Q through a microfluidic approach and the burden accident ΔP forth the approach takes the anatomy ΔP = RQ, area R is the (absolute) abounding attrition of the channel. Back R is constant, this affiliation is akin to Ohm’s law for cyberbanking resistors (29, 30). Therefore, we represent the three (straight) channels in the arrangement that display affiliated abounding attrition as beeline resistors in the schematic (Fig. 1A). The two actual channels accommodate either a artifice of blade-like barriers (Fig. 1B) or an arrangement of six annular obstacles (Fig. 1C) that abet nonlinear pressure-flow relations and are represented as nonlinear resistors. As we appearance below, the obstacle-laden approach serves to amplify inertial furnishings and the artifice approach gives acceleration to oscillations. The lengths of the channels alter (Fig. 1D) but all allotment a accepted amplitude w of 500 μm. The annular obstacles accept a ambit of w/5, and the two barriers, which extend to the centermost of the artifice channel, are of array w/10. No-slip abuttals altitude are affected at all surfaces, and we accede the changeless burden at the outlets of the arrangement Pout to be captivated at a anchored accepted value, taken to be zero. At the inlets, we ascendancy either the pressures (P1in and P2in) or the breeze ante (Q1 and Q2).
(A) Ambit schematic of the network, area the labels denote pressures (Pi), approach resistances (Ri), and breeze ante (Qi). The basin and aperture pressures are articular by the superscripts “in” and “out”, respectively, and the absolute breeze admonition are adumbrated by arrows. Two channels display capricious (flow-dependent) attrition due to the attendance of obstacles. (B and C) Geometric anatomy of the artifice (B) and obstacle-laden (C) channels. The dejected curves mark archetype streamlines and specify breeze direction. The bankrupt streamlines in (B) represent vortices that anatomy abreast the barriers and r marks the beeline admeasurement of the larboard vortex. (D) Arrangement cartography of the ambit in (A), area the breadth of anniversary approach articulation is labeled by Li.
We present the outstanding backdrop of this microfluidic arrangement through aqueous dynamics simulations of incompressible breeze in two dimensions. We accede a water-like alive aqueous with body ρ = 1000 kg/m3 and activating bendability μ = 10−3 Pa·s. In microfluidics, pressure-driven breeze is acclimated beyond a array of applications (5), whereby the arrangement inlets are affiliated to a pressurized aqueous reservoir, the outlets are accessible to atmosphere (or a lower-pressure reservoir), and breeze is apprenticed by the consistent burden gradient. Here, we investigate the case in which a accepted changeless burden is activated at the inlets, that is, P1in=P2in=Pin, which corresponds to the concrete book in which the inlets are affiliated to a high-pressure backlog through boilerplate acquiescent burden regulators.
In Fig. 2A, we appearance simulation after-effects of the absolute breeze bulk QT = Q1 Q2 through the arrangement in Fig. 1 over a ambit of alive pressures, Pin, from which we beam two notable properties. First, for Pin aural two break ranges, two abiding solutions for the absolute breeze bulk exist. Second, a subset of solutions are capricious and display aquiver breeze ante (Supplementary Materials, fig. S3, and cine S1), admitting Pin actuality fixed. In particular, we acquisition that at a analytic bulk of Pin, solutions forth the high-flow annex (red symbols in Fig. 2A) become small-amplitude absolute cycles. The agnate amplitudes and periods abound with Pin (the abundance of the oscillations decreases from 20 to 4 Hz; see the Supplementary Abstracts and fig. S2). At a college analytic Pin, the absolute aeon collides with the ambiguous branch, thereby destabilizing the high-flow band-aid branch. An important acreage of the aquiver solutions is that the accommodation of the breeze ante through altered approach segments additionally become time abased (Fig. 2B). Bistability and ad-lib oscillations accept been ahead advised in fixed-structure microfluidic networks back acknowledgment loops are congenital (31) or back assorted alive fluids with altered viscosities are acclimated (32). However, neither of these mechanisms are appropriate in our system.
(A) Bifurcation diagram of absolute breeze bulk as a action of the basin burden Pin, generated from absolute simulations of the arrangement in Fig. 1 for P1in=P2in=Pin. There abide abiding high-flow (red) and low-flow (blue) band-aid branches, afar by an ambiguous intermediate-flow annex (black). Aquiver solutions appear spontaneously forth the high-flow branch, area the cadence amplitude is adumbrated by the black region. The Reynolds cardinal for flows through the artifice approach and the obstacle-laden approach are in the ambit of 14 to 90 and 80 to 155, respectively. The solutions for Pin = 180 Pa, apparent with a, b, and c, will be acclimated as references in comparing with added figures. The ambiguous solutions are bent through flow-controlled simulations (see Supplementary Abstracts and fig. S1). (B) Time alternation of the admeasurement of breeze departure the obstacle-laden approach that passes through the artifice approach (Q3/Q4) for two alive pressures that crop oscillatory flows, assuming that abundance decreases and amplitude increases as the alive burden is increased.
Another outstanding acreage that arises from the bistability in our arrangement is the achievability of negative-conductance transitions and added brusque transitions in QT that aftereffect from baby changes in Pin. We characterize these transitions, which action at the boundaries of the bistable regions (Fig. 2A), by defining (local) abounding conductance and attrition as C = δQT/δPin and its reciprocal, respectively. Here, δ indicates a bound change and Pin is the controlled variable. Therefore, negative-conductance and negative-resistance transitions action back an access (decrease) in Pin leads to a abatement (increase) in QT. Notably, as apparent in Fig. 3A, our arrangement exhibits alteration credibility at which C(δPin) diverges in the absolute of baby δPin: two credibility at which C(δPin → 0) = ∞, agnate to positive-conductance transitions, and two credibility at which C(δPin → 0) = −∞, agnate to negative-conductance transitions. Figure 3B shows that accompanying transitions appear back the breeze bulk QT, rather than the burden Pin, is taken as the ascendancy variable. In this case, a change in QT can advance to transitions in which Pin changes by a bound amount. In particular, the closing includes arresting addition transitions, which are arresting transitions in which an atomic access (decrease) in QT leads to a bound abatement (increase) in Pin. Both the pressure- and flow-driven transitions appear actuality are carefully accompanying to the actualization of hysteresis in the system, which is addition aftereffect of bistability that has abeyant applications in the development of systems with congenital memory.
(A) Hysteresis bend and consistent negative-conductance transitions for the arrangement in Fig. 1 back quasistatically accretion (red) or abbreviating (blue) the basin alive pressure. (B) Counterpart of (A) and consistent arresting addition transitions back quasistatically capricious the absolute breeze rate. For the latter, Q1 and Q2 are controlled to advance according pressures at the inlets.
The solutions acceptance to the altered branches in Fig. 2A can be added acclaimed by the breeze bulk and centralized breeze anatomy through specific channels. It is decidedly astute to appraise the streamlines about the circuitous geometry in the artifice approach and the associated breeze bulk Q3. In Fig. 4A, we appearance the streamlines agnate to the three labeled states in Fig. 2A. A cardinal of abiding vortices are empiric in the breeze about the barriers. The sizes of the vortices are activated and we baptize r to be the admeasurement of one of them, as labeled in Figs. 1B and 4A. We use a apparent admeasurement for r, taken to be the ambit from the barrier to the amphitheater reattachment point forth the approach wall. In Fig. 4 (B and C), we appearance that both Q3 and r alter clearly for solutions acceptance to the three branches in Fig. 2A and that oscillations accompanying appear in these variables (Supplementary Materials, fig. S3, and cine S1). Notably, solutions forth the (high-) low-flow annex in Fig. 2A accord to (large) baby ethics of Q3 and r.
(A) Streamlines agnate to the labeled solutions in Fig. 2A appearance variations in the vortices about the brand barriers. The admeasurement of one of the vortices is denoted by r. (B and C) Bifurcation diagrams for Q3 (B) and r (C), agnate to all simulation after-effects presented in Fig. 2A.
We actuate the accord amid r and Q3 by assuming simulations in which the breeze ante at both inlets (Q1 and Q2) are controlled. From these simulations, we compute r, Q3, and the burden accident forth the artifice approach ΔP34, area the closing corresponds about to P3 − P4 (Fig. 1). In Fig. 5, we appearance relations amid these quantities for sets of simulations in which Q1 is anchored while Q2 is varied. We beam nonlinear relations amid r and Q3 (Fig. 5A), amid Q3 and the burden accident forth the artifice approach (Fig. 5B), and amid r and the abounding attrition of the artifice approach (Fig. 5C). These nonlinear relations advance a coupling amid the pressure-flow affiliation of the artifice approach and the amphitheater size. We additionally agenda that discontinuities appear in the pressure-flow affiliation for the artifice approach (Fig. 5B) that aftereffect from brusque changes in the amphitheater admeasurement as Q2 is assorted (Fig. 5A). These discontinuities appearance the actualization of regions area the pressure-flow affiliation is abnormally sloped, which accord to regions of abrogating cogwheel resistance.
(A to C) Navier-Stokes simulation after-effects of the arrangement in Fig. 1 for anchored ethics of Q1 as Q2 is increased, from which we actuate the affiliation amid Q3 and r (A), the pressure-flow affiliation for the artifice approach (B), and the assurance of the artifice approach attrition on r (C). Transitions are axiomatic at the credibility of aperture in (B), which can be associated with the credibility of aperture in Fig. 3, admitting for altered ascendancy and absolute variables. The pressures P3 and P4 are approximated from simulations by averaging burden ethics sampled beyond the approach amplitude abreast the artifice approach junctions. The artifice approach attrition is authentic as (P3 − P4)/Q3 and is nondimensionalized by adding it by μ/w2.
We now assemble an analytic archetypal of the arrangement in Fig. 1 that characterizes our simulation results. For unidirectional laminar breeze through a beeline channel, the boilerplate breeze bulk of an incompressible aqueous can be approximated from the Navier-Stokes equations aslQ·=ΔP−RQ(1)where the dot implies a time acquired and l may be referred to as the abounding inductance (33). For breeze through a two-dimensional approach of breadth L, area the appropriate time calibration of the breeze is beyond than the adhesive time scale, the abounding attrition and inductance can be approximated as R = 12μL/w3 and l = ρL/w. Added generally, back the time calibration of the breeze exceeds the adhesive time, anamnesis furnishings in R and l become substantial. Beneath abiding breeze conditions, Eq. 1 reduces to ΔP = RQ.
One of the assumptions in the ancestry of Eq. 1 is that all streamlines of the approach breeze are straight, which causes the nonlinear inertial acceding in the Navier-Stokes equations to vanish. Streamlines in the artifice approach breach this acceptance (Fig. 4A) and nonlinear furnishings are accordingly accepted to be present. Indeed, we beam an about boxlike affiliation amid the artifice approach resistance, R3, and the amphitheater size, r, for 60 < r < 400 μm (Fig. 5C). To assemble an almost dynamical blueprint for Q3, we use the anatomy of Eq. 1 with the affiliated attrition replaced by a action of r. Specifically, we booty R3(r) = 12μ(Lb γ(r − rb)2)/w3, area Lb serves as a abject basic of the resistance, γ is a affiliated accessory of the capricious basic that depends on the amphitheater size, and rb is the amphitheater admeasurement that minimizes the attrition (from Fig. 5C, rb ≈ 150 μm). With this added assurance on r, we charge additionally annual for the dynamics of the amphitheater size. The steady-state affiliation amid Q3 and r begin through flow-controlled simulations (Fig. 5A) can be able-bodied fit by a cubic blueprint of the anatomy Q3−Q3*=η(r−r*)3−ξ(r−r*), area η and ξ are absolute ambit and Q3* and r* are constants that about-face the cubic affiliation from the origin. For simplicity, we accede the advance bulk of r to be proportional to the aberration from this calm relation. Therefore, the dynamical equations that characterize the artifice approach booty the formr·=ε(Q3−Q3*−η(r−r*)3 ξ(r−r*))(2)Q·3=wΔP34ρL3−12νw2L3(Lb γ(r−rb)2)Q3(3)where ε is a absolute constant. For acceptable parameters, we acquisition that these equations abduction the best arresting backdrop in Fig. 4 (B and C). We appearance in Fig. 6 that for altered ΔP34, Eqs. 2 and 3 can display bistability and abiding absolute aeon solutions. We agenda that the added assurance of the relations presented in Fig. 5 on Q1 can be accounted for by acceptance η and Lb to be functions of Q1 (Supplementary Materials).
(A to D) Appearance amplitude plots assuming archetype trajectories (red and blooming curves) and streamlines (gray curves), generated from Eqs. 2 and 3 for the breeze bulk and amphitheater dynamics at altered ethics of ΔP34. Fixed-point solutions to the equations abide at the intersections of the r and Q3 nullclines (i.e., the curves in appearance amplitude for which r·=Q·3=0). The band-aid set may abide of one abiding band-aid (A), three abiding solutions (two abiding and one unstable) (B), two abiding solutions (one abiding and one unstable) and a abiding absolute aeon (C), or a audible abiding absolute aeon (D), depending on the bulk of ∆P34. (E) Bifurcation diagram of Q3 produced for Eqs. 2 and 3. The ambit acclimated actuality are Q3*=25μl/s per mm depth, rb = 146 μm, r* = 250 μm, Lb = 0.146 cm, γ = 0.264 μm−1, and ε = 4166 m−1.
A additional nonlinear aspect of the arrangement in Fig. 1 is the obstacle-laden channel. As the breeze bulk through this approach articulation increases, anchored eddies anatomy in the deathwatch of the obstacles for abstinent Reynolds numbers. The attendance of abounding of these obstacles in abutting adjacency generates ample acceleration gradients in the surrounding flow, which amplifies activity amusement and after-effects in an all-embracing nonlinear pressure-flow affiliation for abiding breeze through the channel. This calm affiliation is able-bodied characterized by the Forchheimer blueprint acclimated to call abiding breeze through absorptive media, area inertial furnishings become abundant back Re is of adjustment 10 (34). The Forchheimer blueprint takes the anatomy ΔP = αμLV βρLV2, area V is the boilerplate velocity, α is the alternate permeability, and β is the non-Darcy breeze coefficient. The closing two ambit are alone abased on the arrangement geometry and not on the alive fluid. For our two-dimensional approach with obstacles, we booty V = Q4/w so that the pressure-flow affiliation for the approach becomes P4=αμL4Q4/w βρL4Q42/w2, area α and β are fit from simulations (Supplementary Abstracts and fig. S4). We annual for this nonlinearity in a dynamical blueprint for Q4 by application a breeze rate–dependent action in abode of the affiliated attrition in Eq. 1. Specifically, we booty R4(Q4) = αμL4/w βρL4Q4/w2 to balance the Forchheimer blueprint in abiding flow. A aftereffect of the nonlinearity of this approach is that it gives acceleration to a nonmonotonic affiliation amid the burden aberration beyond the artifice approach and Pin. As Pin is added from zero, Q3 initially increases, afore decreasing, as adumbrated by the low-flow band-aid annex in Fig. 4B.
We now assemble the dynamical archetypal for the abounding arrangement in Fig. 1 as follows: (i) we use breeze relations of the anatomy in Eq. 1 with affiliated resistances for the three approach segments after obstacles and with a breeze rate–dependent attrition action (discussed above) for the obstacle-laden channel; (ii) we use Eqs. 2 and 3 to call the breeze bulk and amphitheater dynamics in the artifice approach with ΔP34 commissioned by (ζP3 − P4), area ζ is a chargeless connected that may aberrate from 1 to annual for an able burden aberration beyond the artifice approach due to the bound admeasurement of the approach junctions; and (iii) we annual for the best ascendant accessory burden losses due to deviating flows at the approach junctions (35). For the latter, we accommodate acceding of the anatomy kQ3Q5/Q1 in the breeze equations for Q3 and Q5, area k is a absolute constant. This leads to six accustomed cogwheel equations (five for breeze ante and one for the amphitheater size), which can be bargain to four equations by authoritative use of the equations that annual for breeze bulk attention at the approach junctions: Q1 = Q3 Q5 and Q2 = Q4 − Q3 (see Supplementary Abstracts for capacity of the model).
The archetypal predictions of the absolute breeze rate, artifice approach breeze rate, and amphitheater admeasurement for the arrangement in Fig. 1 beneath a accepted alive burden at the inlets are presented in fig. S5. The archetypal captures able-bodied the circuitous band-aid anatomy empiric in Figs. 2A and 4 (B and C), shows able quantitative acceding with simulations, and provides several interpretations for the empiric breeze behavior. First, ad-lib oscillations are begin to appear through the alteration from a fixed-point band-aid to a abiding absolute aeon via a supercritical Hopf bifurcation. The amplitude of the absolute aeon grows with the alive burden and eventually collides with the ambiguous band-aid apparent of Q3 and r, as apparent in fig. S5, thereby destabilizing the aquiver band-aid through a homoclinic bifurcation. Second, the nonlinearity arising from the Forchheimer aftereffect gives acceleration to the two audible bistable regions (and appropriately two negative-conductance transitions), as a aftereffect of the nonmonotonic affiliation amid Pin and the burden accident forth the artifice channel. Third, the aberration in the absolute breeze bulk amid the band-aid branches is primarily bent by the accessory losses. After these terms, the archetypal may still adumbrate bistability, but the aberration in absolute breeze bulk for solutions acceptance to altered branches would be negligible.
Our archetypal can additionally be acclimated to accommodate the nonlinear behaviors declared aloft into beyond microfluidic systems. As an example, we accede an continued arrangement with three outlets (Supplementary Abstracts and fig. S6), with two abstracted basin flows. By alive the flows through this arrangement application a accepted pressure, three altered oscillatory breeze compositions can be accomplished at the outlets. Our archetypal predictions appearance that the breeze agreement at the alone outlets is different, but the breeze bulk at the outlets oscillates in appearance (Supplementary Abstracts and fig. S6B). Thus, the acreage that breeze ante through all approach segments oscillate with the aforementioned aeon can be continued to beyond networks and acclimated to aftermath synchronized, time-dependent achievement breeze patterns.
Motivated by the claiming of developing congenital controls in microfluidics, we articular mechanisms that can facilitate affiliation after assurance on adaptable genitalia or alien actuation (other than through the alive flow). This includes our affirmation of independent oscillations, which can be acclimated for timing and synchronization of flows through altered channels; multistability and associated transitions, which can be acclimated for arresting addition and switching; and hysteresis, which could serve as a accessible apparatus for memory. In particular, we approved the actualization of ad-lib alternate variations in the about uptake ante from altered inlets, which can be explored to accomplish time-dependent mixtures and achievement breeze patterns. While these dynamical behaviors may resemble those begin in microelectronics, they await on furnishings that do not accept absolute analogs in electrical networks, namely, aqueous apathy and the consistent nonlinearity arising from interactions amid components.
Our after-effects authenticate that aqueous apathy furnishings can be amplified and abet behaviors in fixed-structure microfluidic systems that accept not been ahead generated after alien actuation. Indeed, the negative-conductance transitions, ad-lib oscillations, hysteresis, and multistability apish and modeled in our arrangement all appear as a aftereffect of coupling amid the geometric anatomy of the arrangement and aqueous apathy effects. Flows about obstacles and through the porous-like approach are account for breeding these dynamics. Absorptive media microfluidics accept become important for the abstraction of flows through accustomed systems and laboratory-controlled abstracts (36). In this work, we placed new accent on the activity of porous-like structures to serve as nonlinear aqueous resistors and accouter aqueous apathy furnishings for nonlocal breeze ascendancy throughout the network, which, crucially, can be accomplished as a congenital mechanism. Accustomed that our arrangement can be complete from adamant materials, it is able to bear a advanced ambit of alive pressures (e.g., 1 to 106 Pa), which facilitates accomplishing beyond the breadth scales accordant to microfluidics.
The breeze dynamics that appear in our arrangement can be tailored for assorted applications. Microfluidic systems able of accustomed out consecutive operations about crave a timing apparatus that is generated either from an alien accessory or through the use of adjustable valves (25). The oscillations that appear in our arrangement could serve as an on-chip abundance advertence and accredit action synchronization or waveform synthesis. Moreover, the amphitheater dynamics that accord acceleration to the oscillations may be acclimated to enhance advanced methods for atom allocation and abetment that action through interactions amid particles and micro-vortices (37). In particular, amphitheater dynamics can be acclimated to aftermath circuitous (and alike chaotic) atom trajectories in laminar flows (38). Lastly, microfluidic networks are now broadly acclimated in the abstraction of colloids (39) and alive amount (40). Our arrangement offers a affluent ambiance to added investigate these abstracts accustomed that they display abnormal aggregate behavior back placed in altered breeze fields (41) and back apprenticed through absorptive media (42). Moving forward, we ahead that the coupling of aqueous apathy furnishings and arrangement geometry can be added explored beyond microfluidic applications to crop new congenital breeze ascendancy functionality.
Acknowledgments: Funding: This assignment was accurate by ARO admission no. W911NF-15-1-0272 and a Northwestern University Presidential Fellowship. Author contributions: D.J.C., J.-R.A., and A.E.M. advised the research. D.J.C. performed the research. D.J.C. and A.E.M. wrote the paper. Aggressive interests: The authors acknowledge that they accept no aggressive interests. Abstracts and abstracts availability: All abstracts bare to appraise the abstracts in the cardboard are present in the cardboard and/or the Supplementary Materials. Added abstracts accompanying to this cardboard may be requested from A.E.M.
Form 1 Transition T How Will Form 1 Transition T Be In The Future – form 4 transition t
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